Every claim, tested

These are the round-4 verdicts, the evidence base the book and the paper both cite: every claim re-scored at two, three, four and five players under Hasbro's 2024 rulebook, 40,000 games per claim cell. The earlier rounds ran on different engine defaults and are kept, unedited, at the historical verdicts so the record can be checked rather than tidied away.

Every claim of E10–E47 re-scored at 2, 3, 4 and 5 players from the round-4 cells (experiments/results/round4/*.json; 40,000 games per claim cell, 100,000–200,000 for the E46/E49 design cells; engine defaults of the 2024 Hasbro rulebook: a Just Say No answered on your own turn costs one of the three plays and cannot be played with all three used, orphaned buildings are discarded; hashed seeds, seed 0 upward in every cell). The historical record (rounds 1–3, old defaults, hand-written) is VERDICTS.md, untouched.

How a verdict is scored. Each row of CLAIM_MAP.md's reading tables is encoded as a rule (CRITERIA in the generator). A rule is scored at every player count where its cells exist: CONFIRMED / REFUTED when the stated condition holds outside the 95 % CI — the paired CI of the difference when two cells are compared, since every cell at a given count plays the same deals as its control — INCONCLUSIVE when neither does, NOT TESTED when a cell or counter is missing. The overall label is the per-count label when they agree; a single label plus the counts where it holds when the rest are inconclusive; CONDITIONAL when counts disagree. Deltas are win rate minus fair share (1/n) in pp; the all-Baseline control sits at fair at every count (E33 row below), so no offset is applied.

Cell numbers are Δ ±95 % CI per count; (paired …) is the difference from the all-Baseline control on the same seeds, (vs <cell>: …) the difference from the named matched control.

Summary

Claims by overall verdict (a claim counts once per rule it appears in): CONFIRMED 95, REFUTED 150, INCONCLUSIVE 15, NOT TESTED 0, CONDITIONAL 30.

Exp	Claims	Question	Verdict (2024 rules, 2–5 players)
E10	#129, #187, #329, #48, #2, #156, #148, #164, #533, #514	delay full sets to dodge the Deal Breaker (delay is right / exposes nothing)	REFUTED at 2p, 3p, 4p; inconclusive at 5p
E10	#32, #456, #163	never completing a set leaves you exposed to Sly/Forced Deal	REFUTED
E10	#130, #288, #471, #544, #51, #477	count the Deal Breakers, then complete	REFUTED
E10	#155, #164	a JSN or DB in hand makes completion safe	CONFIRMED
E10	#30, #257, #514, #470, #356	the Deal Breaker has no target once everyone delays	CONDITIONAL (2p confirmed, 3p refuted, 4p refuted, 5p refuted)
E11	#545, #444, #94, #296, #208, #13, #251, #538	un-completing a set with a wild at end of turn (the Deal Breaker dodge) is worth it	REFUTED
E11	#252	dodging trades a small DB risk for a larger steal risk (poor trade)	CONFIRMED
E12	#238, #310, #13	flipping wilds for rent (and back) is excellent	CONDITIONAL (2p refuted, 3p inconclusive, 4p confirmed, 5p confirmed)
E12	#468	free wild movement is overpowered	REFUTED at 2p; inconclusive at 3p, 4p, 5p
E13	#269, #180, #507, #203, #204, #205, #341	bank money first, before laying property	REFUTED at 3p, 4p, 5p; inconclusive at 2p
E13	#6, #151, #137, #295	holding property while waiting for money loses (the higher the floor the worse)	CONFIRMED at 3p, 4p, 5p; inconclusive at 2p
E13	#563	bank everything you do not need (floor $5)	REFUTED
E13	#366	the never-bank-money challenge is a handicap	CONFIRMED
E14	#548, #75, #157, #503	pass the first turn (especially at 4 players)	CONDITIONAL (2p refuted, 3p refuted, 4p confirmed, 5p confirmed)
E14	#158	at 2 players speed wins (passing costs more than at 4)	CONFIRMED
E14	#77, #253, #339, #426	keep a low profile early (little visible value)	REFUTED
E14	#457	fast empire builders lose (slow openings win at 4p)	CONDITIONAL (2p refuted, 3p refuted, 4p confirmed, 5p confirmed)
E15	#319, #438, #320, #111	early Birthday/rent is wasted; wait for rich targets	INCONCLUSIVE
E15	#212	Birthday / Debt Collector are strongest early (fire at once)	REFUTED
E15	#554, #480	rent is a game of chicken: strike when the charge is big or takes property	CONDITIONAL (2p refuted, 3p confirmed, 4p confirmed, 5p confirmed)
E15	#340, #342	batch charges into one big turn (wait for $8)	REFUTED
E16	#57, #476, #298	shed the big bill / overpay to protect small change (Baseline's way is at least as good)	CONDITIONAL (2p confirmed, 3p confirmed, 4p refuted, 5p confirmed)
E16	#272	pay near-exact with small bills rather than one big one	CONFIRMED
E16	#550, #278, #192	give dead railroads/utilities before cash	REFUTED
E16	#410	never hand over the card that completes their set	CONFIRMED at 4p, 5p; inconclusive at 2p, 3p
E17	#239, #399, #250, #186, #115, #154, #166, #397, #398, #381	Forced Deal into Deal Breaker is the best move in the game	REFUTED
E17	#567, #487, #162, #332, #169, #191, #89	pay them the completing card, then Deal Breaker the set	REFUTED
E17	#200	they win before you can Deal Breaker (the gift loses)	INCONCLUSIVE
E18	#1	hoard the Just Say No for Deal Breakers	REFUTED at 2p, 3p, 4p; inconclusive at 5p
E18	#218, #685, #716	a Just Say No counters anything: use it	REFUTED at 3p; inconclusive at 2p, 4p, 5p
E18	#19	countering a Just Say No with a Just Say No is not always best	REFUTED at 2p, 3p; inconclusive at 4p, 5p
E18	#167, #277	bait the Just Say No with a Sly Deal, then Deal Breaker	REFUTED
E19	#168, #263	empty the hand to draw five	CONFIRMED
E19	#549, #138, #139	discard what they need rather than lay it	REFUTED
E19	#255	do nothing until a playable hand appears	REFUTED
E19	#215, #216, #673, #703	Pass Go: play it first (#216) rather than hold it (#215)	CONFIRMED
E20	#225	charging a play for wild moves lengthens games without adding anything	REFUTED
E20	#15, #11, #413	charging a play for flips is right (it removes a real edge)	REFUTED at 2p; inconclusive at 3p, 4p, 5p
E20	#496, #497	free flipping weakens the Deal Breaker and strengthens Sly Deal	REFUTED
E20	#559	free movement plus ×4 rents lets one player farm rents	REFUTED
E21	#375	the 2024 rule (a Just Say No on your own turn costs a play) kills Just Say No wars	CONFIRMED
E21	#285	the rule created a play-big-action-last meta	REFUTED
E22	#509	Double the Rent played right is the most devastating card	INCONCLUSIVE
E22	#315	Double the Rent is banked 90 % of the time	REFUTED
E22	#7, #80	×4 rents are rare and harmless	INCONCLUSIVE
E22	#8, #176, #559	×4 stacking should be banned	REFUTED
E22	#25, #26, #303, #304	a Just Say No on a doubled rent cancels only the doubler (UK reading) — does it matter?	REFUTED
E22	#78, #190, #194, #152, #188, #453, #510, #472	giant rents ($30+, up to $60) happen	CONFIRMED
E23	#243, #244, #38, #390, #256, #557	4–5 sets to win: longer games, Deal Breakers more useful, less luck	CONFIRMED
E23	#513, #96, #328, #266, #39	2 players needs 4–5 sets (cuts the first-seat edge)	REFUTED
E23	#133, #450	4 plays / 4 sets ($15M bank) house rules	REFUTED
E23	#248, #432	a bank requirement to win adds luck	CONDITIONAL (2p confirmed, 3p confirmed, 4p refuted, 5p refuted)
E23	#236	Speed Deal (draw 3, five plays) is faster	CONFIRMED
E24	#3, #355, #0	without Deal Breakers games run longer	REFUTED at 4p, 5p; inconclusive at 2p, 3p
E24	#327, #71, #481, #96, #328	no Deal Breakers = more skill, less luck	CONFIRMED at 3p, 4p, 5p; inconclusive at 2p
E24	#358	remove one Deal Breaker and one Just Say No at 2p	REFUTED
E24	#518	toss the $10M	REFUTED
E24	#387	without big money, late rent matters at 2p (more property payments)	CONFIRMED
E24	#72	too many Pass Go cards (six instead of ten lengthens games)	REFUTED
E24	#495	two-colour wilds are overpowered (removing them lengthens games materially)	CONFIRMED
E24	#558	a skill-over-luck deck (the no-DB half)	CONFIRMED
E25	#560	Monopoly Deal is mostly luck	REFUTED
E25	#561, #461	deep strategy: good players win a high share	CONFIRMED
E25	#60, #62, #389	more luck with more players (the skill spread shrinks with the count)	CONFIRMED
E25	#570, #529	streaks are common (arithmetic on the seat rates)	CONFIRMED
E26	#123, #83, #370, #367	seeing the banks is essential (blind targeting loses ≥ 1 pp)	CONFIRMED
E26	#56	a visible $10M draws Debt Collectors (blind targeting loses income)	CONFIRMED
E27	#553, #44	dismantle whoever can win (target the leader)	REFUTED
E27	#458, #457	an early leader gets ganged up on and loses	REFUTED
E27	#193, #343, #425	the strongest player gets targeted and cannot build	REFUTED
E28	#55	an early $10M is a curse: hold it	REFUTED
E28	#54	bank the $10M at once	CONFIRMED
E29	#132, #198, #79, #666	two-card sets are the easiest win: go for them first	CONFIRMED at 5p; inconclusive at 2p, 3p, 4p
E29	#267, #185, #153	dark blue is the key colour (high-rent colours first)	REFUTED
E30	#551, #267, #494, #565, #493	do not expose pairs or rainbow wilds	CONDITIONAL (2p refuted, 3p refuted, 4p inconclusive, 5p confirmed)
E30	#131, #214	hold every wild until it completes a set	REFUTED
E30	#150, #185, #462	lay property only with the rent card in hand	REFUTED
E30	#454	pure holding (everything for a one-turn win) is too slim to win	CONFIRMED
E30	#219	avoid obvious Sly Deal targets (hold pairs; steal counts)	CONDITIONAL (2p refuted, 3p refuted, 4p inconclusive, 5p confirmed)
E31	#546, #29	never bank a two-colour rent card at 4–5 players	CONFIRMED at 4p, 5p; inconclusive at 2p, 3p
E31	#317	rent is weak at 2p and dominant at 4+ (the never-bank-rent edge grows with the count)	CONFIRMED
E31	#42	a no-banking-rent house rule gives rent cards purpose (more rents per game)	CONDITIONAL (2p confirmed, 3p refuted, 4p refuted, 5p refuted)
E31	#547, #112	bank buildings unless the set is safe	INCONCLUSIVE
E32	#179	farming rent instead of winning is bad play (and renting first on the winning turn is free)	INCONCLUSIVE
E33	#198, #199	three-turn wins are once-in-thousands	CONDITIONAL (2p confirmed, 3p inconclusive, 4p refuted, 5p refuted)
E33	#234	winning with 4 sets is common, 5 needs a combo	CONFIRMED
E33	#562, #254, #696	someone's big move hands the next player the win	CONFIRMED
E33	#189	comebacks from two sets behind happen	CONFIRMED
E33	#555, #470, #257, #30	Deal Breakers are rarely played successfully / get banked	REFUTED
E33	#31	two Deal Breakers plus an own set wins at once	CONFIRMED
E33	#315, #80, #510, #152, #709, #710, #711	Double the Rent usage, ×4 rents, maximum rents	CONFIRMED
E33	#375, #19	Just Say No wars	CONFIRMED
E33	#418, #500, #501, #159, #181, #212	starting-hand composition decides a lot	CONFIRMED
E33	#459	early money snowballs	CONFIRMED
E33	#318	at 2 players banks get so big that rent is useless	CONFIRMED
E33	#0	the Deal Breaker is game-breaking at 2p	REFUTED
E34	#670, #671	bank the Pass Go when nearly out of cards	REFUTED at 3p; inconclusive at 2p, 4p, 5p
E34	#672	play Pass Go unless it is your last card and last action	INCONCLUSIVE
E34	#707	Pass Go turns are Pass-Go-only	REFUTED
E35	#668	bank rent / House / Hotel / Forced Deal early	REFUTED
E35	#669	the any-colour rent is $3M in the bank unless it collects ≥ $3M	REFUTED at 2p, 3p; inconclusive at 4p, 5p
E35	#700	never play an action as money unless broke	INCONCLUSIVE
E35	#697	bank $10M before chasing sets	REFUTED
E35	#714	hold the $10M until a $6M small-bill buffer	REFUTED
E36	#704	2+5+5 is the perfect opener (big bills only)	REFUTED
E36	#705	keep the small bills under the five	REFUTED
E36	#706	don't play three cards in the opening round unless holding attacks	REFUTED at 2p, 4p, 5p; inconclusive at 3p
E37	#693	hold the Deal Breaker for the winning moment / until the other one is gone	REFUTED at 2p, 3p; inconclusive at 4p, 5p
E37	#694	Deal Breaker only with a Just Say No in hand	REFUTED
E37	#681	Deal Breaker the empty-handed	REFUTED
E37	#688	wait for another opponent to draw their Just Say No out	REFUTED
E37	#680	bank the Deal Breaker to refill the hand	CONFIRMED
E37	#679	bait them into completing a set, then Deal Breaker it	REFUTED
E38	#682	steal two-card-set pieces first	REFUTED at 3p, 4p; inconclusive at 2p, 5p
E38	#683	take the wild, not the solid card	INCONCLUSIVE
E38	#684	at 2 players use every rent and Sly Deal at once (offence is king)	REFUTED
E38	#99	Sly Deal the dark blues, then rent them (steal for rent)	CONFIRMED at 5p; inconclusive at 2p, 3p, 4p
E39	#675	charge whoever must overpay	REFUTED
E39	#690	Debt Collect the bank-poor and property-rich	CONFIRMED
E39	#691	aim the Debt Collector at many small bills	REFUTED
E39	#689	go after whoever has spent a Just Say No	REFUTED
E39	#708	the next seat is weakest when you act	REFUTED
E39	#695	pay with as few cards as possible	CONDITIONAL (2p inconclusive, 3p refuted, 4p confirmed, 5p inconclusive)
E40	#667	keep railroads in hand and get paid into the set	CONFIRMED at 2p, 4p, 5p; inconclusive at 3p
E40	#676	show your worst property first	REFUTED at 2p, 3p; inconclusive at 4p, 5p
E40	#677	lay wilds freely once the six steal cards are gone	INCONCLUSIVE
E40	#687	discard colours you can no longer complete	REFUTED
E41	#692	steal first on the winning turn (against opponents who Just Say No the winning play)	CONFIRMED
E42	#686	the any-colour rent is worth more at 2p, the two-colour rents at 3+	CONFIRMED
E43	#713	myforwik's simulation-derived bundle beats folk play and every component	CONFIRMED at 2p; inconclusive at 3p, 4p, 5p
E44	#285, #375	under the 2024 rule, fire the attack you care about first and keep a play to answer (the mirror, attacks last, loses)	CONFIRMED
E46	#167, #277	fish the Just Say No out with a Sly Deal before the Deal Breaker	REFUTED
E47	#713	the bundle decomposed: dump-to-zero (D), JSN-anything (J), steal two-card colours (S), hold pairs (H)	CONFIRMED at 2p, 3p, 4p; inconclusive at 5p

