STAR CLUSTERS

Multiway pots

One opponent rarely has it. Eight opponents, together, often do.

The board is Ah 7d 2s and you hold 9c 8c, so 3 aces are left among the 47 unseen cards. The ace column is exact hypergeometric counting. The pair column checks each opponent for a pocket pair or a card matching the board.

Chance at least one opponent has it. The ace columns are exact counts; the pair-or-better column is a simulation of 200,000 deals per row.

Opponents	Holds an ace before the flop (you hold none)	Holds an ace on Ah 7d 2s	Has a pair or better on Ah 7d 2s
1	15.5%	12.5%	40.0%
2	29.1%	23.9%	64.6%
3	41.1%	34.3%	79.7%
4	51.4%	43.6%	88.7%
5	60.3%	52.1%	93.8%
6	67.9%	59.6%	96.9%
7	74.4%	66.4%	98.4%
8	79.9%	72.3%	99.2%

Heads-up, an ace is out there about 1 in 8.0. With eight opponents it is 72%, and someone has at least a pair 99% of the time.

On an ace-high flop, one opponent holds an ace 12% of the time; with eight opponents it is 72%. — The ace line is an exact count. The pair-or-better line is a simulation of 200,000 deals per point. 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.

More players, more hands that connect