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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 | 500,939,052 | 0.000025 | 39,791.73 | 16.04 | 0.020105 |
| Straight Flush | 50 | 2,100,881,124 | 0.000105 | 9,488.03 | 0.25 | 0.005270 |
| Four Aces | 160 | 4,227,828,456 | 0.000212 | 4,714.77 | 5.36 | 0.033936 |
| Four 2's, 3's, 4's | 80 | 10,805,737,116 | 0.000542 | 1,844.69 | 3.38 | 0.043368 |
| Four 5's through K's | 25 | 32,637,746,136 | 0.001637 | 610.74 | 0.94 | 0.040934 |
| Full House | 6 | 221,816,724,732 | 0.011128 | 89.86 | 0.28 | 0.066768 |
| Flush | 5 | 218,528,448,744 | 0.010963 | 91.22 | 0.17 | 0.054815 |
| Straight | 4 | 222,049,864,176 | 0.011140 | 89.77 | 0.10 | 0.044559 |
| Three of a Kind | 3 | 1,498,821,724,476 | 0.075192 | 13.30 | 0.30 | 0.225576 |
| Two Pair | 2 | 2,584,323,520,380 | 0.129649 | 7.71 | 0.13 | 0.259298 |
| Jacks or Better | 1 | 4,218,354,616,968 | 0.211624 | 4.73 | 0.00 | 0.211624 |
| Nothing | 0 | 10,919,062,485,840 | 0.547782 | 1.83 | 0.55 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.21 | 27.52 | 1.006252 | |
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 | 497,894,136 | 0.000025 | 40,035.08 | 15.95 | 0.019982 |
| Straight Flush | 50 | 2,095,039,488 | 0.000105 | 9,514.49 | 0.25 | 0.005255 |
| Four Aces | 160 | 4,277,510,484 | 0.000215 | 4,660.01 | 5.42 | 0.034335 |
| Four 2's, 3's, 4's | 80 | 10,808,900,712 | 0.000542 | 1,844.15 | 3.38 | 0.043380 |
| Four 5's through K's | 25 | 32,632,611,936 | 0.001637 | 610.84 | 0.94 | 0.040927 |
| Full House | 6 | 221,953,184,028 | 0.011135 | 89.81 | 0.28 | 0.066809 |
| Flush | 5 | 218,713,025,556 | 0.010972 | 91.14 | 0.18 | 0.054861 |
| Straight | 4 | 220,900,551,576 | 0.011082 | 90.24 | 0.10 | 0.044328 |
| Three of a Kind | 3 | 1,500,385,878,372 | 0.075271 | 13.29 | 0.30 | 0.225812 |
| Two Pair | 2 | 2,585,867,028,084 | 0.129726 | 7.71 | 0.13 | 0.259453 |
| Jacks or Better | 1 | 4,206,902,604,300 | 0.211050 | 4.74 | 0.00 | 0.211050 |
| Nothing | 0 | 10,928,196,288,528 | 0.548240 | 1.82 | 0.56 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.21 | 27.48 | 1.006193 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | Straight Flush; Royal Flush |
| 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 | 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK |
| 2 Pair | (more)2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 22JJ; 22QQ; 22KK; 22AA... |
| 4 to a Straight Flush | (more)A234; A235; A245; A345; 2345; 2346; 2356; 2456; 3456; 3457; 3467; 3567... |
| 1 Pair | JJ; QQ; KK; AA |
| 3 to a Royal Flush | TJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA |
| 4 to a Flush | (more)2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J... |
| 4 to a Straight | 9TJQ; TJQK |
| 1 Pair | 22; 33; 44; 55; 66; 77; 88; 99; TT |
| 3 to a Straight Flush | 8JQ; 9JQ |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; JQKA |
| 3 to a Straight Flush | 89J; 8TJ; 9TJ; 9TQ; 9JK; 9QK |
| 2 to a Royal Flush | JA; JQ; JK; QA; QK |
| 3 to a Straight Flush | A23; A24; A25; A34; A35; A45; 456; 567; 678; 789; 89T |
| 2 to a Royal Flush | KA |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 3 to a Straight | JQK |
| 3 to a Straight Flush | 345; 7TJ; 9TK |
| 2 to a Straight | JQ |
| 3 to a Straight Flush | 78J; 79J; 89Q; 8TQ |
| 2 to a Straight | JK |
| Single Card | an Ace |
| 2 to a Royal Flush | TJ |
| 3 to a Straight Flush | 234; 235; 245; 346; 356; 457; 467; 568; 578; 679; 689; 78T; 79T |
| 2 to a Straight | JA; QK |
| 2 to a Royal Flush | 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 |
| 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: QK | Single Card: an Ace | |
| 2 to a Straight: QA | Single Card: an Ace | |