Every Forced Deal verdict below was scored on an engine that forbade one legal play. The 2024 card reads "Swap any one of your properties with any one of another player's. You may not TAKE a property that's part of a complete set" — the limit is on the card TAKEN, so a player may offer a card out of one of their own complete sets, breaking it (and discarding any House or Hotel on it). The engine forbade both sides until 2026-09-20; RuleOptions.forced_deal_give_from_full now defaults to True and False reproduces the engine every cell below ran on. E50/E50b (RESULTS.md) measure the difference. What it does NOT affect: every verdict here, because all of them are scored on cells in which neither side had the play, and the recommended policy's own win rate moves by at most 0.20 pp when it is granted (66.74 → 66.64 at 2p, 41.05 → 40.85 at 4p, 40,000 games a cell on identical seeds, E50b) — and 85–90 % of even that is the longer legal-play list crowding its truncated win search, not the play (E50d). What it DOES affect: the size of the gap between strong and folk play. The folk Baseline offers a card from one of its own complete sets on 28–38 % of its Forced Deals once the rule allows it, and each such play is worth +15.5 / +9.3 / +6.8 / +5.4 pp to a strong opponent at 2/3/4/5 players. Against a table that plays the printed card, the recommended policy is about two points better than every number in this file (E50b). Forced Deal claim rows below — E17 (Forced Deal into Deal Breaker), E38 (steal targeting), E05/E05b (which card to give), E03/E45 (card values), E10/E11 (exposure to Sly and Forced Deal) — keep their labels; only the margin widens.

Controls

Cell	2p	3p	4p	5p
`baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39
`E49:baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39

E10 — Set-completion timing (delay full sets to dodge Deal Breaker)

Cell	2p	3p	4p	5p
`delay_always`	-14.12 ±0.47 (paired -14.26 ±0.46)	-13.69 ±0.39 (paired -13.55 ±0.42)	-9.69 ±0.35 (paired -9.89 ±0.38)	-5.73 ±0.34 (paired -5.93 ±0.34)
`delay_protected`	-4.75 ±0.49 (paired -4.89 ±0.36)	-2.97 ±0.45 (paired -2.82 ±0.34)	-0.96 ±0.42 (paired -1.16 ±0.31)	-0.06 ±0.39 (paired -0.26 ±0.27)
`delay_counting`	-10.91 ±0.48 (paired -11.05 ±0.44)	-6.62 ±0.43 (paired -6.47 ±0.41)	-2.47 ±0.41 (paired -2.67 ±0.36)	-0.82 ±0.39 (paired -1.02 ±0.31)
`E49:delay_always`	-14.12 ±0.47 (paired -14.26 ±0.46)	-13.69 ±0.39 (paired -13.55 ±0.42)	-9.69 ±0.35 (paired -9.89 ±0.38)	-5.73 ±0.34 (paired -5.93 ±0.34)
`E49:delay_always_table`	-0.43 ±0.49 (paired -0.57 ±0.58)	-0.20 ±0.46 (paired -0.06 ±0.56)	-0.27 ±0.42 (paired -0.47 ±0.51)	+0.07 ±0.39 (paired -0.13 ±0.46)
`E33:baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39

REFUTED at 2p, 3p, 4p; inconclusive at 5p — #129, #187, #329, #48, #2, #156, #148, #164, #533, #514 (delay full sets to dodge the Deal Breaker (delay is right / exposes nothing)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p INCONCLUSIVE. #129 "Avoid making full sets until you can make three in one turn; exceptions when holding a DB, JSN, or matching re…" pmne01; #187 "Making 3 full sets in one turn means the opponent never knew which property to steal and can't use a DB" vg9tq4; #329 "It's very easy to play around Deal Breakers: don't leave sets complete until you're going to win with them" kr4b27o
REFUTED — #32, #456, #163 (never completing a set leaves you exposed to Sly/Forced Deal). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. outcome from the E10 cell; exposure from E49's per-seat steal counters (the delayer vs the all-Baseline control on the same seeds). #32 "Never completing a set until the last turn keeps you constantly vulnerable to Sly Deal and Forced Deal" fwvak20; #456 "Only 8 cards in the deck steal property; don't put anything on the board you can't live with losing; don't bui…" mxvvlhb; #163 "Holding a Deal Breaker is valuable even unused because nobody else has it; players who refuse to complete sets…" hyr8hwg
REFUTED — #130, #288, #471, #544, #51, #477 (count the Deal Breakers, then complete). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #130 "Never run out a full set (easy DB target), but once both DBs are accounted for, completing sets is great becau…" hestptx; #288 "Don't flip a wild to complete a set until both DBs are gone or you spring a trap, accepting Sly/Forced exposur…" jra65ar; #471 "Once you hold the remaining Deal Breakers, or a DB and a JSN, leave a full set out to protect from Sly/Forced;…" n1uxiej
CONFIRMED — #155, #164 (a JSN or DB in hand makes completion safe). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #155 "If you hold both DBs you can make full sets freely since nobody can steal them" hxiz4bb; #164 "Lock down full sets when holding a DB, JSN, or a high-value rent card" hyslm7q
CONDITIONAL (2p confirmed, 3p refuted, 4p refuted, 5p refuted) — #30, #257, #514, #470, #356 (the Deal Breaker has no target once everyone delays). Per count: 2p CONFIRMED, 3p REFUTED, 4p REFUTED, 5p REFUTED. Deal Breakers played per game at an all-delay table vs the all-Baseline table. #30 "DB is useless because everyone holds completing cards and lays full sets in one turn" gck8mx; #257 "The 3-set rule can make Deal Breakers useless since you can complete all three in one turn" j2149qb; #514 "We effectively play without DB because nobody assembles full sets until they're ready to go out at the end" ok38iog

E11 — Un-complete sets with wilds at end of turn (Deal Breaker dodge)

Cell	2p	3p	4p	5p
`wild_dodge`	-4.15 ±0.49 (paired -4.29 ±0.38)	-3.23 ±0.45 (paired -3.08 ±0.40)	-1.41 ±0.42 (paired -1.61 ±0.37)	-1.12 ±0.38 (paired -1.32 ±0.33)

REFUTED — #545, #444, #94, #296, #208, #13, #251, #538 (un-completing a set with a wild at end of turn (the Deal Breaker dodge) is worth it). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #545 "Full sets are immune to Forced/Sly but DB ruins you: rearrange wilds before ending your turn so no monopoly is…" rw0kt; #444 "Splitting a complete set (if one card is a wild) on your turn is a common strategy to nerf the Deal Breaker, a…" mhizxqj; #94 "Online players often break up their monopolies to avoid being Deal Broken" gmngt02
CONFIRMED — #252 (dodging trades a small DB risk for a larger steal risk (poor trade)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #252 "Keeping same-colour cards separate is a poor trade: ~2% chance of DB vs ~10% chance of Sly/Forced Deal (author…" iz836uc

E12 — Flip wilds to maximise rent, flip back before ending

Cell	2p	3p	4p	5p
`wild_rentflip`	-0.13 ±0.49 (paired -0.27 ±0.22)	+0.93 ±0.47 (paired +1.07 ±0.26)	+2.25 ±0.44 (paired +2.05 ±0.26)	+2.12 ±0.41 (paired +1.92 ±0.25)

CONDITIONAL (2p refuted, 3p inconclusive, 4p confirmed, 5p confirmed) — #238, #310, #13 (flipping wilds for rent (and back) is excellent). Per count: 2p REFUTED, 3p INCONCLUSIVE, 4p CONFIRMED, 5p CONFIRMED. #238 "Breaking and re-forming full sets with wilds to maximise rent is excellent strategy, not abuse" iuuyn4o; #310 "Sliding the rainbow wild to another colour to rent, then back to re-complete the set before ending the turn, i…" kd5cdbn; #13 "Official rules let you flip wilds freely: flip to charge rent on two colours in one turn, and flip to un-compl…" fkwkpz9
REFUTED at 2p; inconclusive at 3p, 4p, 5p — #468 (free wild movement is overpowered). Per count: 2p REFUTED, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #468 "Free wild movement feels overpowered because you can move it between sets and rent repeatedly" 1lo50r1

E13 — Bank floor before laying property

Cell	2p	3p	4p	5p
`bank_floor_3`	+0.02 ±0.49 (paired -0.12 ±0.37)	-1.71 ±0.46 (paired -1.56 ±0.44)	-3.44 ±0.40 (paired -3.65 ±0.43)	-3.48 ±0.36 (paired -3.68 ±0.40)
`bank_floor_5`	-1.86 ±0.49 (paired -2.00 ±0.41)	-4.71 ±0.44 (paired -4.57 ±0.46)	-6.35 ±0.38 (paired -6.55 ±0.44)	-5.76 ±0.34 (paired -5.96 ±0.41)
`bank_floor_8`	-7.75 ±0.48 (paired -7.89 ±0.45)	-9.77 ±0.42 (paired -9.62 ±0.48)	-10.24 ±0.35 (paired -10.44 ±0.44)	-7.94 ±0.32 (paired -8.14 ±0.41)
`never_bank_money`	-8.72 ±0.48 (paired -8.86 ±0.32)	-6.76 ±0.43 (paired -6.62 ±0.31)	-4.46 ±0.40 (paired -4.67 ±0.28)	-2.71 ±0.37 (paired -2.91 ±0.24)

REFUTED at 3p, 4p, 5p; inconclusive at 2p — #269, #180, #507, #203, #204, #205, #341 (bank money first, before laying property). Per count: 2p INCONCLUSIVE, 3p REFUTED, 4p REFUTED, 5p REFUTED. #269 "Never play properties until you have at least $5M banked to cover a Debt Collector" ja4xjgq; #180 "Wait until you have enough bank before dropping property in general, or you'll lose the cards to rent" i9vurpu; #507 "Laying down a full set without money to back it is a bold move" ojdm1cb
CONFIRMED at 3p, 4p, 5p; inconclusive at 2p — #6, #151, #137, #295 (holding property while waiting for money loses (the higher the floor the worse)). Per count: 2p INCONCLUSIVE, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #6 "Held three sets in hand all game waiting for money/rent, never got any, lost" er4v3ps; #151 "Started with both dark blues and never laid them because a rent card or JSN never came" hjc4sq1; #137 "Drawing 2 and playing nothing to avoid putting property down (which you'd have to pay with) is a pro move" hegfqz6
REFUTED — #563 (bank everything you do not need (floor $5)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #563 "Bank every card you don't think you need to protect your properties; charging an empty player wastes the card" jr7k90p
CONFIRMED — #366 (the never-bank-money challenge is a handicap). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #366 "Challenge: never bank money cards, only action cards and received money" 1dz4q5k

