33

33 (pocket threes) wins 53.7% of the time against a single random opponent, which places it 67th out of the 169 starting hands — the top 39.6% of the range. At a six-handed table (five opponents) its equity falls to 16.6% and its rank moves to 89; nine-handed (eight opponents) it holds 12.8% for rank 63. A small pair — cheap to play, huge when it flops a set.

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 Q8o at 53.7% and one place below is Q6s at 53.6%. 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, 33 is a favourite against 125 of them and an underdog against 43. Its best matchup is 32o at 89.2% and its worst is 88 at 18.3% — a spread of 70.9 points, which is why calling 33 simply "strong" or "weak" says very little. 8 opponents land inside one point of a coinflip, the closest being QTo at 50.0%.

33 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 18.3%. The table further down lists all 168 opponents individually.

Within the 13 pocket pairs it comes 12 of 13. The strongest hand in that group, AA, is 31.5 points away, and the weakest, 22, sits 3.5 points below. Measured against the average equity of all 169 hands, 51%, 33 lands +2.7 points from the middle of the pack, and 66 hands in the full ranking are still ahead of it.

Adding players costs equity steadily: 53.7% against one opponent, 33.1% against two, 19.1% against four and 12.8% against eight. That last figure is 115% of an even nine-way share (11.1%). The Chen formula scores this hand at 5 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 33 reads as 53.7% 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.

33 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.

When the set misses, all three flop cards come in below 3 — leaving an overpair — 0.0204% of the time, while at least one higher card lands 88.2% of the time (1 in 1.1). The chance of staying an overpair is 0.286% for 44 (one pair up), and 0.0000% for 22 (one pair down).

Against one random hand, 33 goes from 53.7% before the flop to 92.1% when it flops a set or better (11.8% of flops). Without a set, it holds 64.5% when all three cards are below 3 (still an overpair) and drops to 48.6% when a card above 3 lands (88.2%, 17,292 of 19,600 flops).

By board shape: rainbow 54.3%, two-tone 53.4%, monotone 51.5%. A monotone flop in one of your suits gives 54.8%. A paired board gives 54.2%, and a connected board (three ranks within five) 49.4%. The best row in the table is "Set or better (at least one 3 on the flop)" at 92.1%, the worst "No set, at least one card above 3" at 48.6%.

The 53.7% 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 53.69% (a gap of 0.01 points). Each equity is taken with the flop out and the turn and river still to come.