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Flawless Poker

Universal Law 25

LAGRANGE POINTS

Ties and split pots

Some all-ins end with nobody winning. The pot is divided by the board.

Two random hands dealt to the river. Simulation of 2,000,000 deals.
EventChancePlain English
The pot is split4.11%about 1 in 24
Split because the five board cards are both players' best hand1.52%about 1 in 66

Mirror matchups.

Every board counted (1,712,304 per row).
MatchupCardsFirst hand winsSplitSecond hand wins
AK vs AK, all four suits differentAsKd vs AhKc2.2%95.7%2.2%
AKs vs AKo, sharing no suitAsKs vs AhKc7.2%90.7%2.2%
AKs vs AKsAsKs vs AdKd7.2%85.7%7.2%
KK vs KKKsKh vs KdKc2.2%95.7%2.2%
AQo vs AQoAsQd vs AhQc2.2%95.7%2.2%
T9s vs T9oTs9s vs Th9d7.2%90.7%2.2%

With no suits shared, a mirror matchup splits about 95.7% of the time. Each side wins only when four or five cards of their suit arrive. A suited hand against the same ranks offsuit wins about 7.2% and loses about 2.2%.

FLAWLESS POKER / STUDY CHART

Mirror hands usually split

Ace-king against ace-king with four different suits splits 95.7% of the time across every board.
Every one of the 1,712,304 boards counted for each mirror matchup. Open full-size chart ↗

These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.