E14 — Opening tempo: pass the first turn(s), low-profile opening

Cell	2p	3p	4p	5p
`pass_first_1`	-6.66 ±0.49 (paired -6.80 ±0.47)	-0.59 ±0.46 (paired -0.45 ±0.53)	+1.04 ±0.43 (paired +0.83 ±0.51)	+2.35 ±0.41 (paired +2.15 ±0.49)
`pass_first_2`	-15.72 ±0.47 (paired -15.86 ±0.54)	-4.81 ±0.44 (paired -4.67 ±0.56)	-3.63 ±0.40 (paired -3.84 ±0.53)	-2.49 ±0.37 (paired -2.69 ±0.50)
`low_profile_2t_cap2`	-5.30 ±0.49 (paired -5.44 ±0.40)	-2.31 ±0.45 (paired -2.16 ±0.47)	-1.87 ±0.41 (paired -2.07 ±0.45)	-1.03 ±0.38 (paired -1.23 ±0.42)
`low_profile_3t_cap2`	-10.42 ±0.48 (paired -10.55 ±0.44)	-6.36 ±0.43 (paired -6.22 ±0.48)	-5.55 ±0.39 (paired -5.75 ±0.46)	-3.88 ±0.36 (paired -4.08 ±0.42)

CONDITIONAL (2p refuted, 3p refuted, 4p confirmed, 5p confirmed) — #548, #75, #157, #503 (pass the first turn (especially at 4 players)). Per count: 2p REFUTED, 3p REFUTED, 4p CONFIRMED, 5p CONFIRMED. #548 "First turn with no way to build money: just draw and end your turn; don't fear discarding" rw0kt; #75 "When going first, draw 2 and play nothing (esp. holding Birthday) so you effectively go last; only cost is a b…" k5y7qk; #157 "In 4-player games it's almost always best to start slower, sometimes not playing anything the first turn; gett…" hxq9y13
CONFIRMED — #158 (at 2 players speed wins (passing costs more than at 4)). Per count: 2p CONFIRMED. #158 "In 1v1 it's usually whoever gets cards down fastest while slowing the opponent" hxq9y13
REFUTED — #77, #253, #339, #426 (keep a low profile early (little visible value)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #77 "Early on, play only low-value cards ($1 money, $1 properties from 3-card sets)" geknfr1; #253 "Only having $1M on the table on turn 1 discourages opponents from wasting Birthday/Debt Collector on you" jfeih17; #339 "Banking $1M is a pro move: nobody will Debt Collect you for $1M and Birthdays get shorted" kwpo38q
CONDITIONAL (2p refuted, 3p refuted, 4p confirmed, 5p confirmed) — #457 (fast empire builders lose (slow openings win at 4p)). Per count: 2p REFUTED, 3p REFUTED, 4p CONFIRMED, 5p CONFIRMED. #457 "The player who jumps out early building an empire often loses; it's a marathon, and an early lead makes everyo…" mxvvlhb

E15 — When to fire money charges (rent / Debt Collector / Birthday)

Cell	2p	3p	4p	5p
`charge_now`	-2.12 ±0.49 (paired -2.25 ±0.40)	-1.68 ±0.46 (paired -1.54 ±0.41)	-3.10 ±0.41 (paired -3.30 ±0.37)	-2.31 ±0.37 (paired -2.51 ±0.34)
`charge_rich_5`	-2.07 ±0.49 (paired -2.21 ±0.30)	-1.39 ±0.46 (paired -1.24 ±0.38)	-0.55 ±0.42 (paired -0.76 ±0.38)	-0.62 ±0.39 (paired -0.82 ±0.36)
`rent_chicken`	-3.24 ±0.49 (paired -3.38 ±0.28)	+1.01 ±0.47 (paired +1.15 ±0.31)	+2.63 ±0.44 (paired +2.43 ±0.27)	+2.11 ±0.41 (paired +1.91 ±0.22)
`charge_rich_8`	-4.72 ±0.49 (paired -4.86 ±0.34)	-3.54 ±0.45 (paired -3.40 ±0.41)	-4.03 ±0.40 (paired -4.24 ±0.42)	-0.90 ±0.39 (paired -1.10 ±0.39)

INCONCLUSIVE — #319, #438, #320, #111 (early Birthday/rent is wasted; wait for rich targets). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #319 "Birthday on the first round when nobody has anything down is a wasted card" khqzy1f; #438 "Renting on the first turn before anyone has cards down is pointless: there is no debt, you pay what you can" mded46n; #320 "Only play It's My Birthday once everyone has enough down to pay you" ki4g662
REFUTED — #212 (Birthday / Debt Collector are strongest early (fire at once)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #212 "Tier list: Deal Breaker is low until late game (niche); Birthday and Debt Collector are high in the first few …" ijeemtf
CONDITIONAL (2p refuted, 3p confirmed, 4p confirmed, 5p confirmed) — #554, #480 (rent is a game of chicken: strike when the charge is big or takes property). Per count: 2p REFUTED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #554 "With a good nest egg, rent becomes a game of chicken: be the finishing blow after others have emptied someone'…" rw0kt; #480 "Use rent cards to empty opponents' banks so later charges take their properties" nrrom6m
REFUTED — #340, #342 (batch charges into one big turn (wait for $8)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #340 "Save up rent/birthday cards, then make all three moves at once: Birthday, drop dark blue, rent (or rent + doub…" kwpo38q; #342 "Play Pass Gos whenever and ditch low-value cards until you can play e.g. Birthday + Green + Green rent in one …" kwmuafw

E16 — Payment policy: exact change vs shed the big bill; dead properties before cash; never gift

Cell	2p	3p	4p	5p
`pay_min_overpay`	+0.75 ±0.49 (paired +0.61 ±0.10)	+0.50 ±0.46 (paired +0.64 ±0.14)	+1.15 ±0.43 (paired +0.95 ±0.16)	+0.75 ±0.40 (paired +0.55 ±0.15)
`pay_dead_props`	-8.85 ±0.48 (paired -8.99 ±0.33)	-8.46 ±0.42 (paired -8.32 ±0.35)	-7.32 ±0.37 (paired -7.53 ±0.35)	-5.06 ±0.35 (paired -5.26 ±0.32)
`pay_never_gift`	+0.35 ±0.49 (paired +0.21 ±0.07)	+0.13 ±0.46 (paired +0.28 ±0.10)	+0.46 ±0.43 (paired +0.26 ±0.11)	+0.45 ±0.40 (paired +0.25 ±0.11)

CONDITIONAL (2p confirmed, 3p confirmed, 4p refuted, 5p confirmed) — #57, #476, #298 (shed the big bill / overpay to protect small change (Baseline's way is at least as good)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p REFUTED, 5p CONFIRMED. #57 "Overpaying with a $10M when you owe $8M is allowed and a great strategy to shed your biggest denomination" g2j8ga1; #476 "The number of money cards matters as much as the amount: paying $5M with a $10M keeps small bills for later sm…" nrm3jfn; #298 "Overpay strategically (no change) to protect properties or specific action cards" jxxnswy
CONFIRMED — #272 (pay near-exact with small bills rather than one big one). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #272 "Two railroads beat a $4M unless low on cash (they can earn rent); two $2M beat one $4M because small rents cos…" jcwxkcw
REFUTED — #550, #278, #192 (give dead railroads/utilities before cash). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #550 "A full railroad set is very hard to finish; pay a $2M railroad rather than $4M cash to a Birthday" rw0kt; #278 "Two railroads are better than $4M cash unless you're low on cash" jcwxkcw; #192 "Sometimes it's better to pay rent with properties than money" ihoke0u
CONFIRMED at 4p, 5p; inconclusive at 2p, 3p — #410 (never hand over the card that completes their set). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p CONFIRMED, 5p CONFIRMED. #410 "A good player knows which cards opponents need to complete sets and never hands them over" lz679pq

E17 — Gift-then-Deal-Breaker: Forced Deal into DB, pay with the completing card then DB

Cell	2p	3p	4p	5p
`combo_fd_db`	+0.11 ±0.49 (paired -0.03 ±0.06)	-0.22 ±0.46 (paired -0.08 ±0.06)	+0.12 ±0.43 (paired -0.09 ±0.05)	+0.14 ±0.39 (paired -0.06 ±0.05)
`E49:combo_fd_db_vs_nojsn`	+7.96 ±0.48 (vs baseline_vs_nojsn: -0.05 ±0.05)	+5.44 ±0.48 (vs baseline_vs_nojsn: -0.07 ±0.06)	+3.59 ±0.44 (vs baseline_vs_nojsn: -0.10 ±0.05)	+2.55 ±0.41 (vs baseline_vs_nojsn: -0.10 ±0.05)
`pay_gift_then_db`	-0.05 ±0.49 (paired -0.19 ±0.06)	-0.21 ±0.46 (paired -0.07 ±0.05)	+0.21 ±0.43 (paired +0.01 ±0.05)	+0.14 ±0.39 (paired -0.06 ±0.05)
`E49:pay_gift_then_db_vs_nojsn`	+7.88 ±0.48 (vs baseline_vs_nojsn: -0.14 ±0.05)	+5.43 ±0.48 (vs baseline_vs_nojsn: -0.08 ±0.05)	+3.67 ±0.44 (vs baseline_vs_nojsn: -0.03 ±0.05)	+2.63 ±0.41 (vs baseline_vs_nojsn: -0.02 ±0.04)

REFUTED — #239, #399, #250, #186, #115, #154, #166, #397, #398, #381 (Forced Deal into Deal Breaker is the best move in the game). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. whole-cell delta, conditional win rate after the combo, and the E49 cell against opponents that never Just Say No (paired with its control). #239 "Using Forced Deal to make a monopoly for another player then Deal Breaker it is legal and a favourite move; ju…" iuwh1mu; #399 "Forced Deal into Deal Breaker is probably the best move in the game" lmcr0ma; #250 "Forced Deal a colour you confirm on your side, then Deal Breaker it: receiver can't alter until their turn; a …" iz37ykk
REFUTED — #567, #487, #162, #332, #169, #191, #89 (pay them the completing card, then Deal Breaker the set). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #567 "Opponent deliberately overpaid rent with a property that completed my set, then Deal Breakered it (r/boardgame…" ovmqw0; #487 "Receiving property as payment can backfire: forced to combine greens into a set, then I Deal Breakered it" o0ode11; #162 "When charged, pay with the property that completes their set (and that they can't move off on your turn), then…" hyozl7s
INCONCLUSIVE — #200 (they win before you can Deal Breaker (the gift loses)). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #200 "Forcing people into full sets when they charge me rent has often let them win that turn before I could Deal Br…" ika5hl6

E18 — Just Say No discipline

Cell	2p	3p	4p	5p
`jsn_only_breaker`	-0.65 ±0.49 (paired -0.79 ±0.20)	-0.94 ±0.46 (paired -0.80 ±0.18)	-0.22 ±0.42 (paired -0.43 ±0.15)	-0.15 ±0.39 (paired -0.35 ±0.14)
`jsn_anything`	+0.49 ±0.49 (paired +0.35 ±0.23)	-0.55 ±0.46 (paired -0.40 ±0.25)	-0.00 ±0.42 (paired -0.21 ±0.24)	-0.24 ±0.39 (paired -0.43 ±0.22)
`jsn_no_counter`	-0.76 ±0.49 (paired -0.90 ±0.10)	-0.82 ±0.46 (paired -0.68 ±0.09)	-0.25 ±0.42 (paired -0.46 ±0.07)	-0.12 ±0.39 (paired -0.32 ±0.07)
`bait_before_db`	+0.12 ±0.49	-0.51 ±0.46	-0.13 ±0.42	-0.05 ±0.39
`E46:bait_before_db`	+0.08 ±0.22 (vs db_first_no_bait: -0.05 ±0.04)	-0.45 ±0.21 (vs db_first_no_bait: -0.34 ±0.05)	-0.22 ±0.19 (vs db_first_no_bait: -0.37 ±0.05)	-0.25 ±0.17 (vs db_first_no_bait: -0.29 ±0.05)
`E46:db_first_no_bait`	+0.13 ±0.22	-0.12 ±0.21	+0.15 ±0.19	+0.04 ±0.18

REFUTED at 2p, 3p, 4p; inconclusive at 5p — #1 (hoard the Just Say No for Deal Breakers). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p INCONCLUSIVE. #1 "With only 3 JSN in the deck, hoard them for Deal Breakers rather than lesser actions" aeo0fr
REFUTED at 3p; inconclusive at 2p, 4p, 5p — #218, #685, #716 (a Just Say No counters anything: use it). Per count: 2p INCONCLUSIVE, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #218 "JSN is the most powerful card since it counters anything including itself; DB is niche and easy to avoid by no…" il56w24; #685 "Two-player: play a JSN early against a Rent or Debt Collector that would wipe out a small bank; 2p games are t…" mds-duoplayer; #716 "Play the Just Say No's fairly quickly / use them against any action you can: shedding a card for free is worth…" bgg-469342
REFUTED at 2p, 3p; inconclusive at 4p, 5p — #19 (countering a Just Say No with a Just Say No is not always best). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #19 "JSN can be played on top of a JSN (allowed; not always best use)" fh4bytb
REFUTED — #167, #277 (bait the Just Say No with a Sly Deal, then Deal Breaker). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. scored from E46 (matched no-bait control on the same seeds, 200k games). #167 "Fish out a JSN by first playing a lesser card (Sly Deal) before the card you really want (Deal Breaker)" jj5imn1; #277 "Fishing: play a throwaway set-completing card to draw out the JSN before the Deal Breaker; the opponent has be…" jd035gq

