Poker winning odds calculation
Poker mathematics is based on the theory of probability, which allows you to calculate the odds of getting combinations, opening the right card, winning the hand. It is important for every beginner to understand how to use these indicators in the game.
The probability of winning in poker is not easy to calculate, but thanks to the reference tables presented in this manual, the player can operate with ready-made indicators. They will be useful to all poker players.
Ready-made tables with indicators of the frequency of falling out of hands
The calculations are not easy to do not only in your head, but also with a calculator. It is easier to use ready-made tables during a real game.
Five-card formulation is not suitable for Hold’em on the turn and river, although it is indicated in many teaching sources for this discipline. This is true for 5 Card Draw or Flop Hold’em.
Chances of making a poker hand from a 5-card set
| Hand | Number of possibilities | Probability in% | Odds |
| Royal Flush | four | 0.0001539077 | 649737: 1 |
| Straight flush | 36 | 0.0013851695 | 72193.5: 1 |
| Square | 624 | 0.0240096038 | 4163.99: 1 |
| Full house | 3744 | 0.144057623 | 693.17: 1 |
| Flush | 5108 | 0.1965401545 | 507.8: 1 |
| Straight | 10200 | 0.3924646782 | 253.8: 1 |
| Thrips | 54912 | 2.1128451381 | 46.3: 1 |
| Two pairs | 123552 | 4.7539015606 | 20: 1 |
| Couple | 1098240 | 42.2569027611 | 1.366: 1 |
| High card | 1302540 | 50.1177394035 | 0.995: 1 |
Seven Card Drafting applies to River Hold’em and 7 Card Stud.
Chances of making a combination from a 7-card set
| Hand | Number of possibilities | Probability in% | Odds |
| Royal Flush | 4324 | 0.003232062 | 30939: 1 |
| Straight flush | 37260 | 0.027850748 | 3589.57: 1 |
| Square | 224848 | 0.168067227 | 594: 1 |
| Full house | 3473184 | 2.596102271 | 37.52: 1 |
| Flush | 4047644 | 3.025494123 | 32.05: 1 |
| Straight | 6180020 | 4.619382087 | 20.65: 1 |
| Thrips | 6461620 | 4.829869755 | 19.7: 1 |
| Two pairs | 31433400 | 23.49553641 | 3.26: 1 |
| Couple | 58627800 | 43.82254574 | 1.28: 1 |
| High card | 23294460 | 17.41191958 | 4.74: 1 |
Flop odds of getting a combination
Of greater practical importance is the table with indicators of the odds of getting a made hand on the flop when entering trades with different pockets.
The table of probabilities of collecting a hand in Texas Hold’em poker
| Starting hand | Hand on the flop | Probability in% | Odds |
| Pocket pair | Seth or better | 11.8 | 6.9: 1 |
| Set | 10.5 | 7.5: 1 | |
| Full house | 0.73 | 136: 1 | |
| Square | 0.24 | 415.67: 1 | |
| 2 unpaired cards | One pair | 32.4 | 2.1: 1 |
| Two pairs | 2 | 48.5: 1 | |
| Suited cards | Flush | 0.842 | 118: 1 |
| Flush draw | 10.9 | 8.17: 1 | |
| Backdoor flush | 41.6 | 1.4: 1 | |
| Connectors 45o-JTo | OESD | 9.6 | 9.42: 1 |
| Connectors 45s-JTs | Straight or Flush Draw | 19.1 | 4.21: 1 |
| Connectors 45o-JTo | Straight | 1.31 | 75: 1 |
It can be used as a guide when entering preflop trading, comparing the size of the pot and the required bet. For example, a player will make a set about 1 hand out of 8 by playing a pocket pair.
This means that if he enters into trades with small pairs, it is necessary that the bank was formed by several limpers and exceeded the rate by 8 times. This will allow you to play according to the pot odds and the bet will be profitable in the long term.
