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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 | 439,463,508 | 0.000022 | 45,358.10 | 14.07 | 0.017637 |
| Straight Flush | 50 | 2,348,724,720 | 0.000118 | 8,486.83 | 0.28 | 0.005891 |
| Four Aces with any 2,3,4 | 800 | 1,402,364,496 | 0.000070 | 14,214.02 | 44.91 | 0.056282 |
| Four 2's, 3's, 4's with any A,2,3,4 | 400 | 3,440,009,028 | 0.000173 | 5,794.53 | 27.47 | 0.069031 |
| Four Aces | 160 | 2,952,442,272 | 0.000148 | 6,751.44 | 3.74 | 0.023699 |
| Four 2's, 3's, 4's | 80 | 6,376,626,780 | 0.000320 | 3,125.98 | 2.00 | 0.025592 |
| Four 5's through K's | 50 | 31,673,324,076 | 0.001589 | 629.34 | 3.82 | 0.079449 |
| Full House | 9 | 206,321,656,284 | 0.010351 | 96.61 | 0.66 | 0.093156 |
| Flush | 7 | 311,320,443,672 | 0.015618 | 64.03 | 0.56 | 0.109327 |
| Straight | 4 | 252,218,322,636 | 0.012653 | 79.03 | 0.11 | 0.050613 |
| Three of a Kind | 2 | 1,468,173,074,448 | 0.073655 | 13.58 | 0.07 | 0.147309 |
| Two Pair | 1 | 2,390,581,734,264 | 0.119929 | 8.34 | 0.00 | 0.119929 |
| Jacks or Better | 1 | 3,944,045,609,748 | 0.197863 | 5.05 | 0.00 | 0.197863 |
| Nothing | 0 | 11,311,936,721,268 | 0.567491 | 1.76 | 0.56 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.31 | 98.28 | 0.995778 | |
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 | 434,954,424 | 0.000022 | 45,828.32 | 13.93 | 0.017456 |
| Straight Flush | 50 | 2,315,524,716 | 0.000116 | 8,608.52 | 0.28 | 0.005808 |
| Four Aces with any 2,3,4 | 800 | 1,403,108,040 | 0.000070 | 14,206.48 | 44.94 | 0.056312 |
| Four 2's, 3's, 4's with any A,2,3,4 | 400 | 3,440,641,692 | 0.000173 | 5,793.46 | 27.48 | 0.069043 |
| Four Aces | 160 | 2,954,889,672 | 0.000148 | 6,745.85 | 3.75 | 0.023718 |
| Four 2's, 3's, 4's | 80 | 6,376,579,260 | 0.000320 | 3,126.01 | 2.00 | 0.025592 |
| Four 5's through K's | 50 | 31,698,922,320 | 0.001590 | 628.83 | 3.82 | 0.079513 |
| Full House | 9 | 206,426,965,752 | 0.010356 | 96.56 | 0.66 | 0.093203 |
| Flush | 7 | 311,560,328,940 | 0.015630 | 63.98 | 0.56 | 0.109411 |
| Straight | 4 | 251,552,883,948 | 0.012620 | 79.24 | 0.11 | 0.050479 |
| Three of a Kind | 2 | 1,469,265,010,884 | 0.073709 | 13.57 | 0.07 | 0.147419 |
| Two Pair | 1 | 2,391,918,837,660 | 0.119997 | 8.33 | 0.00 | 0.119997 |
| Jacks or Better | 1 | 3,942,976,347,000 | 0.197809 | 5.06 | 0.00 | 0.197809 |
| Nothing | 0 | 11,310,905,522,892 | 0.567440 | 1.76 | 0.56 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.31 | 98.17 | 0.995761 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | (more)Four 2's, 3's, 4's with any A,2,3,4; Four Aces with any 2,3,4; Straigh... |
| 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 + 1 Kicker | 2223; 2224; 222A; 3332; 3334; 333A; 4442; 4443; 444A; AAA2; AAA3; AAA4 |
| 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 |
| 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... |
| 4 to a Flush | (more)2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J... |