E19 — Hand management: dump to zero, deny discards, pass when weak, Pass Go last

Cell	2p	3p	4p	5p
`dump_to_zero`	+0.98 ±0.49 (paired +0.84 ±0.15)	+0.97 ±0.47 (paired +1.11 ±0.16)	+0.88 ±0.43 (paired +0.68 ±0.12)	+0.50 ±0.40 (paired +0.30 ±0.08)
`discard_deny`	-0.70 ±0.49 (paired -0.84 ±0.25)	-2.10 ±0.45 (paired -1.96 ±0.28)	-1.29 ±0.42 (paired -1.50 ±0.28)	-0.94 ±0.38 (paired -1.14 ±0.27)
`pass_when_weak`	-6.46 ±0.49 (paired -6.60 ±0.30)	-5.55 ±0.44 (paired -5.41 ±0.31)	-3.53 ±0.40 (paired -3.74 ±0.28)	-1.78 ±0.38 (paired -1.98 ±0.24)
`passgo_last`	-1.41 ±0.49 (paired -1.55 ±0.50)	-2.93 ±0.45 (paired -2.79 ±0.50)	-2.80 ±0.41 (paired -3.01 ±0.47)	-3.04 ±0.37 (paired -3.24 ±0.43)

CONFIRMED — #168, #263 (empty the hand to draw five). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #168 "Generally pass the first turn (game of chicken); then empty your hand to zero ASAP to draw five next turn" i1931w6; #263 "If the first player didn't draw they'd run out of cards and draw a fresh 5 on turn 4, an insane advantage" j63pexd
REFUTED — #549, #138, #139 (discard what they need rather than lay it). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #549 "When cleaned out, discarding properties from hand can be better than letting someone take them" rw0kt; #138 "Intentionally end with more than 7 cards so you can discard a property your opponent is waiting for" hegpyzq; #139 "Played three Pass Go to reach 10 cards and discarded 3 properties the opponent wanted" hzegj4n
REFUTED — #255 (do nothing until a playable hand appears). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #255 "You never have to play; you can do nothing each turn and discard down to 7 until a playable hand appears" j0ntrtz
CONFIRMED — #215, #216, #673, #703 (Pass Go: play it first (#216) rather than hold it (#215)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. CONFIRMED = playing Pass Go first beats holding it (passgo_last below fair). #215 "Pass Go should be near the bottom; any two-colour rent is worth more than the any-colour rent; the $10M puts y…" ijey5zs; #216 "Theory: players who play more Pass Go cards win more (+1 card advantage), despite costing a play and conflicti…" ijspldp; #673 "Seven not Five: on a turn where you drew five, always play any Pass Go drawn (up to nine new cards in one turn…" mds-future

E20 — House rule: moving a wild costs one of the three plays

Cell	2p	3p	4p	5p
`rule_wildcost_baseline`	+0.19 ±0.49	-0.33 ±0.46	+0.28 ±0.43	+0.37 ±0.39
`E49:rule_wildcost_baseline`	+0.19 ±0.49	-0.33 ±0.46	+0.28 ±0.43	+0.37 ±0.39
`rule_wildcost_wild_rentflip`	+0.26 ±0.49 (vs rule_wildcost_baseline: +0.07 ±0.24)	-0.66 ±0.46 (vs rule_wildcost_baseline: -0.33 ±0.28)	+0.96 ±0.43 (vs rule_wildcost_baseline: +0.68 ±0.28)	+1.04 ±0.40 (vs rule_wildcost_baseline: +0.67 ±0.26)
`E12:wild_rentflip`	-0.13 ±0.49 (paired -0.27 ±0.22)	+0.93 ±0.47 (paired +1.07 ±0.26)	+2.25 ±0.44 (paired +2.05 ±0.26)	+2.12 ±0.41 (paired +1.92 ±0.25)
`E49:wild_dodge_table_free`	—	-0.07 ±0.46 (paired +0.07 ±0.48)	+0.30 ±0.43 (paired +0.10 ±0.47)	+0.01 ±0.39 (paired -0.18 ±0.44)
`E49:wild_dodge_table_costs`	—	+0.30 ±0.46 (vs wild_dodge_table_free: +0.37 ±0.44)	+0.35 ±0.43 (vs wild_dodge_table_free: +0.04 ±0.43)	+0.17 ±0.39 (vs wild_dodge_table_free: +0.16 ±0.41)
`E33:baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39

REFUTED — #225 (charging a play for wild moves lengthens games without adding anything). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. game length under the rule (flip-capable Baseline, E49) vs E33. #225 "House rules that restrict wild movement add time to the average game without adding fun" ipe2y75
REFUTED at 2p; inconclusive at 3p, 4p, 5p — #15, #11, #413 (charging a play for flips is right (it removes a real edge)). Per count: 2p REFUTED, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #15 "Most tables treat moving/flipping a wild as costing one of three moves (poll gcloo7) even though official rule…" fdndx1l; #11 "Changing a wild's colour should cost one of your three plays" f5cjwef; #413 "We made wild changes cost a turn and Forced-Dealt wilds keep their colour because constant flipping made DB/Sl…" ltxxlu2
REFUTED — #496, #497 (free flipping weakens the Deal Breaker and strengthens Sly Deal). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. all-dodge tables with flips free vs costing a play: Deal Breakers and steals per game. #496 "Free flipping makes Deal Breaker weaker, Sly Deal stronger, houses/hotels weaker; adds variety" odg7eap; #497 "Deal Breaker is supposed to be strongest (only 2), so free flipping that lets you keep sets apart breaks it" odjgerd
REFUTED — #559 (free movement plus ×4 rents lets one player farm rents). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #559 "Free movement of wilds and buildings plus quadruple rent lets one player charge huge rents every round and kil…" 1ds2drf

E21 — The 2008 reading: Just Say No is free on your own turn (the 2024 rule is now the engine default; this cell tests the opposite switch)

Cell	2p	3p	4p	5p
`rule_jsnfree_baseline`	+0.11 ±0.49	-0.16 ±0.46	+0.23 ±0.43	+0.15 ±0.39
`E33:baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39
`E44:attack_third`	-3.20 ±0.49 (paired -3.34 ±0.31)	-3.87 ±0.45 (paired -3.73 ±0.38)	-4.07 ±0.40 (paired -4.28 ±0.40)	-4.23 ±0.36 (paired -4.42 ±0.38)
`E44:attack_first_db`	+0.15 ±0.49 (paired +0.01 ±0.02)	-0.13 ±0.46 (paired +0.01 ±0.02)	+0.22 ±0.43 (paired +0.02 ±0.03)	+0.20 ±0.39 (paired -0.00 ±0.03)

CONFIRMED — #375 (the 2024 rule (a Just Say No on your own turn costs a play) kills Just Say No wars). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. JSN wars per game under the 2024 default (E33) vs the 2008 reading (this cell). #375 "The new JSN-counts-as-a-card rule is stupid; a JSN war is classic" lflacvz
REFUTED — #285 (the rule created a play-big-action-last meta). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. scored from E44: playing attacks last must beat fair for the claim to hold. #285 "Tried 'JSN consumes a move if you have moves left'; it created a play-big-action-last strategy but was confusi…" jmdwuae

E22 — Double the Rent: always double; x4 stacking rule; JSN cancels only the doubler

Cell	2p	3p	4p	5p
`always_double`	+0.83 ±0.49 (paired +0.69 ±0.12)	+0.78 ±0.46 (paired +0.93 ±0.15)	+1.08 ±0.43 (paired +0.88 ±0.17)	+0.96 ±0.40 (paired +0.76 ±0.15)
`E44:evolved_table`	-0.14 ±0.49	-0.32 ±0.46	-0.02 ±0.42	-0.06 ±0.39
`rule_nostack_baseline`	+0.09 ±0.49	-0.15 ±0.46	+0.20 ±0.43	+0.18 ±0.39
`E33:baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39
`rule_nostack_always_double`	+0.88 ±0.49 (vs rule_nostack_baseline: +0.79 ±0.12)	+0.85 ±0.46 (vs rule_nostack_baseline: +1.00 ±0.15)	+1.17 ±0.43 (vs rule_nostack_baseline: +0.97 ±0.17)	+1.01 ±0.40 (vs rule_nostack_baseline: +0.83 ±0.15)
`rule_jsn_doubler_only_always_double`	+0.97 ±0.49	+1.00 ±0.47	+1.33 ±0.43	+1.10 ±0.40

INCONCLUSIVE — #509 (Double the Rent played right is the most devastating card). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #509 "Double the Rent, played right, is the most devastating card in the game, more than DB: a massive rent cripples…" ojgwoia
REFUTED — #315 (Double the Rent is banked 90 % of the time). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. the folk Baseline never banks a doubler by construction; the all-evolved table (E44) is the informative one. #315 "Double the Rent is played for cash 90% of the time; our house rule makes it a free move to incentivise using i…" kfgyiva
INCONCLUSIVE — #7, #80 (×4 rents are rare and harmless). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #7 "Allow quadruple rent with two Double the Rent cards; rare and not game-breaking" ex5unf9; #80 "Quadruple rent is so rare (both doublers in one hand, played together) it should stay in for the fun" myl99zr
REFUTED — #8, #176, #559 (×4 stacking should be banned). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #8 "Two Double the Rent cards must be played separately, not stacked" etpwzub; #176 "Two doublers quadruple the rent and consume two actions; a JSN cancels only one Double the Rent" i7gozbm; #559 "Free movement of wilds and buildings plus quadruple rent lets one player charge huge rents every round and kil…" 1ds2drf
REFUTED — #25, #26, #303, #304 (a Just Say No on a doubled rent cancels only the doubler (UK reading) — does it matter?). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #25 "JSN against a rent with Double the Rent cancels the whole rent, doubles included (video game)" fmd886g; #26 "JSN against a doubled rent cancels only the Double the Rent; base rent still due" g8rz6zf; #303 "One JSN countering rent+doubler is too powerful; cancelling only the doubler is another way to force the JSN o…" kvtxsv3
CONFIRMED — #78, #190, #194, #152, #188, #453, #510, #472 (giant rents ($30+, up to $60) happen). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #78 "Dark blue full set + house + rent + two Double the Rent took $44M and won the game outright" gh6gv7j; #190 "Blue set + hotel + rent-all + two doublers = $48M took everyone's everything" if167d4; #194 "Two doublers on yellows with a house = $36M from each player, game ender" j6vl65y

E23 — Sets/bank needed to win, plays per turn (house rules), Speed Deal

Cell	2p	3p	4p	5p
`sets4_baseline`	+0.04 ±0.49	-0.13 ±0.46	+0.04 ±0.42	+0.32 ±0.39
`sets4_feature_es`	+14.43 ±0.47 (vs sets4_baseline: +14.39 ±0.50)	+19.88 ±0.49 (vs sets4_baseline: +20.01 ±0.55)	+18.84 ±0.49 (vs sets4_baseline: +18.80 ±0.54)	+18.10 ±0.48 (vs sets4_baseline: +17.78 ±0.53)
`E25:feature_es`	+10.88 ±0.48 (paired +10.74 ±0.48)	+15.57 ±0.49 (paired +15.71 ±0.53)	+14.25 ±0.48 (paired +14.04 ±0.52)	+12.14 ±0.46 (paired +11.95 ±0.49)
`sets5_baseline`	-0.16 ±0.49	+0.11 ±0.46	-0.08 ±0.42	+0.15 ±0.39
`sets4_plays4_baseline`	-0.10 ±0.49	+0.20 ±0.46	+0.22 ±0.43	+0.25 ±0.39
`sets4_bank15_plays4_baseline`	+0.10 ±0.49	+0.52 ±0.46	+0.21 ±0.43	+0.24 ±0.39
`sets3_bank10_baseline`	+0.28 ±0.49	-0.10 ±0.46	+0.20 ±0.43	+0.52 ±0.40
`sets3_bank10_random`	-47.01 ±0.17	-32.45 ±0.09	-24.70 ±0.05	-19.72 ±0.05
`E25:random`	-46.60 ±0.18 (paired -46.74 ±0.51)	-32.30 ±0.10 (paired -32.15 ±0.47)	-24.65 ±0.06 (paired -24.86 ±0.43)	-19.73 ±0.05 (paired -19.93 ±0.40)
`speed_deal_baseline`	+0.38 ±0.49	+0.13 ±0.46	-0.28 ±0.42	+0.15 ±0.39

CONFIRMED — #243, #244, #38, #390, #256, #557 (4–5 sets to win: longer games, Deal Breakers more useful, less luck). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #243 "Play to 4 sets instead of 3; makes Deal Breakers and JSN more useful" iyicuqg; #244 "With 4 sets to win you can't just complete three in one turn; completed sets must sit on the table exposed" iyjtvpy; #38 "2 players: play to 5 sets; 3+ players: play to 4 sets" fwyljhh
REFUTED — #513, #96, #328, #266, #39 (2 players needs 4–5 sets (cuts the first-seat edge)). Per count: 2p REFUTED. #513 "2p: five monopolies to win; wilds/buildings move only at END of turn so you wait a round to capitalise" ok2tqjd; #96 "2-player house rules: no DB (DB becomes Sly Deal), or set owner chooses which set is taken, or 4 sets to win" lfr0fm; #328 "House rules: no DB; Forced Deal can take from completed sets; 4 sets to win" kqs4b1j
REFUTED — #133, #450 (4 plays / 4 sets ($15M bank) house rules). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #133 "'Mega' variant: play up to 4 cards a turn and need 4 sets to win; you empty your hand faster and draw 5 more o…" ppt7tv; #450 "For a longer game: 4 moves per turn, 4 sets to win, minimum $15M bank to win" mjcl7du
CONDITIONAL (2p confirmed, 3p confirmed, 4p refuted, 5p refuted) — #248, #432 (a bank requirement to win adds luck). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p REFUTED, 5p REFUTED. #248 "Win = 3 sets plus $10M in bank, money face down" j1k5cvc; #432 "House rules: $15M minimum bank to win; money face down; at most two of three sets may be 2-card sets" mbbxq1z
CONFIRMED — #236 (Speed Deal (draw 3, five plays) is faster). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #236 "'Speed Deal': start 7, draw 3, five moves (wild flips and banked-action replays count)" yabsy0