If the pot and the size of the bet do not allow you to play according to the odds, it is worth considering the stacks of your opponents. They should be of such a size that, when receiving a set, a poker player can form at the expense of an opponent such a bank that would recoup 7 losing investments in a similar situation.
Improving hands on the turn and river
Any player is often faced with such a situation that the hand turns out to be unfinished on the flop or turn, but there are chances to make it on the next street. Rivals rarely provide the opportunity to watch the following cards for free. Knowing the chances of getting the right out to build a combination, you can determine the advisability of calling your opponent’s bet. The tables provide the necessary metrics for different trading rounds.
Improving your hand on the turn
| Our hand | Hand on the turn | Probability in% | Odds |
| Flush draw | Flush | 19.1 | 4.24: 1 |
| OESD | Straight | 17 | 4.9: 1 |
| Gutshot | Straight | 8.5 | 10.76: 1 |
| Thrips or set | Square | 2.1 | 46.61: 1 |
| Two pairs | Full house | 8.5 | 10.76: 1 |
| One pair | Thrips | 4.3 | 22.26: 1 |
| Two unpaired | Couple | 12.8 | 6.8: 1 |
Improving your hand on the river
| Our hand | Hand on the turn | Probability in% | Odds |
| Flush draw | Flush | 19.6 | 4.1: 1 |
| OESD | Straight | 17.4 | 4.74: 1 |
| Gutshot | Straight | 8.7 | 10.5: 1 |
| Thrips or set | Square | 2.2 | 45.46: 1 |
| Two pairs | Full house | 8.7 | 10.5: 1 |
| One pair | Thrips | 4.3 | 22.26: 1 |
| Two unpaired | Couple | thirteen | 6.7: 1 |
Draw Pairs
Most often, a pair is made in the game, and when playing it, it is important to take into account the chance of losing with a higher similar combination. The following table shows the indicators reflecting the possibility of opponents getting high pairs preflop. Thanks to her, you can understand the value of your starter in such situations.
| Our hand | The probability of having one top pair in% for x opponents | ||||||||
| Number of rivals | one | 2 | 3 | four | five | 6 | 7 | 8 | nine |
| KK | 0.49 | 0.98 | 1.47 | 1.96 | 2.44 | 2.93 | 3.42 | 3.91 | 4.39 |
| 0.98 | 1.95 | 2.92 | 3.88 | 4.84 | 5.79 | 6.73 | 7.66 | 8.59 | |
| JJ | 1.47 | 2.92 | 4.36 | 5.77 | 7.17 | 8.56 | 9.92 | 11.27 | 12.59 |
| TT | 1.96 | 3.89 | 5.78 | 7.64 | 9.46 | 11.24 | 12.99 | 14.7 | 16.37 |
| 99 | 2.45 | 4.84 | 7.18 | 9.46 | 11.68 | 13.84 | 15.93 | 17.95 | 19.9 |
| 88 | 2.94 | 5.8 | 8.57 | 11.25 | 13.84 | 16.34 | 18.73 | 21.01 | 23.18 |
| 77 | 3.43 | 6.74 | 9.94 | 13.01 | 15.95 | 18.74 | 21.38 | 23.87 | 26.19 |
| 66 | 3.92 | 7.69 | 11.3 | 14.73 | 17.99 | 21.04 | 23.89 | 26.51 | 28.9 |
| 55 | 4.41 | 8.62 | 12.63 | 16.42 | 19.96 | 23.24 | 26.23 | 28.92 | 31.29 |
| 44 | 4.9 | 9.56 | 13.95 | 06/18 | 21.86 | 25.32 | 28.41 | 31.09 | 33.34 |
| 33 | 5.39 | 10.48 | 15.26 | 19.67 | 23.7 | 27.29 | 30.4 | 33 | 35.03 |
| 22 | 5.88 | 11.41 | 16.54 | 21.24 | 25.46 | 29.14 | 32.22 | 34.64 | 36.33 |