Odds are an important part of Poker. If you don`t know how to calculate hand odds, poker odds and pot odds you will have a hard time playing your hands correctly in difficult situations. Although many successful poker players claim to play by “feel,” a solid grounding in math is vital for successful poker play.
How to calculate Texas Hold`em odds
All gambling is based on odds. If the odds of a horse winning a race are 10-to-1 against, you win ten times your bet if the horse you`re betting on wins the race. If the horse wins just once for every ten times it loses, you break even. If it wins more often you should win and if it wins less often you come out behind.
In most bets, like a horse race, you do not get the opportunity for repeated trials, so you either have to be lucky enough to have placed your bet the one time out of eleven that the horse wins, or you need to continually make bets where the odds of hitting are shorter than the odds you are getting paid off at. Pot odds in Texas Hold`em work exactly the same way. If the bet is $1 to you and there is $5 in the pot, you are getting 5-to-1 pot odds. Just as in the horse race, you need to win that pot once for every five times you lose it to break even. If you`ll win the pot more often, you have positive expected value or +EV. If you`ll win it less often, you have a negative expected value play (-EV).
- Calculating Pot Odds in Poker Usually, the bet will be more than $1 to you. Simply reduce the ratio by dividing the size of the pot by the size of the bet to you. For example if there is a $10 bet to you and you have a chance to win a $50 pot, divide 50 by 10 to reach 5-to-1 pot odds. If the pot is $97 and the bet is $25 to you, you are getting about 4-to-1. These calculations do not need to be exact (it`s 3.88-to-1 exactly, but this precision is not worth the distraction during an in-game situation).
- Using Pot Odds in Poker Games Once you know how to calculate pot odds, you`ll know whether you should call a bet by knowing your odds of winning the hand, also known as poker odds. This can be established by calculating the ratio of cards remaining to cards that will give you the win. Poker odds most often come into play when you are on a drawing hand.You`ll want to know if the odds the pot is offering you are better than your actual odds of hitting your hand. To calculate your odds of making your hand, simply count the number of cards that you can consider to be “outs,” cards that will complete your hand, and compare them to the number of cards that remain.For example, let`s say you hold AK on a board of 3 9 5 8 and you are convinced your opponent has top pair. This means that any ace or king should give you the pot. This gives you six outs, for the three remaining aces and three remaining kings. Since you know your two cards and the four on the board, there are 46 cards you have not seen, 52 minus six. Out of those 46, six give you the win and 40 do not. This is an odds ratio of 40-to-6, which reduces to about 6.5-to-1. This means you need better than 6.5-to-1 pot odds to continue.
