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Video Poker Strategy Calculator
Introduction
The following table shows the results when following perfect strategy (basic strategy and all of the exceptions):
| Perfect Strategy Analysis | ||||||
|---|---|---|---|---|---|---|
| Hand | Payoff | Combinations | Probability | Hit Frequency | Variance | Return |
| Royal Flush | 800 | 477,905,592 | 0.000024 | 41,709.56 | 15.31 | 0.019180 |
| Straight Flush | 50 | 2,167,478,628 | 0.000109 | 9,196.51 | 0.26 | 0.005437 |
| Four Aces with any 2,3,4 | 400 | 1,201,420,908 | 0.000060 | 16,591.38 | 9.60 | 0.024109 |
| Four Aces with any J,Q,K | 320 | 1,261,846,488 | 0.000063 | 15,796.87 | 6.44 | 0.020257 |
| Four 2's, 3's, 4's with any A,2,3,4 | 160 | 2,924,360,292 | 0.000147 | 6,816.27 | 3.71 | 0.023473 |
| Four J's, Q's, K's with any J,Q,K,A | 160 | 3,866,393,568 | 0.000194 | 5,155.51 | 4.90 | 0.031035 |
| Four Aces | 160 | 2,214,677,664 | 0.000111 | 9,000.51 | 2.81 | 0.017777 |
| Four 2's, 3's, 4's | 80 | 7,874,359,224 | 0.000395 | 2,531.41 | 2.47 | 0.031603 |
| Four 5's through K's | 50 | 27,739,345,860 | 0.001392 | 718.59 | 3.34 | 0.069581 |
| Full House | 7 | 210,593,130,372 | 0.010565 | 94.65 | 0.38 | 0.073954 |
| Flush | 6 | 224,213,751,720 | 0.011248 | 88.90 | 0.28 | 0.067489 |
| Straight | 4 | 250,348,316,388 | 0.012559 | 79.62 | 0.11 | 0.050237 |
| Three of a Kind | 3 | 1,509,438,225,228 | 0.075725 | 13.21 | 0.30 | 0.227174 |
| Two Pair | 1 | 2,457,560,812,572 | 0.123290 | 8.11 | 0.00 | 0.123290 |
| Jacks or Better | 1 | 4,236,518,487,276 | 0.212535 | 4.71 | 0.00 | 0.212535 |
| Nothing | 0 | 10,994,830,005,420 | 0.551583 | 1.81 | 0.55 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.23 | 50.46 | 0.997132 | |
The following table shows the results when following basic strategy only (not its exceptions):
| Basic Strategy Analysis | ||||||
|---|---|---|---|---|---|---|
| Hand | Payoff | Combinations | Probability | Hit Frequency | Variance | Return |
| Royal Flush | 800 | 475,400,412 | 0.000024 | 41,929.35 | 15.23 | 0.019080 |
| Straight Flush | 50 | 2,164,416,168 | 0.000109 | 9,209.52 | 0.26 | 0.005429 |
| Four Aces with any 2,3,4 | 400 | 1,209,061,320 | 0.000061 | 16,486.53 | 9.66 | 0.024262 |
| Four Aces with any J,Q,K | 320 | 1,268,704,128 | 0.000064 | 15,711.49 | 6.48 | 0.020367 |
| Four 2's, 3's, 4's with any A,2,3,4 | 160 | 2,925,791,676 | 0.000147 | 6,812.94 | 3.71 | 0.023485 |
| Four J's, Q's, K's with any J,Q,K,A | 160 | 3,852,906,360 | 0.000193 | 5,173.56 | 4.89 | 0.030926 |
| Four Aces | 160 | 2,230,468,296 | 0.000112 | 8,936.79 | 2.83 | 0.017904 |
| Four 2's, 3's, 4's | 80 | 7,874,798,856 | 0.000395 | 2,531.27 | 2.47 | 0.031605 |
| Four 5's through K's | 50 | 27,744,822,168 | 0.001392 | 718.45 | 3.34 | 0.069594 |
| Full House | 7 | 210,643,099,812 | 0.010567 | 94.63 | 0.38 | 0.073972 |
| Flush | 6 | 224,045,858,220 | 0.011240 | 88.97 | 0.28 | 0.067439 |
| Straight | 4 | 251,481,678,396 | 0.012616 | 79.26 | 0.11 | 0.050465 |
| Three of a Kind | 3 | 1,509,855,014,940 | 0.075746 | 13.20 | 0.30 | 0.227237 |
