What this 2-7 lowball odds calculator does
Deuce-to-seven is the lowball game where everything that would be good news in high poker is bad news: the ace is high only, straights and flushes count against you, and the best possible hand is 7-5-4-3-2 of mixed suits. That ranking produces trap hands everywhere, which is why people get 2-7 odds wrong by eye more than in any other game. 2-3-4-5-6 looks like a six-low and is a straight; A-2-3-4-5 looks like a wheel and is ace-high; a one-card draw to 7-5-4-3 has eight cards that look like outs and three that are.
This calculator scores every hand under the real deuce-to-seven ranking and deals the draw from the remaining deck. With one card to come for one player there are 43 outcomes, and even two players drawing two is under a million, so the number is exact in almost every spot. It covers 2-7 single draw completely, and the final draw of 2-7 triple draw.
Entering hands
Type what each player keeps, spaces between players: 8c7d5h4s2c 7h5c4d3s is a pat eight against a one-card draw to a seven. A four-card hand draws one, three cards draw two, and so on. Up to eight players. Known discards go in Dead cards; unknown ones stay in the deck.
Worked examples, computed by this engine
| Match-up | Equity | Method | |
|---|---|---|---|
| Pat 8-7-5-4-2 vs 7-5-4-3 one-card draw8c7d5h4s2c vs 7h5c4d3s | 93.02% / 6.98% | Exact · 43 deals | Load → |
| Pat 9-8-5-3-2 vs 8-6-4-2 one-card draw9c8d5h3s2c vs 8h6c4d2s | 76.74% / 23.26% | Exact · 43 deals | Load → |
| Pat ten vs two-card draw to 7-4-2Tc8d6h4s2c vs 7h4c2d | 82.88% / 17.12% | Exact · 946 deals | Load → |
| Pat 7-6-5-4-2 vs pat 8-5-4-3-27c6d5h4s2c vs 8h5c4d3s2d | 100.00% / 0.00% | Exact · 1 deal | Load → |
The first row is the lesson of the game. A pat 8-7-5-4-2 against a draw to 7-5-4-3 is a 93% favourite, because the draw's "outs" are mostly fake: a six makes 7-6-5-4-3, which is a straight; a seven or a five pairs; an ace is ace-high. Only a deuce makes a seven, the pat hand holds one of them, and three outs from 43 cards is 6.98%. A pat nine against a draw to 8-6-4-2 is more honest, 77-23, because the eight-draw has real outs with a seven, a five or a three. The fourth row, two pat hands, is there to show the ranking: 7-6-5-4-2 is a seven-low and beats any eight-low, however smooth, every time.
The ranking, exactly as the calculator applies it
Invert the high ranking. Any hand with no pair, no straight and no flush beats any hand that has one of those; among those hands, the lowest highest card wins, then the next card down. One pair beats two pair, which beats three of a kind, which beats a straight, which beats a flush, which beats a full house. The ace is always high, so 7-5-4-3-A is ace-high and loses to K-Q-J-T-8. Straights and flushes are scored as the high hands they are, so a flush that happens to be low is still a flush and loses to a pair of aces. The hand distribution table groups results by the low they made: seven-low, eight-low, nine-low, and so on down to "pair or worse", which in this game includes the straights.
Single draw, triple draw and what this calculator can and cannot do
In 2-7 single draw there is one draw, and this calculator gives you the exact equity for any spot in the game. In 2-7 triple draw there are three, and the right play on the first and second draws depends on what you will do after them, which depends on what you catch. The equity of "pat nine against a two-card draw with two draws to come" has no single value; it depends on whether the drawing player breaks a rough nine on the next draw, stands pat with an eight, and so on. We give you the one-draw number, which is exact and is the last draw's answer, and we say so rather than invent a figure. For ace-to-five and badugi, which share the draw format, there are separate calculators: A-5 Lowball and Badugi.
Frequently asked questions
7-5-4-3-2 with at least two suits. In deuce-to-seven the ace is always high, so A-2-3-4-5 is not a wheel, it is an ace-high hand that loses to any king-high. Straights and flushes are high hands too, so 2-3-4-5-6 is a straight and loses to a pair of kings.
Take the normal high-hand ranking and turn it upside down. Any no-pair hand beats any pair, which beats two pair, and so on. Among no-pair hands, compare from the highest card down: 8-6-4-3-2 beats 8-7-4-3-2 because the second card is lower. Straights and flushes are high hands, so 7-6-5-4-3 is a straight and loses to a pair, and the ace is always high, so 7-5-4-3-A is an ace-high hand that loses to king-high. The calculator applies exactly these rules, including the trap hands.
For the last draw, exactly. With two or three draws left, the equity depends on what each player discards after each draw, which depends on what they catch, which a calculator cannot know without modelling both players' strategy. We give the one-draw number and say so rather than pretend. For single draw it is the whole game.
Count the real outs. The draw needs a card that makes a seven-low: a six gives 7-6-5-4-3, which is a straight and loses; a seven or a five pairs; an ace is ace-high. Only a deuce works, making 7-5-4-3-2, and the pat hand holds one of the four. Three outs from 43 unseen cards is 6.98%, which is what the calculator shows, not the 'eight outs' a quick glance suggests.