| Probability | Percentage | Probability / Odds |
| Pair pre-flop | 6 % | 1 in 17 – 16:1 |
| Suited cards pre-flop | 24 % | 1 in 4.2 – 3.2:1 |
| Suited Connectors (23, KQ) | 4 % | 1 in 25 – 24:1 |
| AA or KK pre-flop | 0.9 % | 1 in 111 – 110:1 |
| AK pre-flop | 1.2 % | 1 in 83 – 82:1 |
| AKs pre-flop | 0.3 % | 1 in 332 – 331:1 |
| A in hand pre-flop | 16 % | 1 in 6.25 – 5.25:1 |
| AA, KK, QQ, JJ | 1.8 % | 1 in 56 – 55:1 |
| Flop being all one kind (JJJ or QQQ) | 0.24 % | 1 in 425 – 424:1 |
| AA versus KK pre-flop (heads up) | 0.004 % | 1 in 22560 – 22559:1 |
| AK dealt pre-flop and hitting an A or K by the river | 50 % | 1 in 2 – even |
| QQ versus AK heads up till river | 56 % | 1 in 1.78 – 14:11 |
| Two cards pre-flop that are Js or higher | 9 % | 1 in 11 – 10:1 |
| Beer Hand (72off) pre-flop (or any other off-suited two card combo) | 0.9 % | 1 in 110 – 109:1 |
| Four flush completing (Js Ts Flop Qs4sAd 6h Ks) | 39 % | 1 in 2.6 – 3:2 |
| Open Ended Straight-Flush completing to flush or straight by river | 54 % | 1 in 1.85 |
| Open Ended Straight completing (JT Flop Q94 86) | 34 % | 1 in 2.9 – ~2:1 |
| Two Pair on flop Improving to Full House | 17 % | 1 in 5.8 – ~5:1 |
| Three of a kind (set) on flop improving to Full House or Quads | 37 % | 1 in 2.7- ~3:2 |
| Pocket pair improving to three of a kind on flop | 12 % | 1 in 8 – 7:1 |
| No pair hand pre-flop improving to a pair on the flop (either card) | 32 % | 1 in 3.125 – ~2:1 |
| If you have suited cards, two will flop | 11 % | 1 in 9 – 8:1 |
| One pair on flop improving to two pair or three of a kind by river | 22 % | 1 in 4.7 – ~4:1 |
| Pocket pair improving to three of a kind after flop | 9 % | 1 in 11 – 10:1 |
| Two over cards improving to a pair by river | 26 % | 1 in 3.9 – ~3:1 |
| Two over cards and a gutshot improving to pair or straight | 43 % | 1 in 2.3 – 4:3 |
| Gutshot straight draw hitting by river | 17 % | 1 in 6 – 5:1 |
| Gutshot and pair improving to two pair or better | 39 % | 1 in 2.6 – 3:2 |
| Backdoor Flush hitting (5s6s Flop 7sAh9c Ks Js) | 4 % | 1 in 24 – 23:1 |
| Runner Runner Straight (56 Flop 3TQ 47) | 1.5 % | 1 in 68 – 67:1 |
| Backdoor Flush and One Over Card improving to that pair or flush | 17 % | 1 in 6 – 5:1 |
| Catching Ace on turn or river (A4 Flop Q63 KA) | 13 % | 1 in 8 – 7:1 |
| Backdoor Flush and Gutshot improving to one by river | 21 % | 1 in 4.8 – 3.8:1 |
| Backdoor Flush And Two Over Cards improving to pair or flush | 30 % | 1 in 3.3 – 2.3:1 |
| 5 players on flop, that someone has an A when one is on board | 58 % | 1 in 1.7 |
| 4 players on flop, that someone has an A when one is on board | 47 % | 1 in 2.1 |
| 3 players on flop, that someone has an A when one is on board | 35 % | 1 in 2.9 |
| 2 players on flop, that someone has an A when one is on board | 23 % | 1 in 4.3 |
| 3 of one suit on board and another coming (QsTs2s) if you have one | 39 % | 1 in 2.6 – 3:2 |