E24 — Deck removals: no Deal Breaker, no $10M, no big money (2p), fewer Pass Go, no 2-colour wilds

Cell	2p	3p	4p	5p
`no_db_baseline`	+0.20 ±0.49	+0.16 ±0.46	+0.10 ±0.42	+0.08 ±0.39
`no_db_feature_es`	+16.70 ±0.46 (vs no_db_baseline: +16.49 ±0.52)	+20.74 ±0.49 (vs no_db_baseline: +20.58 ±0.55)	+17.65 ±0.48 (vs no_db_baseline: +17.55 ±0.53)	+14.27 ±0.47 (vs no_db_baseline: +14.19 ±0.49)
`no_db_random`	-45.66 ±0.20 (vs no_db_baseline: -45.87 ±0.52)	-32.55 ±0.09 (vs no_db_baseline: -32.71 ±0.47)	-24.76 ±0.05 (vs no_db_baseline: -24.86 ±0.43)	-19.85 ±0.04 (vs no_db_baseline: -19.93 ±0.39)
`E25:feature_es`	+10.88 ±0.48 (paired +10.74 ±0.48)	+15.57 ±0.49 (paired +15.71 ±0.53)	+14.25 ±0.48 (paired +14.04 ±0.52)	+12.14 ±0.46 (paired +11.95 ±0.49)
`E25:random`	-46.60 ±0.18 (paired -46.74 ±0.51)	-32.30 ±0.10 (paired -32.15 ±0.47)	-24.65 ±0.06 (paired -24.86 ±0.43)	-19.73 ±0.05 (paired -19.93 ±0.40)
`one_db_two_jsn_baseline`	+0.13 ±0.49	+0.13 ±0.46	+0.13 ±0.43	-0.27 ±0.39
`no_ten_baseline`	-0.20 ±0.49	+0.17 ±0.46	+0.33 ±0.43	+0.08 ±0.39
`no_big_money_baseline`	-0.03 ±0.49	+0.02 ±0.46	-0.14 ±0.42	+0.02 ±0.39
`six_pass_go_baseline`	-0.21 ±0.49	+0.07 ±0.46	-0.05 ±0.42	-0.02 ±0.39
`no_two_colour_wilds_baseline`	+0.29 ±0.49	+0.08 ±0.46	+0.04 ±0.42	-0.30 ±0.39

REFUTED at 4p, 5p; inconclusive at 2p, 3p — #3, #355, #0 (without Deal Breakers games run longer). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p REFUTED, 5p REFUTED. #3 "Removing the Deal Breaker cards makes games last longer" b9wkc6; #355 "Deal Breaker is the only real foil to complete-set protection and it improves pacing; without it a round could…" l6k808o; #0 "Deal Breaker feels semi-game-breaking, especially 1v1; one card yields the result of three actions" aeo0fr
CONFIRMED at 3p, 4p, 5p; inconclusive at 2p — #327, #71, #481, #96, #328 (no Deal Breakers = more skill, less luck). Per count: 2p INCONCLUSIVE, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #327 "Removing Deal Breaker in 2-player games gives more strategy and less luck; keep it for 3+" 1asqb5k; #71 "With just 2 players we remove the Deal Breakers since they make it more about luck than strategy" ghniw7b; #481 "1v1 modifiers: no DB (bank it), only one wild allowed, wilds never stolen, opponent picks your over-7 discards" nrtqq4n
REFUTED — #358 (remove one Deal Breaker and one Just Say No at 2p). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #358 "At 2 players remove one DB and one JSN to make them more valuable" l7mooyj
REFUTED — #518 (toss the $10M). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #518 "Toss out the $10M card; it doesn't fit the game" ok4viih
CONFIRMED — #387 (without big money, late rent matters at 2p (more property payments)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #387 "Removing the $4/$5/$10M cash cards makes rent relevant late in 2-player games" liwuiwr
REFUTED — #72 (too many Pass Go cards (six instead of ten lengthens games)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #72 "There are too many Pass Go cards; convert some into custom cards (Property Insurance, Taxman, Free Parking)" gcaqg8l
CONFIRMED — #495 (two-colour wilds are overpowered (removing them lengthens games materially)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #495 "The 2-colour wilds are super overpowered anyway" of4gp2t
CONFIRMED — #558 (a skill-over-luck deck (the no-DB half)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #558 "Skill-over-luck variant: remove DB, Sly Deal, Debt Collector, Pass Go, buildings and rainbow wilds; 9 Forced D…" 1mh1qf9

E25 — Skill vs luck: strong (ES FeaturePolicy) and no-skill (RandomLegal) probes by player count

Cell	2p	3p	4p	5p
`random`	-46.60 ±0.18 (paired -46.74 ±0.51)	-32.30 ±0.10 (paired -32.15 ±0.47)	-24.65 ±0.06 (paired -24.86 ±0.43)	-19.73 ±0.05 (paired -19.93 ±0.40)
`feature_es`	+10.88 ±0.48 (paired +10.74 ±0.48)	+15.57 ±0.49 (paired +15.71 ±0.53)	+14.25 ±0.48 (paired +14.04 ±0.52)	+12.14 ±0.46 (paired +11.95 ±0.49)

REFUTED — #560 (Monopoly Deal is mostly luck). Per count: 4p REFUTED. #560 "Monopoly Deal is mostly luck, not much strategy (r/monopoly)" uyebf3
CONFIRMED — #561, #461 (deep strategy: good players win a high share). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #561 "There is a lot of strategy layered deep in Deal that you only see with more play" ia5zolx; #461 "There is an optimal strategy for every starting hand; adjust by player count; good players win a high share" mxwaujh
CONFIRMED — #60, #62, #389 (more luck with more players (the skill spread shrinks with the count)). Per count: 5p CONFIRMED. spread = feature_es − random, 2p vs 5p (in pp of the count's fair share; note 2p and 5p fair shares differ). #60 "3 players is the most fun; with more players it becomes more about luck (who gets rent cards)" g5vm68y; #62 "2 players not advised" g578ior; #389 "With 2 players it's not that fun" ln4ms58
CONFIRMED — #570, #529 (streaks are common (arithmetic on the seat rates)). Per count: 2p CONFIRMED. arithmetic only: P(8 in a row) for equals at 2p = 2·(1/2)^8 = 0.8 % per 8-game window; a 100-game series contains such a run 31.5 % of the time. #570 "100 games between a couple ended 50-50 with big win streaks (r/boardgames, s=770)" zxhi4q; #529 "Winning streaks seem especially common in Deal even among evenly matched players" oullbfi

E26 — Value of seeing banks: blind (random) targeting

Cell	2p	3p	4p	5p
`blind_target`	—	-4.58 ±0.44 (paired -4.44 ±0.36)	-4.79 ±0.39 (paired -5.00 ±0.37)	-4.03 ±0.36 (paired -4.23 ±0.35)

CONFIRMED — #123, #83, #370, #367 (seeing the banks is essential (blind targeting loses ≥ 1 pp)). Per count: 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #123 "Seeing everyone's bank total is essential when deciding whom to rent so you can strip properties too" hc5vv72; #83 "Stack your bank so only the top card shows (monopolyrules.com); opponents must track what you banked" kpk0wn; #370 "Bank face down makes Debt Collector a gamble (two $1M cards)" les92xo
CONFIRMED — #56 (a visible $10M draws Debt Collectors (blind targeting loses income)). Per count: 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #56 "A visible $10M in the bank encourages opponents to use Debt Collector on you" ghfjnfd

E27 — Table politics: target the leader; being ganged up on

Cell	2p	3p	4p	5p
`target_leader`	—	-0.68 ±0.46 (paired -0.54 ±0.31)	+0.09 ±0.42 (paired -0.12 ±0.33)	+0.17 ±0.39 (paired -0.03 ±0.30)
`E49:target_leader`	—	—	+0.02 ±0.27 (paired -0.12 ±0.33)	-0.00 ±0.25 (paired -0.03 ±0.30)
`aggro_vs_gangup`	—	-1.17 ±0.46 (vs baseline_vs_gangup: -1.45 ±0.50)	-3.15 ±0.40 (vs baseline_vs_gangup: -3.45 ±0.46)	-3.18 ±0.37 (vs baseline_vs_gangup: -3.51 ±0.41)
`E04:aggro`	+0.80 ±0.49 (vs control: +0.67 ±0.48)	-1.63 ±0.46 (vs control: -1.49 ±0.48)	-3.67 ±0.40 (vs control: -3.88 ±0.43)	-3.68 ±0.36 (vs control: -3.88 ±0.39)
`feature_es_vs_gangup`	—	+16.48 ±0.49 (vs baseline_vs_gangup: +16.20 ±0.54)	+15.57 ±0.48 (vs baseline_vs_gangup: +15.27 ±0.54)	+12.96 ±0.46 (vs baseline_vs_gangup: +12.63 ±0.51)
`E25:feature_es`	+10.88 ±0.48 (paired +10.74 ±0.48)	+15.57 ±0.49 (paired +15.71 ±0.53)	+14.25 ±0.48 (paired +14.04 ±0.52)	+12.14 ±0.46 (paired +11.95 ±0.49)

REFUTED — #553, #44 (dismantle whoever can win (target the leader)). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #553 "If any opponent can pull a victory, notify the other players and dismantle one piece of their move" rw0kt; #44 "Working together isn't cheating but explicit collusion goes against the spirit of the game" fx236nv
REFUTED — #458, #457 (an early leader gets ganged up on and loses). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #458 "With more than two players, an early leader incentivises everyone to gang up on them" mxvvlhb; #457 "The player who jumps out early building an empire often loses; it's a marathon, and an early lead makes everyo…" mxvvlhb
REFUTED — #193, #343, #425 (the strongest player gets targeted and cannot build). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #193 "Friends gang up on the player who taught them and used to always win" ihrrasr; #343 "A consistently winning player gets targeted by the other two at 3p and can't build a bank" m8kg8g5; #425 "When targeted at 3p it boils down to luck of the draw and building a solid bank" m8znbl4

E28 — The $10M: hold it vs bank it at once

Cell	2p	3p	4p	5p
`hold_ten`	-0.48 ±0.49 (paired -0.62 ±0.10)	-0.61 ±0.46 (paired -0.46 ±0.10)	-0.07 ±0.42 (paired -0.27 ±0.09)	+0.07 ±0.39 (paired -0.13 ±0.07)
`bank_ten_now`	+0.50 ±0.49 (paired +0.36 ±0.11)	+0.16 ±0.46 (paired +0.30 ±0.13)	+0.34 ±0.43 (paired +0.13 ±0.14)	+0.29 ±0.39 (paired +0.09 ±0.13)

REFUTED — #55 (an early $10M is a curse: hold it). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #55 "A $10M card early is more a curse than protection" g0ycdag
CONFIRMED — #54 (bank the $10M at once). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #54 "House rule: $10M must be banked as soon as drawn; wards off early Debt Collector power" i6t52t

E29 — Colour priority: 2-card sets first vs high-rent colours first

Cell	2p	3p	4p	5p
`colour_two_card`	-0.19 ±0.49 (paired -0.33 ±0.28)	-0.30 ±0.46 (paired -0.16 ±0.33)	+0.29 ±0.43 (paired +0.09 ±0.33)	+0.41 ±0.39 (paired +0.21 ±0.31)
`colour_high_rent`	-0.80 ±0.49 (paired -0.93 ±0.27)	-1.36 ±0.46 (paired -1.22 ±0.32)	-0.78 ±0.42 (paired -0.99 ±0.32)	-0.67 ±0.39 (paired -0.86 ±0.30)

CONFIRMED at 5p; inconclusive at 2p, 3p, 4p — #132, #198, #79, #666 (two-card sets are the easiest win: go for them first). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p CONFIRMED. #132 "You can win with three 2-card sets; easiest win is dark blue, brown and utilities" hd1sd8j; #198 "The only way to lay 3 full sets in two rounds is if all are 2-card sets (utility, dark blue, brown)" ik9uch9; #79 "Dark blue is the only set you can lay in full and charge rent on in the same turn (2-card set)" hr6ggmr
REFUTED — #267, #185, #153 (dark blue is the key colour (high-rent colours first)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #267 "Winning is all about dark blue: never play a dark blue without making the set, and hold until you also have a …" ja4xjgq; #185 "'Full set drop': lay the whole dark blue set plus rent in one turn for an easy $8M before anyone can react" vg9tq4; #153 "Signature move: lay the whole dark blue set and rent it in one turn, early, to build a foundation even if you …" hxiz4bb

E30 — Hold-in-hand strategies: pairs & rainbow wilds, all wilds, until rent, everything

