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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 | 407,996,136 | 0.000020 | 48,856.42 | 13.07 | 0.016375 |
| Straight Flush | 40 | 2,246,820,576 | 0.000113 | 8,871.75 | 0.17 | 0.004509 |
| Four of a Kind | 20 | 46,408,342,368 | 0.002328 | 429.52 | 0.84 | 0.046564 |
| Full House | 8 | 225,551,321,712 | 0.011315 | 88.38 | 0.55 | 0.090523 |
| Flush | 8 | 337,669,884,048 | 0.016940 | 59.03 | 0.83 | 0.135520 |
| Straight | 4 | 211,428,761,496 | 0.010607 | 94.28 | 0.10 | 0.042427 |
| Three of a Kind | 3 | 1,447,605,621,228 | 0.072623 | 13.77 | 0.29 | 0.217868 |
| Two Pair | 2 | 2,512,952,292,996 | 0.126068 | 7.93 | 0.13 | 0.252137 |
| Jacks or Better | 1 | 3,869,317,270,692 | 0.194114 | 5.15 | 0.00 | 0.194114 |
| Nothing | 0 | 11,279,642,205,948 | 0.565871 | 1.77 | 0.57 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.30 | 16.54 | 1.000037 | |
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 | 408,674,160 | 0.000021 | 48,775.36 | 13.09 | 0.016402 |
| Straight Flush | 40 | 2,247,577,548 | 0.000113 | 8,868.76 | 0.17 | 0.004510 |
| Four of a Kind | 20 | 46,395,103,872 | 0.002328 | 429.64 | 0.84 | 0.046551 |
| Full House | 8 | 225,510,380,208 | 0.011313 | 88.39 | 0.55 | 0.090506 |
| Flush | 8 | 337,509,833,232 | 0.016932 | 59.06 | 0.83 | 0.135456 |
| Straight | 4 | 211,357,623,156 | 0.010603 | 94.31 | 0.10 | 0.042413 |
| Three of a Kind | 3 | 1,447,151,300,256 | 0.072600 | 13.77 | 0.29 | 0.217800 |
| Two Pair | 2 | 2,512,463,070,816 | 0.126044 | 7.93 | 0.13 | 0.252088 |
| Jacks or Better | 1 | 3,873,152,267,316 | 0.194306 | 5.15 | 0.00 | 0.194306 |
| Nothing | 0 | 11,277,034,686,636 | 0.565740 | 1.77 | 0.57 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.30 | 16.56 | 1.000032 | |
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... |
| 4 to a Flush | (more)2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J... |
| 3 to a Royal Flush | TJQ; JQK |
| 1 Pair | JJ; QQ; KK; AA |
| 3 to a Royal Flush | TJA; TJK; TQA; TQK; TKA; JQA; JKA; QKA |
| 4 to a Straight | 9TJQ; TJQK |
| 1 Pair | 88; 99; TT |
| 3 to a Straight Flush | 9JQ |
| 1 Pair | 22; 33; 44; 55; 66; 77 |
| 3 to a Straight Flush | 7TJ; 8JQ; 9TJ; 9TQ; 9QK |
| 4 to a Straight | 2345; 3456; 4567; 5678; 789T; 89TJ |
| 3 to a Straight Flush | 345; 456; 567; 89T; 89J; 8TJ; 8TQ; 9TK; 9JK |
| 4 to a Straight | 6789 |
| 3 to a Straight Flush | 678; 789; 78J; 79J |
| 3 to a Flush | (more)2JA; 2JQ; 2JK; 2QA; 2QK; 2KA; 3JA; 3JQ; 3JK; 3QA; 3QK; 3KA; 4JA; 4JQ... |
| 2 to a Royal Flush | JQ; JK; QK |
| 4 to a Straight | JQKA |
| 2 to a Royal Flush | JA; QA |
| 3 to a Straight Flush | A23; A24; A25; A34; A35; A45; 89Q |
| 2 to a Royal Flush | KA |
| 3 to a Straight Flush | (more)234; 235; 245; 346; 356; 457; 467; 568; 578; 589; 679; 67T; 689; 68T... |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 3 to a Flush | (more)23J; 23Q; 23K; 24J; 24Q; 24K; 25J; 25Q; 25K; 26A; 26J; 26Q; 26K; 27A... |
| 2 to a Royal Flush | TJ |
| 3 to a Straight | JQK |
| 3 to a Straight Flush | 458; 468; 478; 569; 579 |
| 2 to a Straight | JQ |
| 2 to a Royal Flush | TQ |
| 3 to a Straight Flush | 236; 246; 256; 347; 357; 367 |
| 2 to a Straight | JK; QK |
| 2 to a Straight | JA; QA |
| 2 to a Royal Flush | TK |
| Single Card | a Jack; a Queen |
| 2 to a Straight | KA |
| 2 to a Royal Flush | TA |
| Single Card | a King; an Ace |
| 3 to a Flush | (more)237; 238; 239; 23T; 247; 248; 249; 24T; 257; 258; 259; 25T; 267; 268... |
| Garbage | Discard everything |
The following table shows the exceptions to the basic strategy:
| Basic Strategy Exceptions | ||
|---|---|---|
| Right Play | Wrong Play | Pattern(s) |
| Single Card: a Jack | 2 to a Straight: JA | |
| 1 Pair: JJ | 3 to a Royal Flush: TJQ | |
| 1 Pair: QQ | 3 to a Royal Flush: TJQ | |
| 4 to a Straight: 89TJ | 3 to a Straight Flush: 9TJ | |
| 3 to a Straight Flush: 236 | 2 to a Straight: JQ | 2♣ 3♣ 6♣ J♦ Q♥ |
| 3 to a Straight Flush: 246 | 2 to a Straight: JQ | 2♣ 4♣ 6♣ J♦ Q♥ |
| 3 to a Straight Flush: 256 | 2 to a Straight: JQ | 2♣ 5♣ 6♣ J♦ Q♥ |
| 3 to a Straight Flush: 347 | 2 to a Straight: JQ | 3♣ 4♣ 7♣ J♦ Q♥ |
| 3 to a Straight Flush: 357 | 2 to a Straight: JQ | 3♣ 5♣ 7♣ J♦ Q♥ |
| 3 to a Straight Flush: 367 | 2 to a Straight: JQ | 3♣ 6♣ 7♣ J♦ Q♥ |