| 5 players in with board paired, chance of one of them having it | 43 % | 1 in 2.4 |
| 4 players in with board paired, chance of one of them having it | 34 % | 1 in 3 |
| 3 players in with board paired, chance of one of them having it | 26 % | 1 in 4 |
| 2 players in with board paired, chance of one of them having it | 17 % | 1 in 5.8 |
| Outs | Draw | Turn (47 cards left) | River (46 cards left) | Turn and River | |||
| Odds | Percent | Odds | Percent | Odds | Percent | ||
| 20 | 1.35 : 1 | 42.6% | 1.30 : 1 | 43.5% | 0.48 : 1 | 67.5% | |
| 19 | 1.47 : 1 | 40.4% | 1.42 : 1 | 41.3% | 0.54 : 1 | 65% | |
| 18 | 1.61 : 1 | 38.3% | 1.56 : 1 | 39.1% | 0.60 : 1 | 62.4% | |
| 17 | 1.76 : 1 | 36.2% | 1.71 : 1 | 37% | 0.67 : 1 | 59.8% | |
| 16 | 1.94 : 1 | 34% | 1.88 : 1 | 34.8% | 0.75 : 1 | 57% | |
| 15 | Flush + Open ended straight | 2.13 : 1 | 31.9% | 2.07 : 1 | 32.6% | 0.85 : 1 | 54.1% |
| 14 | 2.36 : 1 | 29.8% | 2.29 : 1 | 30.4% | 0.95 : 1 | 51.2% | |
| 13 | 2.62 : 1 | 27.7% | 2.54 : 1 | 28.3% | 1.08 : 1 | 48.1% | |
| 12 | Flush + Gut shot straight | 2.92 : 1 | 25.5% | 2.83 : 1 | 26.1% | 1.22 : 1 | 45% |
| 11 | 3.27 : 1 | 23.4% | 3.18 : 1 | 23.9% | 1.40 : 1 | 41.7% | |
| 10 | 3.70 : 1 | 21.3% | 3.60 : 1 | 21.7% | 1.60 : 1 | 38.4% | |
| 9 | Flush | 4.22 : 1 | 19.2% | 4.11 : 1 | 19.6% | 1.86 : 1 | 35% |
| 8 | Open ended straight | 4.88 : 1 | 17% | 4.75 : 1 | 17.4% | 2.18 : 1 | 31.5% |
| 7 | 5.71 : 1 | 14.9% | 5.57 : 1 | 15.2% | 2.59 : 1 | 27.8% | |
| 6 | 6.83 : 1 | 12.8% | 6.67 : 1 | 13% | 3.14 : 1 | 24.1% | |
| 5 | 8.40 : 1 | 10.6% | 8.20 : 1 | 10.9% | 3.91 : 1 | 20.4% | |
| 4 | Gut shot straight | 10.75 : 1 | 8.5% | 10.50 : 1 | 8.7% | 5.07 : 1 | 16.5% |
| 3 | 14.67 : 1 | 6.4% | 14.33 : 1 | 6.5% | 7.01 : 1 | 12.5% | |
| 2 | 22.50 : 1 | 4.3% | 22.00 : 1 | 4.4% | 10.88 : 1 | 8.4% | |
| 1 | 46.00 : 1 | 2.1% | 45.00 : 1 | 2.2% | 22.50 : 1 | 4.3% |
| You have NO ACE in your hand.Chances in 1000 Total Hands Dealt | |||
| Number of Other Players | # Hands w Pair of Aces Dealt | # Hands w NO Pair of Aces Dealt | Frequency Shown in Percentages: Pr. Aces/ NO Aces |
| 9 | 41 | 959 | 4.1% / 95.9% |
| 8 | 36 | 964 | 3.6% / 96.4% |
| 7 | 32 | 968 | 3.2% / 96.8% |
| 6 | 27 | 973 | 2.7% / 97.3% |
| 5 | 23 | 977 | 2.3% / 97.7% |
| 4 | 18 | 982 | 1.8% / 98.2% |
| 3 | 14 | 986 | 1.4% / 98.6% |
| 2 | 9 | 991 | 0.90% / 99.1% |
| 1 | 5 | 995 | 0.45% / 99.5% |
| You have ONE ACE in your handChances in 1000 Total Hands Dealt | |||
| Number of Other Players | # Hands w Pair of Aces Dealt | # Hands w NO Pair of Aces Dealt | Frequency Shown in Percentages: Pr. Aces/ NO Aces |
| 9 | 24 | 976 | 2.4% / 97.6% |
| 8 | 21 | 979 | 2.1% / 97.9% |
| 7 | 19 | 981 | 1.9% / 98.1% |
| 6 | 16 | 984 | 1.6% / 98.4% |
| 5 | 13 | 987 | 1.3% / 98.7% |
| 4 | 11 | 989 | 1.1% / 98.9% |
| 3 | 8 | 992 | 0.80% / 99.2% |
| 2 | 5 | 995 | 0.53% / 99.5% |
| 1 | 3 | 997 | 0.26% / 99.7% |
| You have NO ACE in your hand.Chances in 1000 Total Hands Dealt | |||
