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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 | 440 | 410,461,032 | 0.000021 | 48,563.03 | 3.97 | 0.009060 |
| Straight Flush | 50 | 2,125,744,584 | 0.000107 | 9,377.06 | 0.26 | 0.005332 |
| Four of a Kind | 25 | 47,096,050,140 | 0.002363 | 423.25 | 1.36 | 0.059067 |
| Full House | 9 | 229,367,862,540 | 0.011507 | 86.91 | 0.74 | 0.103561 |
| Flush | 6 | 233,782,985,124 | 0.011728 | 85.26 | 0.29 | 0.070370 |
| Straight | 4 | 221,217,479,808 | 0.011098 | 90.11 | 0.10 | 0.044392 |
| Three of a Kind | 3 | 1,482,740,547,840 | 0.074385 | 13.44 | 0.30 | 0.223156 |
| Two Pair | 2 | 2,572,968,359,880 | 0.129079 | 7.75 | 0.13 | 0.258159 |
| Jacks or Better | 1 | 4,274,704,495,008 | 0.214451 | 4.66 | 0.00 | 0.214451 |
| Nothing | 0 | 10,868,816,531,244 | 0.545261 | 1.83 | 0.53 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.20 | 7.69 | 0.987549 | |
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 | 440 | 399,687,984 | 0.000020 | 49,871.98 | 3.86 | 0.008823 |
| Straight Flush | 50 | 2,120,204,808 | 0.000106 | 9,401.56 | 0.26 | 0.005318 |
| Four of a Kind | 25 | 47,082,167,676 | 0.002362 | 423.37 | 1.36 | 0.059050 |
| Full House | 9 | 229,223,229,804 | 0.011500 | 86.96 | 0.74 | 0.103496 |
| Flush | 6 | 238,188,899,628 | 0.011949 | 83.69 | 0.30 | 0.071696 |
| Straight | 4 | 220,405,080,120 | 0.011057 | 90.44 | 0.10 | 0.044229 |
| Three of a Kind | 3 | 1,481,592,024,720 | 0.074328 | 13.45 | 0.30 | 0.222983 |
| Two Pair | 2 | 2,570,439,033,144 | 0.128952 | 7.75 | 0.13 | 0.257905 |
| Jacks or Better | 1 | 4,266,120,720,456 | 0.214021 | 4.67 | 0.00 | 0.214021 |
| Nothing | 0 | 10,877,659,468,860 | 0.545705 | 1.83 | 0.53 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.20 | 7.59 | 0.987520 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | Full House; 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; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK; AAA |
| Pat Hand | Straight; Flush |
| 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 |
| 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 | TJQK |
| 1 Pair | 22; 33; 44; 55; 66; 77; 88; 99; TT |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ |
| 3 to a Straight Flush | 345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TJ; 9TQ; 9JQ; 9JK; 9QK |
| 4 to a Straight | JQKA |
| 3 to a Flush | (more)2JA; 2QA; 2KA; 3JA; 3QA; 3KA; 4JA; 4QA; 4KA; 5JA; 5QA; 5KA; 6JA; 6QA... |
| 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 |
| 2 to a Straight | JQ; JK; QK |
| 2 to a Straight | JA; QA; KA |
| Single Card | a Queen; a King |
| 2 to a Royal Flush | TJ; TQ |
| Single Card | a Jack; an Ace |
| 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 Royal Flush: TQ | Single Card: a Queen | |
| 2 to a Royal Flush: TJ | 2 to a Straight: JA | |
| Single Card: a Jack | 2 to a Royal Flush: TJ | |
| 2 to a Royal Flush: JA | 3 to a Flush: 2JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 3JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 4JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 5JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 6JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 7JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 8JA | |
| 2 to a Royal Flush: JA | 3 to a Flush: 9JA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 2QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 3QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 4QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 5QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 6QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 7QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 8QA | |
| 2 to a Royal Flush: QA | 3 to a Flush: 9QA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 2KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 3KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 4KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 5KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 6KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 7KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 8KA | |
| 2 to a Royal Flush: KA | 3 to a Flush: 9KA | |
| 3 to a Straight Flush: 79J | 4 to a Straight: 9JQK | 7♣ 9♣ J♣ Q♦ K♥ |
| 3 to a Straight Flush: 7TJ | 4 to a Straight: TJQA | 7♣ 10♣ J♣ Q♦ A♥ |
| 3 to a Straight Flush: 7TJ | 4 to a Straight: TJKA | 7♣ 10♣ J♣ K♦ A♥ |
| 3 to a Straight Flush: 8TQ | 4 to a Straight: TQKA | 8♣ 10♣ Q♣ K♦ A♥ |