| Two Pair | 1 | 2,457,217,360,908 | 0.123272 | 8.11 | 0.00 | 0.123272 |
| Jacks or Better | 1 | 4,226,440,953,096 | 0.212030 | 4.72 | 0.00 | 0.212030 |
| Nothing | 0 | 11,003,800,182,444 | 0.552033 | 1.81 | 0.55 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.23 | 50.48 | 0.997067 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | (more)Four J's, Q's, K's with any J,Q,K,A; Four 2's, 3's, 4's with an... |
| 4 of a Kind | (more)2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK... |
| 4 to a Royal Flush | TJQA; TJQK; TJKA; TQKA; JQKA |
| 3 of a Kind | 222; 333; 444; AAA |
| Pat Hand | Straight; Flush; Full House |
| 3 of a Kind + 1 Kicker | JJJQ; JJJK; JJJA; QQQJ; QQQK; QQQA; KKKJ; KKKQ; KKKA |
| 3 of a Kind | 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK |
| 4 to a Straight Flush | (more)A234; A235; A245; A345; 2345; 2346; 2356; 2456; 3456; 3457; 3467; 3567... |
| 1 Pair | AA |
| 2 Pair | (more)2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 22JJ; 22QQ; 22KK; 3344... |
| 1 Pair | JJ; QQ; KK |
| 4 to a Flush | (more)2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J... |
| 3 to a Royal Flush | TJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA |
| 4 to a Straight | 89TJ; 9TJQ; TJQK |
| 1 Pair | 22; 33; 44; 88; 99; TT |
| 3 to a Straight Flush | 9JQ |
| 1 Pair | 55; 66; 77 |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T |
| 3 to a Straight Flush | 345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TJ; 9TQ; 9JK; 9QK |
| 4 to a Straight | JQKA |
| 2 to a Royal Flush | JA; JQ; JK; QA; QK; KA |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 3 to a Straight Flush | (more)A23; A24; A25; A34; A35; A45; 234; 235; 245; 346; 356; 457; 467; 568... |
| 3 to a Straight | JQK |
| 4 to a Straight | 89JQ; 8TJQ; 9TJK; 9TQK |
| Single Card | an Ace |
| 2 to a Straight | JQ; JK; QK |
| 2 to a Royal Flush | TJ; TQ |
| Single Card | a Jack; a Queen; a King |
| 3 to a Straight Flush | 236; 246; 256; 347; 357; 367; 458; 468; 478; 569; 579; 589; 67T; 68T; 69T |
| 4 to a Straight | (more)2346; 2356; 2456; 3457; 3467; 3567; 4568; 4578; 4678; 5679; 5689; 5789... |
| Garbage | Discard everything |
The following table shows the exceptions to the basic strategy:
| Basic Strategy Exceptions | ||
|---|---|---|
| Right Play | Wrong Play | Pattern(s) |
| 2 to a Straight: JQ | Single Card: an Ace | |
| 2 to a Royal Flush: TK | Single Card: a King | |
| 2 to a Straight: JQ | 4 to a Straight: 89JQ | |
| 2 to a Straight: JK | Single Card: an Ace | |
| 2 to a Straight: QK | Single Card: an Ace | |
| 2 to a Royal Flush: TJ | 2 to a Straight: JK | |
| 2 to a Straight: JA | Single Card: an Ace | |
| 2 to a Straight: QA | Single Card: an Ace | |
| 2 to a Straight: KA | Single Card: an Ace | |
| Single Card: a Queen | 2 to a Royal Flush: TQ | |
| 2 to a Royal Flush: TJ | Single Card: an Ace | |
| Single Card: an Ace | 3 to a Straight Flush: 235 | 2♣ 3♣ 5♣ 6♦ A♥ |
| Single Card: an Ace | 3 to a Straight Flush: 245 | 2♣ 4♣ 5♣ 6♦ A♥ |