| Number of Other Players | # Hands w 1 or More Aces Dealt | # Hands w NO Aces Dealt | Frequency Shown in Percentages: Aces(s)/ NO Aces |
| 9 | 844 | 156 | 84.4% / 15.6% |
| 8 | 799 | 201 | 79.9% / 20.1% |
| 7 | 744 | 256 | 74.4% / 25.6% |
| 6 | 680 | 320 | 68.0% /32.0% |
| 5 | 603 | 397 | 60.3% / 39.7% |
| 4 | 514 | 486 | 51.4% / 48.6% |
| 3 | 411 | 589 | 41.1% / 58.9% |
| 2 | 291 | 709 | 29.1% / 70.9% |
| 1 | 155 | 845 | 15.5% / 84.5% |
| You have ONE ACE in your handChances in 1000 Total Hands Dealt | |||
| Number of Other Players | # Hands w 1 or More Aces Dealt | # Hands w NO Aces Dealt | Frequency Shown in Percentages: Aces(s)/ NO Aces |
| 9 | 747 | 253 | 74.7% / 25.3% |
| 8 | 695 | 305 | 69.5% / 30.5% |
| 7 | 636 | 364 | 63.6% / 36.4% |
| 6 | 570 | 430 | 57.0% / 43.0% |
| 5 | 496 | 504 | 49.6% / 50.4% |
| 4 | 414 | 586 | 41.4% / 58.6% |
| 3 | 324 | 676 | 32.4% / 67.6% |
| 2 | 226 | 774 | 22.6% / 77.4% |
| 1 | 118 | 882 | 11.8% / 88.2% |
| The Probabilities of Being Dealt Pairs 1326 Possible Hold`em Hands | ||
| Pair(s) / Combinations | % Of Total | Odds Against |
| AA or any specific pair / 6 | 0.45% | 220 to 1 |
| KK or higher pair / 12 | 0.90% | 110 to 1 |
| QQ or higher pair / 18 | 1.36% | 72.5 to 1 |
| JJ or higher pair / 24 | 1.81% | 54.2 to 1 |
| TT or higher pair / 30 | 2.27% | 43 to 1 |
| 99 or higher pair / 36 | 2.71% | 35.8 to 1 |
| 88 or higher pair / 42 | 3.17% | 30.5 to 1 |
| 77 or higher pair / 48 | 3.62% | 26.6 to 1 |
| 66 or higher pair / 54 | 4.07% | 23.6 to 1 |
| 55 or higher pair / 60 | 4.52% | 21.1 to 1 |
| 44 or higher pair / 66 | 5.00% | 19 to 1 |
| 33 or higher pair / 72 | 5.43% | 17.4 to 1 |
| 22 or higher pair (any pair) / 78 | 5.88% | 16 to 1 |
| The Probabilities of Being Dealt Various High Card Hands High Cards= A-10 . . 1326 Possible Hold`em Hands | ||
| High Card Hands / Combinations | % Of Total | Odds Against |
| AK suited / 4 | 0.30% | 331 to 1 |
| AK off-suite / 12 | 0.90% | 110 to 1 |
| Any AK / 16 | 1.2% | 82 to 1 |
| A w/ Q, J, or T suited / 12 | 0.90% | 110 to 1 |
| A w/ Q, J, or T off-suite / 36 | 2.71% | 36 to 1 |
| K w/ Q, J, or T suited / 12 | 0.90% | 110 to 1 |
| K w/ Q, J, or T off-suite / 36 | 2.71% | 36 to 1 |
| Q w/ J, or T suited / 8 | 0.60% | 116 to 1 |
| Q w/ J, or T off-suite / 24 | 1.81% | 54 to 1 |
| J, T suited / 4 | 0.30% | 331 to 1 |
| J, T off-suite / 12 | 0.90% | 110 to 1 |
| Any 2 unpaired high cards / 160 | 12.01% | 7.3 to 1 |
| Probabilities of Various Types of Flops Each category is individually compared to the 22,100 possible three card combinations | |||
| Flops With These Properties / Examples | Number Of Combinations | Probabilities For 1000 Dealt Flops | Shown In Percentages |
| Three of a Kind ie: 7, 7, 7 | 52 | 2 | 0.24% |
| Three Cards Suited ie: 3h, 6h, 10h | 1144 | 52 | 5.2% |
| Three Card Straight ie: 10, J, Q | 768 | 35 | 3.5% |
| Pair ie: 5, 5, x | 3744 | 169 | 16.9% |
| Two Cards Suited ie: 4d, 9d, x | 12168 | 550 | 55.0% |
| No Gap Connector, only, to a Straight ie: 9, 10, x | 10400 | 471 | 47.1% |
