Q3o

Q3o (queen-three offsuit) wins 48.1% of the time against a single random opponent, which places it 100th out of the 169 starting hands — the top 59.2% of the range. At a six-handed table (five opponents) its equity falls to 12.9% and its rank moves to 139; nine-handed (eight opponents) it holds 7.9% for rank 143. Two unconnected offsuit cards — the class of hand most often overvalued.

Its suited/offsuit twin Q3s runs at 51.0% (rank 81), a gap of 2.9 points. Losing the shared suit costs 2.9 points of raw equity. The hand directly above it in the ranking is T7o at 48.1%, and directly below is 87s at 47.9%, so three hands are packed into a band of 0.2 points.

Played heads-up against each of the other 168 hands, Q3o is a favourite against 92 of them and an underdog against 76. Its best matchup is J3o at 74.5% and its worst is QQ at 6.0% — a spread of 68.5 points, which is why calling Q3o simply "strong" or "weak" says very little. 2 opponents land inside one point of a coinflip, the closest being Q2s at 50.3%.

Q3o dominates 8 hands that share one of its ranks, pushing hardest against J3o at 74.5%. It is dominated by 8 hands in return, the worst of them AQs, which leaves Q3o with only 22.3%. A single kicker can move the number by tens of points, and the full table below lists every one of those opponents.

Within the 78 offsuit hands it comes 40 of 78. The strongest hand in that group, AKo, is 17.3 points away, and the weakest, 32o, sits 15.8 points below. Measured against the average equity of all 169 hands, 51%, Q3o lands -2.9 points from the middle of the pack, and 99 hands in the full ranking are still ahead of it.

Adding players costs equity steadily: 48.1% against one opponent, 29.9% against two, 16.0% against four and 7.9% against eight. That last figure is 71% of an even nine-way share (11.1%). The Chen formula scores this hand at 2 points, and it arrives 0.9% of the time (12 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 Q3o reads as 48.1% 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.

Q3o pairs the board on the flop — at least one of its two ranks hits — 32.4% of the time, and flops top pair or better (the paired card is the highest on the board, or two pair and up) 13.2%. By the river it has made a pair or better 48.7% of the time.

For straights, the flop completes one 0.0000% of the time (zero flops — the two cards are too far apart), gives an eight-out draw 1.31% and a four-out gutshot 5.22%. By the river a straight using a hole card completes 2.49% of the time.

Put together, Q3o flops a pair or better or a strong draw (an eight-out straight draw) 33.7% of the time — rank 143 of the 156 unpaired hands (tied with 6 others). The highest is JTs, T9s, 98s and 4 others at 50.6% and the lowest AKo, A2o at 32.8%.

Against one random hand, Q3o goes from 48.2% before the flop up to 69.3% when either card pairs, and down to 38.1% when both miss. It connects 32.4% of the time (6,356 of 19,600 flops). Missing with a card above Q on board leaves 41.1%; missing with nothing above Q leaves 35.6%.

By board shape: rainbow 48.6%, two-tone 48.0%, monotone 48.1%. A monotone flop in one of your suits gives 56.5%. A paired board gives 50.2%, and a connected board (three ranks within five) 45.1%. The best row in the table is "Either card hits (a matching rank on the flop)" at 69.3%, the worst "and nothing above Q" at 35.6%.

The 48.1% 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 48.22% (a gap of 0.12 points). Each equity is taken with the flop out and the turn and river still to come.