Cell	2p	3p	4p	5p
`hold_pairs`	-0.50 ±0.49 (paired -0.64 ±0.32)	-0.64 ±0.46 (paired -0.50 ±0.35)	+0.29 ±0.43 (paired +0.08 ±0.33)	+0.68 ±0.40 (paired +0.48 ±0.29)
`hold_wilds`	-2.98 ±0.49 (paired -3.12 ±0.39)	-3.37 ±0.45 (paired -3.22 ±0.40)	-1.92 ±0.41 (paired -2.13 ±0.37)	-0.91 ±0.39 (paired -1.10 ±0.33)
`hold_until_rent`	-22.98 ±0.44 (paired -23.12 ±0.47)	-17.12 ±0.36 (paired -16.97 ±0.44)	-9.48 ±0.35 (paired -9.69 ±0.41)	-4.27 ±0.36 (paired -4.47 ±0.37)
`hold_all`	-44.76 ±0.22 (paired -44.90 ±0.50)	-27.06 ±0.24 (paired -26.91 ±0.46)	-18.39 ±0.24 (paired -18.59 ±0.43)	-12.54 ±0.26 (paired -12.74 ±0.40)

CONDITIONAL (2p refuted, 3p refuted, 4p inconclusive, 5p confirmed) — #551, #267, #494, #565, #493 (do not expose pairs or rainbow wilds). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p CONFIRMED. #551 "2-card sets are always dangerous; avoid laying pieces of them without good reason; same for rainbow wilds" rw0kt; #267 "Winning is all about dark blue: never play a dark blue without making the set, and hold until you also have a …" ja4xjgq; #494 "Big strategy: never put rainbow wilds down unless completing a set so they can't be stolen" nx447ze
REFUTED — #131, #214 (hold every wild until it completes a set). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #131 "Dad never puts down even the rainbow wilds until he can make three sets in one turn" hetiec3; #214 "Even with flips banned, avoiding DBs is easy: don't lay wilds that could complete sets until you can lay the 3…" ijektg3
REFUTED — #150, #185, #462 (lay property only with the rent card in hand). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #150 "Hold property in hand and play it together with a rent card" hj908a8; #185 "'Full set drop': lay the whole dark blue set plus rent in one turn for an easy $8M before anyone can react" vg9tq4; #462 "Build your cash moat first, then play non-wild properties, keep valuable properties and wilds in hand until yo…" mxwgo1q
CONFIRMED — #454 (pure holding (everything for a one-turn win) is too slim to win). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #454 "A property-holding strategy could win in two rounds but dark blue and brown get stolen too fast and it's too s…" mszkgkd
CONDITIONAL (2p refuted, 3p refuted, 4p inconclusive, 5p confirmed) — #219 (avoid obvious Sly Deal targets (hold pairs; steal counts)). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p CONFIRMED. #219 "Avoid Sly Deals by playing properties deliberately so there are no obvious targets" il56w24

E31 — Rent-card and building retention

Cell	2p	3p	4p	5p
`never_bank_rent`	+0.14 ±0.49 (paired +0.00 ±0.12)	+0.00 ±0.46 (paired +0.14 ±0.12)	+0.84 ±0.43 (paired +0.63 ±0.12)	+0.81 ±0.40 (paired +0.61 ±0.11)
`bank_dead_rent`	-0.42 ±0.49 (paired -0.56 ±0.18)	-1.48 ±0.46 (paired -1.34 ±0.21)	-1.96 ±0.41 (paired -2.16 ±0.21)	-2.26 ±0.37 (paired -2.46 ±0.19)
`rule_nobankrent_all`	+0.01 ±0.49	-0.22 ±0.46	+0.35 ±0.43	+0.28 ±0.39
`build_only_safe`	-0.39 ±0.49 (paired -0.53 ±0.14)	-0.42 ±0.46 (paired -0.28 ±0.14)	+0.13 ±0.43 (paired -0.07 ±0.13)	+0.23 ±0.39 (paired +0.03 ±0.11)
`E49:build_only_safe`	-0.32 ±0.31 (paired -0.53 ±0.14)	-0.17 ±0.29 (paired -0.28 ±0.14)	+0.05 ±0.27 (paired -0.07 ±0.13)	+0.15 ±0.25 (paired +0.03 ±0.11)

CONFIRMED at 4p, 5p; inconclusive at 2p, 3p — #546, #29 (never bank a two-colour rent card at 4–5 players). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p CONFIRMED, 5p CONFIRMED. #546 "Never turn a 2-colour rent card into money at 4/5 players; a good 2-colour rent brings a nest egg almost every…" rw0kt; #29 "The game is fine as printed; players who never get to charge rent are holding the wrong cards or playing subop…" fwvczwy
CONFIRMED — #317 (rent is weak at 2p and dominant at 4+ (the never-bank-rent edge grows with the count)). Per count: 5p CONFIRMED. #317 "Rent is weak in 2-player (you get rented less per cycle), balanced at 3, and at 4+ one or two players dominate…" kgnw6fo
CONDITIONAL (2p confirmed, 3p refuted, 4p refuted, 5p refuted) — #42 (a no-banking-rent house rule gives rent cards purpose (more rents per game)). Per count: 2p CONFIRMED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #42 "It's too easy to build an unburnable bank; house rule 'no banking rent cards' gives rent cards purpose" gbg0av8
INCONCLUSIVE — #547, #112 (bank buildings unless the set is safe). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #547 "Bank houses and hotels unless you KNOW you'll use them in the next turn or two; bonus rent rarely worth losing…" rw0kt; #112 "Houses/hotels are extremely niche with a physical deck; only used when you're certain you can't be Deal Broken" oxlqgt

E32 — The winning turn: rent first then win; farm rent instead of winning

Cell	2p	3p	4p	5p
`farm_rent_1`	+0.04 ±0.49 (paired -0.10 ±0.04)	-0.23 ±0.46 (paired -0.09 ±0.04)	+0.08 ±0.42 (paired -0.12 ±0.04)	+0.10 ±0.39 (paired -0.10 ±0.05)
`rent_then_win`	+0.06 ±0.49 (paired -0.08 ±0.04)	-0.17 ±0.46 (paired -0.03 ±0.03)	+0.16 ±0.43 (paired -0.04 ±0.02)	+0.20 ±0.39 (paired +0.00 ±0.02)

INCONCLUSIVE — #179 (farming rent instead of winning is bad play (and renting first on the winning turn is free)). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #179 "Players who have the win but break up monopolies to keep charging rent and drag the game out are annoying" i9vejy6

E33 — Descriptive statistics of folk-Baseline play (all seats Baseline, instrumented)

Cell	2p	3p	4p	5p
`baseline_stats`	+0.14 ±0.49	-0.14 ±0.46	+0.20 ±0.43	+0.20 ±0.39

CONDITIONAL (2p confirmed, 3p inconclusive, 4p refuted, 5p refuted) — #198, #199 (three-turn wins are once-in-thousands). Per count: 2p CONFIRMED, 3p INCONCLUSIVE, 4p REFUTED, 5p REFUTED. share of games won within 3 rounds. #198 "The only way to lay 3 full sets in two rounds is if all are 2-card sets (utility, dark blue, brown)" ik9uch9; #199 "Fastest win in thousands of games was 3 turns, once; plans get foiled by rent/steals" ika5hl6
CONFIRMED — #234 (winning with 4 sets is common, 5 needs a combo). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. mean full sets at the win. #234 "Winning with 4 sets is common because the last cards arrive together; 5 sets needs Forced Deal + DB + completi…" y9j81e
CONFIRMED — #562, #254, #696 (someone's big move hands the next player the win). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. share of wins that use a received card. #562 "The ending is underwhelming: someone plays a huge damaging move and the next player simply wins" wtcb9b; #254 "Cleaning a player out only wins late when huge building rents hand you enough properties for 3 sets" jfeih17; #696 "Make your opponent work for you: let them complete the blue set and add a house and hotel, then Deal Breaker t…" wizzley
CONFIRMED — #189 (comebacks from two sets behind happen). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #189 "Games are swingy with comeback mechanics; forfeiting is bad manners because two draws could be two Deal Breake…" id0zqd1
REFUTED — #555, #470, #257, #30 (Deal Breakers are rarely played successfully / get banked). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. folk Deal Breaker success rate (Baseline never banks one). #555 "Once players know the basics, Deal Breakers are rarely played successfully" rw0kt; #470 "When nobody ever leaves a full set out, all the Deal Breakers end up banked, until the Forced Deal + Deal Brea…" n1uwn48; #257 "The 3-set rule can make Deal Breakers useless since you can complete all three in one turn" j2149qb
CONFIRMED — #31 (two Deal Breakers plus an own set wins at once). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. arithmetic: P(both Deal Breakers in one five-card hand) = 20/(106·105) ≈ 0.18 %. #31 "DB is too powerful: two DBs plus one own set wins in one go; group removed them" frf9uq4
CONFIRMED — #315, #80, #510, #152, #709, #710, #711 (Double the Rent usage, ×4 rents, maximum rents). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. descriptive: x4 rents per game, rent ≥ $30 share, max rent. #315 "Double the Rent is played for cash 90% of the time; our house rule makes it a free move to incentivise using i…" kfgyiva; #80 "Quadruple rent is so rare (both doublers in one hand, played together) it should stay in for the fun" myl99zr; #510 "Highest possible single rent is $60M: dark blue set + house + hotel = $15M, doubled twice" ojm5m3z
CONFIRMED — #375, #19 (Just Say No wars). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. descriptive: wars per game under the 2024 default. #375 "The new JSN-counts-as-a-card rule is stupid; a JSN war is classic" lflacvz; #19 "JSN can be played on top of a JSN (allowed; not always best use)" fh4bytb
CONFIRMED — #418, #500, #501, #159, #181, #212 (starting-hand composition decides a lot). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. win rate by starting-hand class. #418 "A starting hand of many properties is terrible since you can't get them all down without some being taken" lynj21s; #500 "A starting hand of 2 DB, 2 JSN and a Sly Deal is 1 in 11.2 million and most would hate it; the holder won quic…" og0k80u; #501 "I'd rather be dealt money and rent cards than DBs and JSNs" og1fdlz
CONFIRMED — #459 (early money snowballs). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. win rate of the early-money leader vs fair. #459 "White paper: early Birthday/matching rent snowballs into a lasting money moat; 3 cards/turn prevents building …" 1lbtqek
CONFIRMED — #318 (at 2 players banks get so big that rent is useless). Per count: 2p CONFIRMED. property payments per game, 2p vs 4p. #318 "After 5-6 turns at 2p, banks are so large that rent/birthday cards feel useless" 18zs4uj
REFUTED — #0 (the Deal Breaker is game-breaking at 2p). Per count: 2p REFUTED. share of wins whose sets include a Deal-Broken set, 2p vs 4p. #0 "Deal Breaker feels semi-game-breaking, especially 1v1; one card yields the result of three actions" aeo0fr

E34 — Pass Go as money: bank it to empty the hand, bank it when last, Pass-Go-only turns

Cell	2p	3p	4p	5p
`passgo_bank_to_empty`	-0.45 ±0.49 (paired -0.59 ±0.13)	-0.74 ±0.46 (paired -0.60 ±0.13)	-0.34 ±0.42 (paired -0.55 ±0.11)	-0.07 ±0.39 (paired -0.27 ±0.09)
`passgo_bank_if_last`	+0.08 ±0.49 (vs passgo_play_if_last: -0.02 ±0.05)	-0.20 ±0.46 (vs passgo_play_if_last: +0.01 ±0.06)	+0.14 ±0.43 (vs passgo_play_if_last: +0.04 ±0.05)	+0.15 ±0.39 (vs passgo_play_if_last: +0.03 ±0.04)
`E49:passgo_bank_if_last`	+0.24 ±0.31 (vs passgo_play_if_last: +0.02 ±0.03)	+0.04 ±0.29 (vs passgo_play_if_last: +0.00 ±0.04)	+0.04 ±0.27 (vs passgo_play_if_last: +0.04 ±0.03)	+0.04 ±0.25 (vs passgo_play_if_last: +0.03 ±0.03)
`E49:passgo_play_if_last`	+0.21 ±0.31	+0.04 ±0.29	+0.01 ±0.27	+0.01 ±0.25
`passgo_only_turn`	-4.02 ±0.49 (paired -4.16 ±0.32)	-1.74 ±0.46 (paired -1.60 ±0.35)	-1.43 ±0.42 (paired -1.63 ±0.34)	-0.69 ±0.39 (paired -0.89 ±0.32)

REFUTED at 3p; inconclusive at 2p, 4p, 5p — #670, #671 (bank the Pass Go when nearly out of cards). Per count: 2p INCONCLUSIVE, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #670 "Don't give in to the Pass Go lottery: when nearly out of cards, bank the Pass Go (for small charges) instead o…" mds-future; #671 "Arithmetic: if you would otherwise empty your hand, playing a Pass Go yields 2.8 cards per turn versus 3.0 wit…" se-9504
INCONCLUSIVE — #672 (play Pass Go unless it is your last card and last action). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. whole-cell delta, and the conditional win rate after the trigger vs the matched control (E49). #672 "Tempo beats card count: play Pass Go as an action unless it is the last card in hand and the last action of th…" se-9504
REFUTED — #707 (Pass Go turns are Pass-Go-only). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #707 "If you are going to play a Pass Go you won't commit anything else that turn, so play multiple Pass Gos togethe…" bgg-548087

