AA

AA (pocket aces) wins 85.2% of the time against a single random opponent, which places it 1th out of the 169 starting hands — the top 0.6% of the range. At a six-handed table (five opponents) its equity falls to 49.2% and its rank moves to 1; nine-handed (eight opponents) it holds 34.5% for rank 1. A premium pair — ahead of almost every other hand before the flop.

As a pocket pair there is no suited twin; instead there are 6 combinations of it in the deck, so you are dealt it 0.45% of the time (6 of 1,326 two-card hands). The hand ranked one place above is — and one place below is KK at 82.5%. Every pocket pair flops a set about 11.8% of the time, so the pecking order among pairs is decided almost entirely before the flop.

Played heads-up against each of the other 168 hands, AA is a favourite against 168 of them and an underdog against 0. Its best matchup is A9o at 93.9% and its worst is 65s at 77.6% — a spread of 16.3 points, which is why calling AA simply "strong" or "weak" says very little.

AA shares a rank with relatively few hands, so it is rarely on the wrong side of a kicker problem. What does hurt it is running into a higher pair, where the number bottoms out at 77.6%. The table further down lists all 168 opponents individually.

Within the 13 pocket pairs it comes 1 of 13. The strongest hand in that group, AA, is 0 points away, and the weakest, 22, sits 35 points below. Measured against the average equity of all 169 hands, 51%, AA lands +34.2 points from the middle of the pack, and 0 hands in the full ranking are still ahead of it.

Adding players costs equity steadily: 85.2% against one opponent, 73.5% against two, 55.9% against four and 34.5% against eight. That last figure is 311% of an even nine-way share (11.1%). The Chen formula scores this hand at 20 points, and it arrives 0.45% of the time (6 of 1,326 combinations).

One caveat worth repeating: every number on this page assumes the opponent holds a completely random hand and that the pot goes to showdown. Real opponents hold ranges, and a range that has already put money in is stronger than random — which is exactly why AA reads as 85.2% here but plays worse than that against a raise. Use the 168 rows in the table below to see which specific holdings are the problem, rather than treating the headline figure as a verdict on the hand.

AA flops a set or better (set, full house or quads) 11.8% of the time — 2,304 of 19,600 flops, or 1 in 8.5 — and exactly a set 10.8%. By the river that rises to 19.2%. Those figures are identical for every pocket pair; what differs from pair to pair is what the flop looks like when the set misses.

Nothing ranks above A, so even without a set all three flop cards are lower and AA is always still an overpair (88.2%). That drops to 67.6% for KK.

Against one random hand, AA goes from 85.2% before the flop to 94.5% when it flops a set or better (11.8% of flops). No rank is higher than A, so even without a set it is always still an overpair, at 84.0%.

By board shape: rainbow 86.4%, two-tone 84.9%, monotone 79.5%. A monotone flop in one of your suits gives 88.1%. A paired board gives 87.7%, and a connected board (three ranks within five) 79.5%. The best row in the table is "Set or better (at least one A on the flop)" at 94.5%, the worst "Connected board (three ranks within five, A can play low)" at 79.5%.

The 85.2% at the top of the page is a 400,000-hand simulation; this table counts every deal of the opponent's two cards and the five-card board (2,097,572,400 per starting hand), which puts the pre-flop figure at 85.20% (a gap of 0.00 points). Each equity is taken with the flop out and the turn and river still to come.