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More players, more monsters: the exact odds
Each opponent is an independent draw from the deck. Stack up enough of them and someone always has something. These figures are straight combinatorics:
| Chance that at least one opponent was dealt… | 4-handed (3 opp) | 8-handed (7 opp) | 12-handed (11 opp) |
|---|---|---|---|
| a pocket pair | 17% | 35% | 49% |
| an ace (when you hold none) | 40% | 69% | 84% |
| a Group A premium (A-A…J-J, A-K) | 9% | 19% | 29% |
Read the ace row again, because it decides how you play half your hands. Holding K-Q at a four-handed table, you're the best hand more often than not. Holding that same K-Q at a twelve-handed table, somebody has an ace 84% of the time — you are usually playing a hand that's already behind, hoping to pair up and get lucky.
(These treat each opponent as an independent draw, which is very slightly optimistic; card-removal effects move the true figures by well under a point. Directionally and practically, they're right.)