E35 — Actions as money: bank House/Hotel/rent early, bank the wild rent under $3, never bank actions, $10 floor, $10M after a buffer

Cell	2p	3p	4p	5p
`bank_actions_early`	-0.77 ±0.49 (paired -0.91 ±0.28)	-1.64 ±0.46 (paired -1.50 ±0.28)	-2.17 ±0.41 (paired -2.38 ±0.25)	-2.15 ±0.38 (paired -2.35 ±0.22)
`bank_wild_rent_lt3`	-0.71 ±0.49 (paired -0.85 ±0.13)	-0.61 ±0.46 (paired -0.47 ±0.13)	-0.34 ±0.42 (paired -0.55 ±0.12)	-0.05 ±0.39 (paired -0.25 ±0.11)
`never_bank_actions`	+0.21 ±0.49 (paired +0.07 ±0.07)	-0.10 ±0.46 (paired +0.04 ±0.05)	+0.35 ±0.43 (paired +0.15 ±0.05)	+0.30 ±0.39 (paired +0.10 ±0.04)
`bank_floor_10`	-11.55 ±0.48 (paired -11.69 ±0.46)	-12.94 ±0.39 (paired -12.80 ±0.48)	-11.89 ±0.33 (paired -12.10 ±0.44)	-8.89 ±0.31 (paired -9.09 ±0.41)
`E13:bank_floor_8`	-7.75 ±0.48 (paired -7.89 ±0.45)	-9.77 ±0.42 (paired -9.62 ±0.48)	-10.24 ±0.35 (paired -10.44 ±0.44)	-7.94 ±0.32 (paired -8.14 ±0.41)
`bank_ten_after_buffer_6`	-0.20 ±0.49 (paired -0.34 ±0.08)	-0.35 ±0.46 (paired -0.21 ±0.08)	+0.07 ±0.42 (paired -0.13 ±0.08)	+0.13 ±0.39 (paired -0.07 ±0.06)
`E28:bank_ten_now`	+0.50 ±0.49 (paired +0.36 ±0.11)	+0.16 ±0.46 (paired +0.30 ±0.13)	+0.34 ±0.43 (paired +0.13 ±0.14)	+0.29 ±0.39 (paired +0.09 ±0.13)
`E28:hold_ten`	-0.48 ±0.49 (paired -0.62 ±0.10)	-0.61 ±0.46 (paired -0.46 ±0.10)	-0.07 ±0.42 (paired -0.27 ±0.09)	+0.07 ±0.39 (paired -0.13 ±0.07)

REFUTED — #668 (bank rent / House / Hotel / Forced Deal early). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #668 "Sometimes an action card is worth more in the bank than in hand: early on, play Rent, House, Hotel and (rarely…" mds-future
REFUTED at 2p, 3p; inconclusive at 4p, 5p — #669 (the any-colour rent is $3M in the bank unless it collects ≥ $3M). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #669 "A wild (any-colour) Rent card is worth $3M in the bank; if no set you own would collect at least $3M, or the t…" mds-future
INCONCLUSIVE — #700 (never play an action as money unless broke). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #700 "Playing any action card as money is a bad idea except when you have run out of money; the two cards a Pass Go …" se-9504
REFUTED — #697 (bank $10M before chasing sets). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #697 "Cash is king early: aim for at least $10M in the bank by mid-game as a safety net before chasing sets" playpartygame
REFUTED — #714 (hold the $10M until a $6M small-bill buffer). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #714 "Don't play the $10M until you have a buffer of at least $6M in small bills (2+2+2, better 2+2+1+1, ideally 5+2…" bgg-548087

E36 — Opening at 3-4 players: big bills only, small bills under the five, pass unless holding an attack

Cell	2p	3p	4p	5p
`open_big_only`	-9.35 ±0.48 (paired -9.48 ±0.53)	-3.46 ±0.45 (paired -3.32 ±0.56)	-3.45 ±0.40 (paired -3.66 ±0.53)	-2.40 ±0.37 (paired -2.60 ±0.50)
`E14:low_profile_2t_cap2`	-5.30 ±0.49 (paired -5.44 ±0.40)	-2.31 ±0.45 (paired -2.16 ±0.47)	-1.87 ±0.41 (paired -2.07 ±0.45)	-1.03 ±0.38 (paired -1.23 ±0.42)
`open_small_under_five`	-4.37 ±0.49 (paired -4.50 ±0.42)	-2.89 ±0.45 (paired -2.75 ±0.47)	-4.06 ±0.40 (paired -4.27 ±0.46)	-4.06 ±0.36 (paired -4.26 ±0.42)
`pass_first_unless_attack`	-1.45 ±0.49 (paired -1.59 ±0.23)	-0.24 ±0.46 (paired -0.10 ±0.25)	+0.22 ±0.43 (paired +0.02 ±0.23)	+0.26 ±0.39 (paired +0.06 ±0.21)
`E14:pass_first_1`	-6.66 ±0.49 (paired -6.80 ±0.47)	-0.59 ±0.46 (paired -0.45 ±0.53)	+1.04 ±0.43 (paired +0.83 ±0.51)	+2.35 ±0.41 (paired +2.15 ±0.49)

REFUTED — #704 (2+5+5 is the perfect opener (big bills only)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #704 "The perfect opening set is $2M+$5M+$5M (only three Birthdays, two Birthdays + a Debt Collector, or two DCs + a…" bgg-548087
REFUTED — #705 (keep the small bills under the five). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #705 "In 2-player the best opener is $1M+$2M+$5M (only three Birthdays, two Debt Collectors or DC + dark-blue rent w…" bgg-548087
REFUTED at 2p, 4p, 5p; inconclusive at 3p — #706 (don't play three cards in the opening round unless holding attacks). Per count: 2p REFUTED, 3p INCONCLUSIVE, 4p REFUTED, 5p REFUTED. #706 "In a 3- or 4-player game don't play all three cards in the opening round unless you hold attack cards (rents, …" bgg-548087

E37 — Deal Breaker timing: only to win, after the other DB, with a JSN, on empty hands, after their JSN, bank it to refill, bait the set

Cell	2p	3p	4p	5p
`db_only_to_win`	-7.83 ±0.48 (paired -7.97 ±0.28)	-6.12 ±0.44 (paired -5.97 ±0.30)	-3.59 ±0.40 (paired -3.79 ±0.28)	-2.74 ±0.37 (paired -2.94 ±0.26)
`db_after_other_db`	-4.59 ±0.49 (paired -4.72 ±0.23)	-2.32 ±0.45 (paired -2.18 ±0.25)	-0.06 ±0.42 (paired -0.27 ±0.24)	+0.03 ±0.39 (paired -0.17 ±0.22)
`db_with_jsn_backup`	-4.12 ±0.49 (paired -4.25 ±0.23)	-3.18 ±0.45 (paired -3.03 ±0.25)	-1.48 ±0.42 (paired -1.69 ±0.24)	-1.18 ±0.38 (paired -1.38 ±0.22)
`db_prefer_empty_hand`	-7.24 ±0.48 (paired -7.38 ±0.28)	-5.21 ±0.44 (paired -5.07 ±0.29)	-2.64 ±0.41 (paired -2.85 ±0.28)	-2.04 ±0.38 (paired -2.23 ±0.26)
`db_wait_jsn_spent`	-5.95 ±0.49 (paired -6.09 ±0.26)	-4.22 ±0.45 (paired -4.08 ±0.28)	-1.79 ±0.41 (paired -1.99 ±0.27)	-1.27 ±0.38 (paired -1.47 ±0.25)
`bank_db_to_refill`	+0.10 ±0.49 (paired -0.04 ±0.04)	-0.16 ±0.46 (paired -0.01 ±0.02)	+0.18 ±0.43 (paired -0.03 ±0.02)	+0.19 ±0.39 (paired -0.01 ±0.01)
`bait_lay_for_db`	+0.15 ±0.49 (paired +0.01 ±0.03)	-0.13 ±0.46 (paired +0.01 ±0.04)	+0.18 ±0.43 (paired -0.03 ±0.05)	+0.20 ±0.39 (paired -0.00 ±0.04)

REFUTED at 2p, 3p; inconclusive at 4p, 5p — #693 (hold the Deal Breaker for the winning moment / until the other one is gone). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #693 "Be patient with the Deal Breaker: hold it for a game-winning moment (playing it early invites counterplay and …" byp
REFUTED — #694 (Deal Breaker only with a Just Say No in hand). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #694 "Wait to play a Deal Breaker until you also hold a Just Say No for reinforcement" medium-zhang
REFUTED — #681 (Deal Breaker the empty-handed). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #681 "Play a Deal Breaker when it can't be defended: prefer opponents with no cards in hand (no JSN possible), which…" mds-dealbreaker
REFUTED — #688 (wait for another opponent to draw their Just Say No out). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #688 "Don't charge in with a Deal Breaker in a multiplayer game: wait for another opponent to force the target's JSN…" mds-weakness
CONFIRMED — #680 (bank the Deal Breaker to refill the hand). Per count: 2p CONFIRMED, 3p NOT TESTED, 4p NOT TESTED, 5p NOT TESTED. conditional win rate after banking a Deal Breaker (rare trigger); E49's solved positions put the per-decision cost at −16 pp. #680 "A Deal Breaker can be worth more as $5M bank: when it is one of at most three cards left, you can't win with t…" mds-dealbreaker
REFUTED — #679 (bait them into completing a set, then Deal Breaker it). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #679 "Bait them into completing a set: holding a Deal Breaker and the card an opponent needs, lay it so they Sly/For…" mds-dealbreaker

E38 — Steal targeting: 2-card colours first, take the wild, steal whenever legal (2p offence), steal for rent

Cell	2p	3p	4p	5p
`steal_two_card_first`	+0.17 ±0.49 (paired +0.03 ±0.28)	-1.02 ±0.46 (paired -0.87 ±0.32)	-0.62 ±0.42 (paired -0.82 ±0.31)	-0.25 ±0.39 (paired -0.45 ±0.28)
`steal_prefer_wild`	+0.15 ±0.49 (paired +0.01 ±0.04)	-0.13 ±0.46 (paired +0.01 ±0.03)	+0.22 ±0.43 (paired +0.01 ±0.03)	+0.21 ±0.39 (paired +0.01 ±0.02)
`E49:steal_prefer_wild`	—	+0.12 ±0.29 (paired +0.01 ±0.03)	+0.10 ±0.27 (paired +0.01 ±0.03)	+0.11 ±0.25 (paired +0.01 ±0.02)
`steal_always`	-1.21 ±0.49 (paired -1.35 ±0.34)	-2.57 ±0.45 (paired -2.43 ±0.35)	-1.66 ±0.41 (paired -1.86 ±0.33)	-0.90 ±0.39 (paired -1.09 ±0.30)
`steal_always_charge_now`	-3.43 ±0.49 (paired -3.56 ±0.44)	-4.62 ±0.44 (paired -4.47 ±0.46)	-5.12 ±0.39 (paired -5.32 ±0.42)	-3.93 ±0.36 (paired -4.12 ±0.38)
`steal_for_rent`	+0.63 ±0.49 (paired +0.49 ±0.14)	+0.08 ±0.46 (paired +0.23 ±0.21)	+0.75 ±0.43 (paired +0.55 ±0.27)	+0.94 ±0.40 (paired +0.74 ±0.26)

REFUTED at 3p, 4p; inconclusive at 2p, 5p — #682 (steal two-card-set pieces first). Per count: 2p INCONCLUSIVE, 3p REFUTED, 4p REFUTED, 5p INCONCLUSIVE. #682 "Being smart about being Sly: unless the steal completes one of your own sets, use Sly/Forced Deal to take a ca…" mds-sly
INCONCLUSIVE — #683 (take the wild, not the solid card). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. whole-cell; E49's 21,000 solved positions: +4.5 / +3.3 pp per decision, 0.03 decisions per game. #683 "Two blue properties aren't the same: when the target has several cards of the colour you want, take the wild c…" mds-sly
REFUTED — #684 (at 2 players use every rent and Sly Deal at once (offence is king)). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #684 "Two-player: offence is king; in the first rounds use every Rent and Sly Deal immediately to keep the opponent …" mds-duoplayer
CONFIRMED at 5p; inconclusive at 2p, 3p, 4p — #99 (Sly Deal the dark blues, then rent them (steal for rent)). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p CONFIRMED. #99 "Classic move: steal the dark blues then charge $8M rent on them with the third card" gvz7kh8

E39 — Charge targeting and payment: overpay, bank-poor, most cards, JSN spent, next seat; pay fewest cards

Cell	2p	3p	4p	5p
`target_overpay`	—	-0.69 ±0.46 (paired -0.55 ±0.18)	-0.51 ±0.42 (paired -0.71 ±0.21)	-0.43 ±0.39 (paired -0.63 ±0.21)
`target_bank_poor`	—	+2.14 ±0.47 (paired +2.29 ±0.26)	+2.76 ±0.44 (paired +2.56 ±0.28)	+2.50 ±0.41 (paired +2.30 ±0.27)
`debt_target_most_cards`	—	-0.62 ±0.46 (paired -0.47 ±0.11)	-0.28 ±0.42 (paired -0.48 ±0.12)	-0.23 ±0.39 (paired -0.43 ±0.12)
`target_jsn_spent`	—	-1.51 ±0.46 (paired -1.36 ±0.19)	-1.26 ±0.42 (paired -1.47 ±0.21)	-1.06 ±0.38 (paired -1.26 ±0.21)
`target_next_seat`	—	-2.41 ±0.45 (paired -2.27 ±0.32)	-1.69 ±0.41 (paired -1.89 ±0.32)	-1.03 ±0.38 (paired -1.23 ±0.28)
`pay_fewest_cards`	+0.68 ±0.49 (paired +0.55 ±0.09)	+0.44 ±0.46 (paired +0.59 ±0.13)	+1.20 ±0.43 (paired +0.99 ±0.16)	+0.78 ±0.40 (paired +0.58 ±0.15)