| One Gap Connector, only, to a Straight ie: 8, 10, x | 6144 | 278 | 27.8% |
| Three High Card Denominations ie: J, K, A | 640 | 29 | 2.9% |
| Two, only, High Card Denominations ie: 10, K, x | 5120 | 232 | 23.2% |
| One, only, High Card Denomination ie: Q, x, x | 9920 | 449 | 44.9% |
| None of the Above | 96 | 4 | 0.43% |
| Backdoor Straight Draws | |||
| You Have, In Your Five Cards After The Flop | No. Of Two Card Combinations | Percent % | Odds Against Approx. |
| 3 Card Straight – No Ace – ie: 4,5,6 | 48 | 4.4% | 22 to 1 |
| 3 Card Straight – With Ace – ie: A,2,3 . .Q,K,A | 16 | 1.5% | 66 to 1 |
| 3 Cards to a Straight – 1 Gap – No Ace – ie: 6,7,9 | 32 | 3.0% | 32 to 1 |
| 3 Cards to a Straight – 1 Gap – With Ace – ie: A,2,4 . .J,Q,A | 16 | 1.5% | 66 to 1 |
| 3 Cards to a Straight – 2 Gaps – ie: A,4,5 . .7,10,J . .7,9,J | 16 | 1.5% | 66 to 1 |
| Backdoor Straight Flush Draws | |||
| You Have, In Your Five Cards After The Flop | No. Of Two Card Combinations | Percent % | Odds Against Approx. |
| 3 Card Straight Flush – No Ace – ie: 4d,5d,6d | 3 | 0.28% | 356 to 1 |
| 3 Card Straight Flush – With Ace – ie: Ah,2h,3h . .Qs,Ks,As | 1 | 0.09% | 1080 to 1 |
| 3 Cards to a Str. Fl. – 1 Gap – No Ace – ie: 6d,7d,9d | 2 | 0.18% | 539 to 1 |
| 3 Cards to a Str. Fl. – 1 Gap – With Ace – ie: Ah,2h,4h . Jd,Qd,Ad | 1 | 0.09% | 1080 to 1 |
| 3 Cards to a Str. Fl.- 2 Gaps – ie: Ac,4c,5c .7s,10s,Js .7d,9d,Jd | 1 | 0.09% | 1080 to 1 |
| Situation | Hands | Odds | Percent |
| Higher pair vs. lower pair | Js Jc vs. 7h 7d | 4.09 : 1 | 80.3% vs. 19.7% |
| Pair vs. two higher cards | 7s 7c vs. Ah Jd | 1.23 : 1 | 55.1% vs. 44.9% |
| Pair vs. two lower card | Qs Qc vs. 9h 7d | 4.77 : 1 | 82.7% vs. 17.3% |
| Pair vs. a higher and a lower card | Js Jc vs. Ah 7d | 2.50 : 1 | 71.4% vs. 28.6% |
| Two higher cards vs. two lower cards | Qs Jc vs. 6h 5d | 1.70 : 1 | 62.9% vs. 37.1% |
| A higher and a lower card vs. two middle cards | As 6c vs. Jh 9d | 1.27 : 1 | 55.9% vs. 44.1% |
| Highest and 3rd highest card vs. lowest | As 6c vs. Jh 2d | 1.73 : 1 | 63.3% vs. 36.7% |
| Highest and common card vs. lowest and common | As Jc vs. Jh 9d | 2.74 : 1 | 73.3% vs. 26.7% |
| Chances of Hitting on Flop | Probability |
| Pocket Pair Into a Set Pocket | 8% |
| Pair Turning Into A Set On Turn | 4% |
| Hitting Pair on Flop | 32% |
| Flopping Four To Flush | 11% |
| Chances of Board Coming All Same | 0.004% |
| Situation – Chances someone hit top pair on board | Probability |
| 5 players see flop | 58% |
| 4 players see flop | 47% |
| 3 players see flop | 35% |
| 2 player see flop | 23% |
| Before Any Cards Are Dealt – Chances of Getting | Probability |
| Royal Flush (All Spades) | 0.0002% |
| Straight Flush (Any same suits) | 0.0012% |
| Four of a Kind (Quads) | 0.0239% |
| Full House (Boat) | 0.144% |
| Flush (all same suit) | 0.19% |
| Straight | 0.35% |
| Three of a Kind | 2.11% |
| Two Pair | 4.7% |
| One Pair | 42% |
| Don’t catch anything | 50% |