| 3 to a Royal Flush | TJQ; TJK; TQK; JQA; JQK; JKA; QKA |
| 1 Pair | JJ; QQ; KK |
| 3 to a Royal Flush | TJA; TQA; TKA |
| 1 Pair | 22; 33; 44 |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ; TJQK |
| 3 to a Straight Flush | 789; 8JQ; 9TJ; 9JQ; 9JK; 9QK |
| 1 Pair | 88 |
| 3 to a Straight Flush | 456; 9TQ |
| 1 Pair | 77 |
| 3 to a Straight Flush | 345; 89J; 8TJ |
| 1 Pair | TT |
| 3 to a Straight Flush | 678 |
| 1 Pair | 66 |
| 3 to a Straight Flush | 89T |
| 1 Pair | 99 |
| 3 to a Straight Flush | 567 |
| 1 Pair | 55 |
| 4 to a Straight | JQKA |
| 3 to a Flush | (more)2JA; 2JQ; 2JK; 2QA; 2QK; 2KA; 3JA; 3JQ; 3JK; 3QA; 3QK; 3KA; 4JA; 4JQ... |
| 2 to a Royal Flush | JA; JQ; JK; QA; QK; KA |
| 3 to a Straight Flush | (more)A23; A24; A25; A34; A35; A45; 234; 235; 245; 346; 356; 457; 467; 568... |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 3 to a Straight Flush | 89Q; 8TQ; 9TK |
| 3 to a Straight | JQK |
| 4 to a Straight | 89JQ; 8TJQ; 9TJK; 9TQK |
| Single Card | an Ace |
| 3 to a Flush | (more)23J; 23Q; 24J; 24Q; 25J; 25Q; 26A; 26J; 26Q; 27A; 27J; 27Q; 27K; 28A... |
| 2 to a Royal Flush | TJ |
| 3 to a Flush | 23K; 24K; 25K; 26K; 34K; 35K; 36K; 45K; 46K; 56K |
| 3 to a Straight | TJQ |
| 2 to a Straight | JQ |
| 3 to a Straight Flush | 458; 468; 478; 569; 579; 589; 67T; 68T; 69T |
| 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 Royal Flush | TK |
| Single Card | a Jack; a Queen; a King |
| 3 to a Flush | (more)237; 238; 239; 23T; 247; 248; 249; 24T; 257; 258; 259; 25T; 267; 268... |
| 4 to a Straight | (more)2346; 2356; 2456; 3457; 3467; 3567; 4568; 4578; 4678; 5679; 5689; 5789... |
| 2 to a Straight Flush | 34 |
| Garbage | Discard everything |
The following table shows the exceptions to the basic strategy:
| Basic Strategy Exceptions | ||
|---|---|---|
| Right Play | Wrong Play | Pattern(s) |
| Garbage: Discard everything | 2 to a Straight Flush: 34 | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 2JQ | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 3JQ | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 4JQ | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 5JQ | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 6JQ | |
| 2 to a Royal Flush: JQ | 3 to a Flush: 7JQ | |
| 3 to a Straight Flush: 89J | 1 Pair: 88 | |
| 3 to a Straight Flush: 8TJ | 1 Pair: 88 | |
| 3 to a Flush: 2TA | Single Card: an Ace | |
| 3 to a Flush: 3TA | Single Card: an Ace | |
| 3 to a Flush: 4TA | Single Card: an Ace | |
| 3 to a Straight Flush: 567 | 1 Pair: 66 | |
| 3 to a Straight Flush: 567 | 1 Pair: 77 | |
| 3 to a Straight Flush: 678 | 1 Pair: 77 | |
| 3 to a Straight Flush: 678 | 1 Pair: 88 | |
| 3 to a Straight Flush: 89T | 1 Pair: 88 | |
| 3 to a Straight Flush: 89T | 1 Pair: TT | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 2TJQ | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 3TJQ | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 4TJQ | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 5TJQ | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 6TJQ | |
