What is the chance of flopping a straight?
It depends on the two hole cards. Connected cards such as 54o flop a straight on 256 of 19,600 flops, 1.31%, or 1 in 76.6. A hand with no straight in reach, such as 72o, flops one never. Out of the 156 unpaired starting hands, 64 cannot flop a straight at all.
| Flops with a straight | Chance | Odds | Hands |
|---|---|---|---|
| 256 | 1.31% | 1 in 76.6 | 54o, 54s, 65o, 65s, 76o, 76s, 87o, 87s, 98o, 98s, JTo, JTs, T9o, T9s |
| 192 | 0.98% | 1 in 102 | 43o, 43s, 53o, 53s, 64o, 64s, 75o, 75s, 86o, 86s, 97o, 97s and 8 more |
| 128 | 0.65% | 1 in 153 | 32o, 32s, 42o, 42s, 52o, 52s, 63o, 63s, 74o, 74s, 85o, 85s and 14 more |
| 64 | 0.33% | 1 in 306 | 62o, 62s, 73o, 73s, 84o, 84s, 95o, 95s, A2o, A2s, A3o, A3s and 20 more |
| 0 | 0.00% | never | 72o, 72s, 82o, 82s, 83o, 83s, 92o, 92s, 93o, 93s, 94o, 94s and 52 more |
Why do some hands flop a straight more often?
A straight needs five consecutive ranks, and the hole cards must be two of them with the flop supplying the other three. Hands whose cards sit one rank apart in the middle of the deck have the most five-card windows to complete, so the chance peaks at 1.31% for connectors from the T-9 window down to 6-5. Hands with a wide gap or cards at the ends of the deck have fewer windows, and ace-high hands have only one.
What if I flop a straight draw instead?
An open-ended straight draw has eight outs and hits by the river 31.45% of the time from the flop, while a gutshot has four outs and hits 16.47%. The outs calculator gives the chance for any count, and the call or fold pages compare it with the price of a bet.
Where do these numbers get used?
The chance to flop a hand is the first number in a plan. The pages below turn it into prices: what a call can cost, how many outs a draw has, and how many ways a hand can be dealt.
How were these numbers computed?
After two hole cards are dealt, 50 cards are unseen and the flop is any 3 of them, so there are C(50, 3) = 19,600 equally likely flops. For each starting hand we deal all 19,600, classify the five cards with our hand evaluator and count. Suits are symmetric, so one combination stands for every combination of the same hand. The closed forms on this page use binomial coefficients and give the same counts.
Source: GeorgeLiPoker's own exact count of the 52-card deck.
Questions
- What is the probability of flopping a straight?
- For the best connected hands it is 1.31%, or 1 in 76.6. For hands without a path to a straight it is zero.
- Which starting hands flop a straight most often?
- 54o and the other connectors in the middle of the deck, each with 256 straight flops out of 19,600.
- What is the chance of an open-ended straight draw hitting?
- 31.45% by the river from the flop, and 17.39% on the river from the turn.