| 2 to a Straight: KA | Single Card: an Ace | |
| 2 to a Straight: JA | Single Card: an Ace | |
| 2 to a Royal Flush: TK | Single Card: a King | |
| 2 to a Royal Flush: TJ | 2 to a Straight: JK | |
| Single Card: an Ace | 2 to a Straight: JK | |
| 2 to a Royal Flush: TJ | Single Card: an Ace | |
| Single Card: an Ace | 3 to a Straight Flush: A23 | |
| Single Card: an Ace | 3 to a Straight Flush: A24 | |
| Single Card: an Ace | 3 to a Straight Flush: A25 | |
| Single Card: an Ace | 3 to a Straight Flush: A34 | |
| Single Card: an Ace | 3 to a Straight Flush: A35 | |
| Single Card: an Ace | 3 to a Straight Flush: A45 | |
| 3 to a Straight Flush: 79J | 2 to a Straight: JQ | |
| 3 to a Straight Flush: 457 | Single Card: an Ace | |
| 3 to a Straight Flush: 467 | Single Card: an Ace | |
| 3 to a Straight Flush: 346 | Single Card: an Ace | |
| 3 to a Straight Flush: 356 | Single Card: an Ace | |
| 3 to a Straight Flush: 568 | Single Card: an Ace | |
| 3 to a Straight Flush: 578 | Single Card: an Ace | |
| 3 to a Straight Flush: 78T | Single Card: an Ace | |
| 3 to a Straight Flush: 79T | Single Card: an Ace | |
| 3 to a Straight Flush: 679 | Single Card: an Ace | |
| 3 to a Straight Flush: 689 | Single Card: an Ace | |
| Single Card: an Ace | 3 to a Straight Flush: 7TJ | |
| Single Card: an Ace | 3 to a Straight Flush: 78J | |
| Single Card: an Ace | 3 to a Straight Flush: 79J | |
| Single Card: a Jack | 3 to a Straight Flush: 356 | |
| Single Card: a Jack | 3 to a Straight Flush: 78T | |
| Single Card: a Jack | 3 to a Straight Flush: 79T | |
| 2 to a Straight: JK | 3 to a Straight Flush: 78J | |
| 2 to a Straight: JK | 3 to a Straight Flush: 79J | |
| 2 to a Straight: JQ | 3 to a Straight Flush: 7TJ | |
| Single Card: an Ace | 3 to a Straight Flush: 8TQ | |
| 3 to a Straight Flush: 78J | 2 to a Straight: JQ | 7♣ 8♣ J♣ Q♦ A♥ |
| 3 to a Straight Flush: 234 | 2 to a Straight: JK | 2♣ 3♣ 4♣ J♦ K♥ |
| 3 to a Straight Flush: 235 | 2 to a Straight: JK | 2♣ 3♣ 5♣ J♦ K♥ |
| 3 to a Straight Flush: 245 | 2 to a Straight: JK | 2♣ 4♣ 5♣ J♦ K♥ |
| 3 to a Straight Flush: 346 | 2 to a Straight: JK | 3♣ 4♣ 6♣ J♦ K♥ |
| 3 to a Straight Flush: 356 | 2 to a Straight: JK | 3♣ 5♣ 6♣ J♦ K♥ |
| 3 to a Straight Flush: 457 | 2 to a Straight: JK | 4♣ 5♣ 7♣ J♦ K♥ |
| 3 to a Straight Flush: 467 | 2 to a Straight: JK | 4♣ 6♣ 7♣ J♦ K♥ |
| 3 to a Straight Flush: 568 | 2 to a Straight: JK | 5♣ 6♣ 8♣ J♦ K♥ |
| 3 to a Straight Flush: 578 | 2 to a Straight: JK | 5♣ 7♣ 8♣ J♦ K♥ |
| 3 to a Straight Flush: 679 | 2 to a Straight: JK | 6♣ 7♣ 9♣ J♦ K♥ |
| 3 to a Straight Flush: 689 | 2 to a Straight: JK | 6♣ 8♣ 9♣ J♦ K♥ |
| Single Card: a Jack | 3 to a Straight Flush: 234 | 2♣ 3♣ 4♣ 6♦ J♥ |
| Single Card: a Jack | 3 to a Straight Flush: 235 | 2♣ 3♣ 5♣ 6♦ J♥ |
| Single Card: a Jack | 3 to a Straight Flush: 245 | 2♣ 4♣ 5♣ 6♦ J♥ |
| Single Card: a Jack | 3 to a Straight Flush: 346 | 2♣ 3♦ 4♦ 6♦ J♥ |
| Single Card: an Ace | 3 to a Straight Flush: 89Q | 8♣ 9♣ 10♦ Q♣ A♥ |
| 3 to a Straight Flush: 568 | 2 to a Royal Flush: TJ | 5♣ 6♣ 8♣ 10♦ J♦ |
| 3 to a Straight Flush: 578 | 2 to a Royal Flush: TJ | 5♣ 7♣ 8♣ 10♦ J♦ |
| 3 to a Straight Flush: 789 | 2 to a Royal Flush: QK | 7♣ 8♣ 9♣ Q♦ K♦ |
| 3 to a Straight Flush: 456 | 2 to a Royal Flush: JA | 4♣ 5♣ 6♣ J♦ A♦ |
| 3 to a Straight Flush: 567 | 2 to a Royal Flush: JA | 5♣ 6♣ 7♣ J♦ A♦ |
| 3 to a Straight Flush: 678 | 2 to a Royal Flush: JA | 6♣ 7♣ 8♣ J♦ A♦ |
| 3 to a Straight Flush: 456 | 2 to a Royal Flush: QA | 4♣ 5♣ 6♣ Q♦ A♦ |
| 3 to a Straight Flush: 567 | 2 to a Royal Flush: QA | 5♣ 6♣ 7♣ Q♦ A♦ |
| 3 to a Straight Flush: 678 | 2 to a Royal Flush: QA | 6♣ 7♣ 8♣ Q♦ A♦ |
| 3 to a Straight Flush: 789 | 2 to a Royal Flush: QA | 7♣ 8♣ 9♣ Q♦ A♦ |