Anthony David Adams · EarthPilot.ai Lab · preprint, September 2026 · 34 pages
Monopoly Deal is a 106-card, two-to-five-player card game of imperfect information with payment sub-decisions, response chains and a large body of folk strategy that has never been tested. We present, to our knowledge, the first full-deck, full-rules analysis of the game at every supported player count. We built an exact rules engine (mdeal), validated it against an independent engine on 180,000 games, and used it for three studies. Every number below comes from one evidence base: 861 cells, 42.2 million games, run under Hasbro's 2024 rulebook defaults at two, three, four and five players, 40,000 games per claim cell and 20,000–200,000 for the design cells, every cell stating its own size and margin. (1) A corpus study: 643 posts and 2,662 comments from r/monopolydeal, 188 BoardGameGeek threads and eleven strategy web sites were reduced to 717 strategy claims, 393 of them testable, and 180 experimental variants run as 666 cells. Re-scored at four player counts, the verdicts are 150 refuted, 95 confirmed, 30 conditional and 15 inconclusive, with nothing left untested. The most widely repeated advice (delay completing sets to dodge the Deal Breaker, bank before you build, hold the Deal Breaker for the winning moment) is among the most costly, at -2.7 to -14.1 percentage points against fair share. (2) A policy study: a 111-parameter linear feature policy optimised by evolution strategies beats the folk policy by +12.7 to +16.8 points across 2–5 players; a paired common-random-number rollout step improves on it by nothing at 2–3 players and by +9.0 and +11.5 points at 4–5 players, locating the remaining edge in multiplayer table dynamics; a one-rule in-turn lookahead for two-step wins recovers +1.5 to +2.1 points of that gap at every count, and the evolved policy with that rule, the recommended strategy, wins 66.9/51.9/41.3/34.4% of games against folk tables at 2–5 players. (3) A bot study (the one component not re-run in round 4): every open-source Monopoly Deal bot we could find, ported into the engine under the printed rules; the strongest wins 13.2% of 2-player and 3.8% of 5-player games against the evolved policy, the un-tuned folk policy beats all of them, and a perfect-information MCTS bot that reads every hand falls from 19.0% to 1.5% as the table grows. (4) Structural facts: seat 1 wins 57.3% of 2-player games between equal folk policies and 56.9% between evolved ones; between folk players the first-seat edge decays to nothing by four players (+2.7, +0.3, -0.2 at 3/4/5p) while between evolved players it holds at +6.9/+6.6/+5.7/+5.2; the ten two-colour rent cards are worth 15.8 points to a 4-player folk seat; a legal-random player wins 0.34% of 4-player games; explicit card counting is worth about one point. (5) The engine's defaults follow Hasbro's 2024 rulebook, under which a Just Say No answered on one's own turn costs one of the three plays; switching from the 2008 reading moves no headline number by more than 0.14 points, but it makes an attack fired as the third play indefensible: a Deal Breaker backed by a Just Say No and a spare play succeeds 99% of the time and 85% without the play, and deliberately firing attacks last costs a folk player 3.2–4.2 points and the evolved policy 6.3–10.8. We also correct one rule the engine had wrong: the Forced Deal restricts only the card taken from a complete set, so a player may offer a card out of their own complete set, and playing the card as printed is worth about two points to a strong player –- all of it from opponents misusing the option on a third of their Forced Deals, none of it from the strong player, whose own win rate moves by at most 0.20 percentage points when granted it. Four folk conclusions reverse against the earlier rounds: all-out aggression is no longer a head-to-head gain (+6.8 to +0.8); passing the first turn is a loss at two players and a gain at four and five; the wild rent-flip edge at two players was an artefact of a permissive engine and is refuted there while holding at four and five; and the Forced-Deal-into-Deal Breaker combo, the most praised move on the forum, scores exactly zero against opponents built never to say no. Fishing for the Just Say No with a Sly Deal before a Deal Breaker is refuted at 3–4 players; hoarding the Just Say No for Deal Breakers is refuted; Houses and Hotels are worth nothing to a strong policy and less than nothing at four and five players; and rent farming cannot be priced at all. We also report negative results (a determinized UCT agent that lost to its own rollout policy, a solver-taught policy weaker than evolution, a teacher-fit of the linear weights that loses to its own starting point) and a seeding bias in the 2-player control that was diagnosed and fixed; under the current seeding the all-folk Baseline control sits at fair share at every player count. All results are versus specific opponent policies inside a heuristic policy class; nothing here is an equilibrium.
@techreport{adams2026monopolydeal,
title = {Monopoly Deal Under the Microscope: Large-Scale Simulation, Folk-Strategy
Testing, and Policy Optimization in a Full-Rules Multiplayer Card Game},
author = {Adams, Anthony David},
year = {2026},
month = {September},
type = {Preprint},
institution = {EarthPilot.ai Lab},
url = {https://winmonopolydeal.com/paper}
}
The engine, the experiment harness and the canonical results are public at github.com/AnthonyDavidAdams/mdeal (MIT for the code, CC BY for the data). The tables behind every number are also on this site: the results log and the claim verdicts.
Corrections are welcome and wanted. If a number here disagrees with your own play or your own simulation, that is worth knowing.