REFUTED — #675 (charge whoever must overpay). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #675 "Exploit the no-change rule when choosing whom to charge: pick the opponent whose bills are larger than the cha…" mds-money
CONFIRMED — #690 (Debt Collect the bank-poor and property-rich). Per count: 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #690 "Debt Collect the bank-poor and property-rich: aim Debt Collector and the wild Rent at the player with properti…" mds-weakness
REFUTED — #691 (aim the Debt Collector at many small bills). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #691 "Prioritise cards over value early: aim Debt Collector at the player with many $1/$2 bills to collect several c…" byp
REFUTED — #689 (go after whoever has spent a Just Say No). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #689 "Wait for the JSN to go: assume each opponent holds at most one JSN; a player who has already played one this r…" mds-weakness
REFUTED — #708 (the next seat is weakest when you act). Per count: 3p REFUTED, 4p REFUTED, 5p REFUTED. #708 "You are weakest against the player who plays just before you (your buffer is lowest after the others have hit …" bgg-548087
CONDITIONAL (2p inconclusive, 3p refuted, 4p confirmed, 5p inconclusive) — #695 (pay with as few cards as possible). Per count: 2p INCONCLUSIVE, 3p REFUTED, 4p CONFIRMED, 5p INCONCLUSIVE. #695 "When paying, give as few cards as possible: owe $7 with 1,1,2,2,2,3,4 -> pay 4+3, keeping more cards for later" instructables

E40 — What to lay and hold: railroads, cheap cushion first, wilds until the steals are gone, dead colours

Cell	2p	3p	4p	5p
`hold_railroads`	+0.09 ±0.49 (paired -0.05 ±0.08)	-0.25 ±0.46 (paired -0.10 ±0.09)	+0.06 ±0.42 (paired -0.14 ±0.09)	+0.11 ±0.39 (paired -0.09 ±0.08)
`lay_cheap_first`	-1.10 ±0.49 (paired -1.23 ±0.36)	-0.73 ±0.46 (paired -0.58 ±0.43)	-0.31 ±0.42 (paired -0.52 ±0.42)	-0.38 ±0.39 (paired -0.57 ±0.39)
`hold_wilds_until_steals_gone`	-2.91 ±0.49 (paired -3.04 ±0.39)	-3.03 ±0.45 (paired -2.89 ±0.40)	-1.54 ±0.42 (paired -1.75 ±0.37)	-0.68 ±0.39 (paired -0.88 ±0.33)
`E30:hold_wilds`	-2.98 ±0.49 (paired -3.12 ±0.39)	-3.37 ±0.45 (paired -3.22 ±0.40)	-1.92 ±0.41 (paired -2.13 ±0.37)	-0.91 ±0.39 (paired -1.10 ±0.33)
`discard_dead_colours`	+0.14 ±0.49 (paired +0.00 ±0.00)	-0.14 ±0.46 (paired +0.00 ±0.01)	+0.21 ±0.43 (paired +0.01 ±0.01)	+0.21 ±0.39 (paired +0.01 ±0.01)

CONFIRMED at 2p, 4p, 5p; inconclusive at 3p — #667 (keep railroads in hand and get paid into the set). Per count: 2p CONFIRMED, 3p INCONCLUSIVE, 4p CONFIRMED, 5p CONFIRMED. #667 "The Railroad business: with two railroads in hand and railroads on opponents' tables, keep yours in hand; oppo…" mds-future
REFUTED at 2p, 3p; inconclusive at 4p, 5p — #676 (show your worst property first). Per count: 2p REFUTED, 3p REFUTED, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #676 "Show your worst first: lay the least valuable properties (railroads, $1M properties) early as an undesirable c…" mds-protection
INCONCLUSIVE — #677 (lay wilds freely once the six steal cards are gone). Per count: 2p INCONCLUSIVE, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #677 "Once all six Sly Deal and Forced Deal cards have been played, lone multicolour wilds (which rent can't take) a…" mds-protection
REFUTED — #687 (discard colours you can no longer complete). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. #687 "Know the numbers: with only 3 browns, if an opponent shows two in a full brown set, the third in your hand is …" mds-memory

E41 — The winning turn: steal first vs opponents who JSN the winning play

Cell	2p	3p	4p	5p
`win_steal_first_vs_jsn_block_win`	-0.52 ±0.49 (vs baseline_vs_jsn_block_win: +0.31 ±0.05)	-0.34 ±0.46 (vs baseline_vs_jsn_block_win: +0.36 ±0.06)	+0.24 ±0.43 (vs baseline_vs_jsn_block_win: +0.30 ±0.06)	+0.22 ±0.39 (vs baseline_vs_jsn_block_win: +0.21 ±0.05)
`baseline_vs_jsn_block_win`	-0.83 ±0.49	-0.70 ±0.46	-0.07 ±0.42	+0.01 ±0.39
`win_steal_first`	+0.32 ±0.49 (paired +0.19 ±0.04)	+0.11 ±0.46 (paired +0.26 ±0.05)	+0.40 ±0.43 (paired +0.20 ±0.04)	+0.36 ±0.39 (paired +0.17 ±0.04)

CONFIRMED — #692 (steal first on the winning turn (against opponents who Just Say No the winning play)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. #692 "On the winning turn do the steals/swaps first: an opponent is less likely to JSN a play that only completes yo…" byp

E42 — Rent-card class value by player count: forbid the any-colour rents, forbid the two-colour rents (one seat)

Cell	2p	3p	4p	5p
`no_wild_rent`	-6.31 ±0.49 (paired -6.45 ±0.28)	-5.49 ±0.44 (paired -5.34 ±0.29)	-4.09 ±0.40 (paired -4.29 ±0.28)	-2.50 ±0.37 (paired -2.70 ±0.25)
`no_two_colour_rent`	-7.03 ±0.49 (paired -7.17 ±0.30)	-12.84 ±0.40 (paired -12.70 ±0.37)	-15.77 ±0.28 (paired -15.97 ±0.39)	-15.20 ±0.21 (paired -15.39 ±0.37)

CONFIRMED — #686 (the any-colour rent is worth more at 2p, the two-colour rents at 3+). Per count: 2p CONFIRMED. drops in pp for the ablated seat, 2p vs 4p. #686 "The multicolour wild Rent is more valuable in 2-player: in a 3+ player game it hits only one opponent while a …" mds-duoplayer

E43 — myforwik's simulation-derived bundle

Cell	2p	3p	4p	5p
`myforwik_bundle`	+2.58 ±0.49 (paired +2.44 ±0.40)	+0.71 ±0.46 (paired +0.85 ±0.44)	+0.80 ±0.43 (paired +0.59 ±0.42)	+0.49 ±0.40 (paired +0.29 ±0.38)
`E19:dump_to_zero`	+0.98 ±0.49 (paired +0.84 ±0.15)	+0.97 ±0.47 (paired +1.11 ±0.16)	+0.88 ±0.43 (paired +0.68 ±0.12)	+0.50 ±0.40 (paired +0.30 ±0.08)
`E38:steal_two_card_first`	+0.17 ±0.49 (paired +0.03 ±0.28)	-1.02 ±0.46 (paired -0.87 ±0.32)	-0.62 ±0.42 (paired -0.82 ±0.31)	-0.25 ±0.39 (paired -0.45 ±0.28)
`E30:hold_pairs`	-0.50 ±0.49 (paired -0.64 ±0.32)	-0.64 ±0.46 (paired -0.50 ±0.35)	+0.29 ±0.43 (paired +0.08 ±0.33)	+0.68 ±0.40 (paired +0.48 ±0.29)
`E18:jsn_anything`	+0.49 ±0.49 (paired +0.35 ±0.23)	-0.55 ±0.46 (paired -0.40 ±0.25)	-0.00 ±0.42 (paired -0.21 ±0.24)	-0.24 ±0.39 (paired -0.43 ±0.22)

CONFIRMED at 2p; inconclusive at 3p, 4p, 5p — #713 (myforwik's simulation-derived bundle beats folk play and every component). Per count: 2p CONFIRMED, 3p INCONCLUSIVE, 4p INCONCLUSIVE, 5p INCONCLUSIVE. #713 "Simulation-derived policy (myforwik): always play 3 cards even if it means banking useful cards; JSN every act…" bgg-469342

E44 — 2024 rule: fire the attack first, keep a play to answer a Just Say No (and the mirror: attack last)

Cell	2p	3p	4p	5p
`attack_first_db`	+0.15 ±0.49 (paired +0.01 ±0.02)	-0.13 ±0.46 (paired +0.01 ±0.02)	+0.22 ±0.43 (paired +0.02 ±0.03)	+0.20 ±0.39 (paired -0.00 ±0.03)
`attack_third`	-3.20 ±0.49 (paired -3.34 ±0.31)	-3.87 ±0.45 (paired -3.73 ±0.38)	-4.07 ±0.40 (paired -4.28 ±0.40)	-4.23 ±0.36 (paired -4.42 ±0.38)
`evolved_attack_third`	-6.29 ±0.49 (vs evolved_table: -6.14 ±0.36)	-9.67 ±0.42 (vs evolved_table: -9.35 ±0.41)	-10.18 ±0.35 (vs evolved_table: -10.16 ±0.41)	-10.84 ±0.28 (vs evolved_table: -10.77 ±0.39)

CONFIRMED — #285, #375 (under the 2024 rule, fire the attack you care about first and keep a play to answer (the mirror, attacks last, loses)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p CONFIRMED. the explicit 'attack first' rule itself adds nothing measurable (inside CI); the claim as stated (#285: play the big action LAST) is the mirror. #285 "Tried 'JSN consumes a move if you have moves left'; it created a play-big-action-last strategy but was confusi…" jmdwuae; #375 "The new JSN-counts-as-a-card rule is stupid; a JSN war is classic" lflacvz

E46 — Just Say No fishing: Sly Deal first to draw the JSN, then the Deal Breaker (matched no-bait control; evolved actor)

Cell	2p	3p	4p	5p
`bait_before_db`	+0.08 ±0.22 (vs db_first_no_bait: -0.05 ±0.04)	-0.45 ±0.21 (vs db_first_no_bait: -0.34 ±0.05)	-0.22 ±0.19 (vs db_first_no_bait: -0.37 ±0.05)	-0.25 ±0.17 (vs db_first_no_bait: -0.29 ±0.05)
`db_first_no_bait`	+0.13 ±0.22	-0.12 ±0.21	+0.15 ±0.19	+0.04 ±0.18
`evolved_bait`	-0.21 ±0.69 (vs evolved_no_bait: +0.04 ±0.09)	-1.05 ±0.65 (vs evolved_no_bait: -0.20 ±0.12)	-0.08 ±0.60 (vs evolved_no_bait: -0.18 ±0.12)	-0.05 ±0.55 (vs evolved_no_bait: -0.24 ±0.12)
`evolved_no_bait`	-0.25 ±0.69	-0.84 ±0.65	+0.10 ±0.60	+0.19 ±0.56

REFUTED — #167, #277 (fish the Just Say No out with a Sly Deal before the Deal Breaker). Per count: 2p REFUTED, 3p REFUTED, 4p REFUTED, 5p REFUTED. paired against the matched no-bait control on the same seeds. #167 "Fish out a JSN by first playing a lesser card (Sly Deal) before the card you really want (Deal Breaker)" jj5imn1; #277 "Fishing: play a throwaway set-completing card to draw out the JSN before the Deal Breaker; the opponent has be…" jd035gq

E47 — myforwik bundle, 2^4 factorial: dump_to_zero (D) x jsn_anything (J) x steal_two_card_first (S) x hold_pairs (H)

Cell	2p	3p	4p	5p
`fact_DJSH`	+2.58 ±0.49 (paired +2.44 ±0.40)	+0.71 ±0.46 (paired +0.85 ±0.44)	+0.80 ±0.43 (paired +0.59 ±0.42)	+0.49 ±0.40 (paired +0.29 ±0.38)
`fact_----`	+0.14 ±0.49 (paired +0.00 ±0.00)	-0.14 ±0.46 (paired +0.00 ±0.00)	+0.20 ±0.43 (paired +0.00 ±0.00)	+0.20 ±0.39 (paired +0.00 ±0.00)

CONFIRMED at 2p, 3p, 4p; inconclusive at 5p — #713 (the bundle decomposed: dump-to-zero (D), JSN-anything (J), steal two-card colours (S), hold pairs (H)). Per count: 2p CONFIRMED, 3p CONFIRMED, 4p CONFIRMED, 5p INCONCLUSIVE. full bundle vs the all-off control (paired); Yates contrasts in RESULTS.md. #713 "Simulation-derived policy (myforwik): always play 3 cards even if it means banking useful cards; JSN every act…" bgg-469342