Summary
Rule-exact bots played 100,000 four-player games of Catan. Each game was tracked from the first settlement to the winning point. The opening decides more than anything that follows. The player with the best starting spots wins 33% of games; the player with the worst wins 15%. A starting pip of ore or wheat is worth about 1.5 pips of wood, and covering all five resources adds about 5 points of win probability on top of the pips. The snake draft gives every seat about the same total pips, but not the same kind. The first pick takes the ore; the last seat gets two picks in a row and the most variety. In the middle game the start becomes a production lead, and by round 12 the player in front wins almost half the time. In the endgame the first player to 8 points wins 63% of games, usually about two rounds later. Cities, a hidden victory-point card, and one of the two awards make up most of the gap. A search bot (MCTS) that beats the best tuned bot draws most of its edge from a handful of decisions per game: where to build roads, when to play a knight, and which trades to refuse.
Key findings
- Pips first, then ore and wheat, then variety. Win rate rises from 11% to 38% across the range of starting pips. Holding pips fixed, ore and wheat pips are worth the most, and a start that touches all five resources wins twice as often as one that touches three.
- The draft order changes what you get, not how much. All four seats end setup with about 19.6 pips. Seat 1 gets the best single spot and the ore; seat 4 gets the widest mix. Seat 1 still wins 25.9% and seat 4 24.0%.
- Production now beats starting pips later. At round 10, a player's current production, development cards, and distance from the leader predict the winner. Once those are known, starting pips add nothing. The start matters through the engine it builds.
- The lead hardens around round 12. The leader's chance of winning climbs from 38% at round 3 to 55% at round 18. The last-place player's falls from 22% to 10%. Never building a city is fatal (5% win rate).
- The endgame is a sprint from 8 points. The first to 8 public points wins 63% of games. Winners take about 2.4 cities, and three in four finish with a hidden victory-point card.
- The search bot plays roads, knights, and refusals. Its edge over the tuned bot comes from better road placement, knights played instead of trades, and declining trades that help the partner more. Most of that edge lands in the middle game.
Figure 1. What the opening is worth, and where the search bot's edge comes from
Table view
| Resource | Per starting pip | Search bot's move | Per game |
|---|---|---|---|
| Ore | +4.5 | Roads | +3.6 |
| Wheat | +4.2 | Knights | +1.8 |
| Sheep | +3.6 | Refusing trades | +1.6 |
| Brick | +3.2 | Monopoly timing | +0.9 |
| Wood | +3.0 | Development cards | +0.7 |
| Settlements | +0.5 | ||
| Cities | +0.15 |
The study in numbers
The opening
The two opening settlements fix about half a player's production for the whole game. Rank the four players in each game by the pips of their two starting spots: the best start wins 33.4% of games and the worst 15.4%, and each extra starting pip adds about 3 points of win probability. Pips are not all equal. Cities and development cards, which produce most of a winner's points, need ore and wheat, and the board has only three ore hexes, so an ore pip is worth about one and a half wood pips. Players whose two settlements touch all five resources win 32.6% of games, against 18.9% for those touching three.
The red numbers are a myth. Players with zero, one or two 6/8 hexes win 24.6%, 25.0% and 25.0%, and with pips held fixed each 6/8 hex costs about 3.3 points: a big number pays out in bursts that push hands over seven cards and draw the robber. The snake draft evens out totals (every seat ends with 19.5 to 19.7 pips) but not kinds: ore is 24.6% of the pips taken by the first pick and 14.5% of those taken by the eighth. So seat 1 should take the ore-and-wheat spot, since its second pick comes last, and seat 4 should choose its two spots as a matched pair.
The middle game
Early leads are fragile: the player ahead at round 3 wins 37.8% of games, and the lead changes hands at least once in 80% of games. By round 12 the leader wins 47.7%, and by round 18 54.6%. A snapshot of every player at round 10 shows what decides it: development cards in hand, production now, and points relative to the leader each move the chance of winning by eight to ten points per standard deviation. Starting pips add nothing once current production is known. The first city is the telling milestone. Players who never build one win 4.9% of games.
Falling behind is rarely one bad roll. For every 100 cards a player's buildings could produce, about 34 never get used: 11 blocked by the robber, 11 discarded on a 7, 8 stolen, 4 taken by Monopoly. The game also pushes back against the leader. When a player steals, they pick the points leader 77% of the time, and from 7 points on, trade offers start to be refused.
The endgame and the search bot
Winners average 10.1 points and the others 6.5. The gap is cities (+1.9), Longest Road (+0.6), victory-point cards (+0.6) and Largest Army (+0.5); settlements are the same for both groups, because winners upgrade theirs. A player holding one award wins 40 to 45% of games, both 91%, neither 8.3%. Monopoly is an endgame weapon: hands are biggest late, and holding the card until it takes seven or more cards is worth about 3 points.
The strongest player is a Monte Carlo tree search bot. Over 600 paired games with hidden hands it beats the evolution-tuned bot, which already beats the balanced style by about 9.6 points, by 7.2 points (95% CI 2.5 to 11.7). It disagrees with the tuned bot only about 3.2 times in a game of roughly 126 decisions, and in a typical game two of those decisions account for 80% of the swing. The gains, in order: roads placed with a plan, knights played where the tuned bot would trade, trades refused because they help the partner more, and the timing of Monopoly and development-card purchases. Two thirds of the road gain and most of the total land in the middle game.
Putting it together
- Open on pips, preferring ore and wheat, and cover as many of the five resources as you can. Treat 6s and 8s as pips, not magic.
- Play your seat. First seat: take the ore-and-wheat spot, since your second pick comes last. Last seat: choose your two spots as a matched pair.
- Build the engine. Get a city up and a third settlement down. Spend cards instead of holding them, and trade or use a port to fix what your start lacks.
- From round 10, stay within a point of the leader and keep a development card or two in hand.
- Close with cities and one award. Hold a hidden victory-point card if you can, and save Monopoly for a big haul.
- Watch for the few decisions that matter: where a road leads, when to play a knight, and when to turn down a trade.
How it was measured
The games are played by bots built on an exact implementation of the base rules, with negotiated trading. Six bot styles (balanced, ore-and-wheat cities, expansion, development cards, port trading, and hoarding), each with randomly varied weights, give 100,000 games of varied but competent play. Every placement, roll, trade, build and steal is logged and related to winning. Effects are reported in points of win probability: in a four-player game an average player wins 25%, so "+5 points" means 30%. Placement effects come from logistic regressions on 400,000 player-games and from placement labs that fixed the position and varied only the choice. The search bot is pitted against the strongest tuned rule-based bot over 600 paired games, and a decision-by-decision attribution credits each point where the two would choose differently.
Caveats
- Bots, not people. People bluff, form alliances, and trade more freely with friends. The size of each effect reflects how these bots play, but the direction mostly follows from the rules and the board, and should carry over.
- Associations, not always causes. The placement findings come from regressions and from labs that fixed the position and varied only the choice. The middle-game snapshot is descriptive: production at round 10 is partly luck.
- Hidden hands. Most runs let bots see opponents' hands. Replays with hidden hands changed no style's win rate by more than a point, and the search-bot games were played with hidden hands.
- Base game only. The expansions and 5 to 6 player boards are not modelled.