| 3 to a Royal Flush: TJQ | 4 to a Flush: 7TJQ | |
| 3 to a Flush: 26A | Single Card: an Ace | |
| 3 to a Flush: 36A | Single Card: an Ace | |
| 3 to a Flush: 46A | Single Card: an Ace | |
| 3 to a Flush: 27A | Single Card: an Ace | |
| 3 to a Flush: 37A | Single Card: an Ace | |
| 3 to a Flush: 47A | Single Card: an Ace | |
| 3 to a Flush: 28A | Single Card: an Ace | |
| 3 to a Flush: 38A | Single Card: an Ace | |
| 3 to a Flush: 48A | Single Card: an Ace | |
| 3 to a Flush: 29A | Single Card: an Ace | |
| 3 to a Flush: 39A | Single Card: an Ace | |
| 3 to a Flush: 49A | Single Card: an Ace | |
| 1 Pair: 55 | 3 to a Straight Flush: 345 | |
| 1 Pair: 55 | 3 to a Straight Flush: 456 | |
| 1 Pair: 66 | 3 to a Straight Flush: 456 | |
| 1 Pair: 55 | 3 to a Straight Flush: 567 | |
| 1 Pair: 66 | 3 to a Straight Flush: 678 | |
| 1 Pair: 77 | 3 to a Straight Flush: 789 | |
| 1 Pair: 88 | 3 to a Straight Flush: 789 | |
| 1 Pair: 99 | 3 to a Straight Flush: 789 | |
| 1 Pair: 99 | 3 to a Straight Flush: 89T | |
| 3 to a Straight Flush: 569 | 2 to a Straight: JQ | 5♣ 6♣ 9♣ J♦ Q♥ |
| 3 to a Straight Flush: 579 | 2 to a Straight: JQ | 5♣ 7♣ 9♣ J♦ Q♥ |
| 3 to a Straight Flush: 67T | 3 to a Straight: TJQ | 6♣ 7♣ 10♣ J♦ Q♥ |
| 3 to a Straight Flush: 8TQ | 4 to a Straight: TQKA | 8♣ 10♣ Q♣ K♦ A♥ |
| 3 to a Flush: 23J | Single Card: an Ace | 2♣ 3♣ 4♦ J♣ A♦ |
| 3 to a Flush: 24J | Single Card: an Ace | 2♣ 3♦ 4♣ J♣ A♦ |
| 3 to a Flush: 34J | Single Card: an Ace | 2♣ 3♦ 4♦ J♦ A♣ |
| 3 to a Flush: 23Q | Single Card: an Ace | 2♣ 3♣ 4♦ Q♣ A♦ |
| 3 to a Flush: 24Q | Single Card: an Ace | 2♣ 3♦ 4♣ Q♣ A♦ |
| 3 to a Flush: 34Q | Single Card: an Ace | 2♣ 3♦ 4♦ Q♦ A♣ |
| 3 to a Flush: 23K | Single Card: an Ace | 2♣ 3♣ 4♦ K♣ A♦ |
| 3 to a Flush: 24K | Single Card: an Ace | 2♣ 3♦ 4♣ K♣ A♦ |
| 3 to a Flush: 34K | Single Card: an Ace | 2♣ 3♦ 4♦ K♦ A♣ |
| 3 to a Straight Flush: 78J | 2 to a Royal Flush: QK | 7♣ 8♣ J♣ Q♦ K♦ |
| 3 to a Straight Flush: 79J | 2 to a Royal Flush: QK | 7♣ 9♣ J♣ Q♦ K♦ |
| 3 to a Straight Flush: 78J | 2 to a Royal Flush: QA | 7♣ 8♣ J♣ Q♦ A♦ |
| 3 to a Straight Flush: 79J | 2 to a Royal Flush: QA | 7♣ 9♣ J♣ Q♦ A♦ |
| 3 to a Straight Flush: 7TJ | 2 to a Royal Flush: QA | 7♣ 10♣ J♣ Q♦ A♦ |
| 3 to a Straight Flush: 78J | 2 to a Royal Flush: KA | 7♣ 8♣ J♣ K♦ A♦ |
| 3 to a Straight Flush: 79J | 2 to a Royal Flush: KA | 7♣ 9♣ J♣ K♦ A♦ |
| 3 to a Straight Flush: 7TJ | 2 to a Royal Flush: KA | 7♣ 10♣ J♣ K♦ A♦ |
| 3 to a Straight Flush: 89Q | 2 to a Royal Flush: KA | 8♣ 9♣ Q♣ K♦ A♦ |
| 3 to a Straight Flush: 8TQ | 2 to a Royal Flush: KA | 8♣ 10♣ Q♣ K♦ A♦ |
| 3 to a Straight Flush: 345 | 1 Pair: 88 | 8♦ 8♣ 3♥ 4♥ 5♥ |
| 3 to a Straight Flush: 567 | 1 Pair: TT | 10♦ 10♣ 5♥ 6♥ 7♥ |
| 1 Pair: 55 | 3 to a Straight Flush: 789 | 5♣ 5♦ 7♥ 8♥ 9♥ |