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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 | 499,034,076 | 0.000025 | 39,943.63 | 15.98 | 0.016690 |
| Straight Flush | 50 | 2,063,206,620 | 0.000104 | 9,661.29 | 0.25 | 0.004313 |
| Four Aces with any 2,3,4 | 400 | 1,221,202,416 | 0.000061 | 16,322.63 | 9.75 | 0.020422 |
| Four 2's, 3's, 4's with any A,2,3,4 | 200 | 3,403,861,164 | 0.000171 | 5,856.06 | 6.76 | 0.028461 |
| Four Aces | 200 | 3,436,748,676 | 0.000172 | 5,800.03 | 6.83 | 0.028736 |
| Four 2's, 3's, 4's | 80 | 21,137,764,092 | 0.001060 | 943.02 | 6.62 | 0.070695 |
| Four 5's through K's | 50 | 96,451,527,648 | 0.004839 | 206.67 | 11.63 | 0.201614 |
| Full House | 9 | 196,807,412,808 | 0.009873 | 101.28 | 0.64 | 0.074050 |
| Flush | 5 | 205,493,400,984 | 0.010309 | 97.00 | 0.17 | 0.042955 |
| Straight | 4 | 230,734,928,952 | 0.011575 | 86.39 | 0.11 | 0.038585 |
| Three of a Kind | 3 | 1,382,387,263,752 | 0.069351 | 14.42 | 0.28 | 0.173377 |
| Two Pair | 1 | 2,453,168,842,596 | 0.123069 | 8.13 | 0.00 | 0.102558 |
| Jacks or Better | 1 | 4,234,723,638,192 | 0.212445 | 4.71 | 0.00 | 0.177038 |
| Nothing | 0 | 11,101,701,685,224 | 0.556944 | 1.80 | 0.53 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.26 | 59.55 | 0.979491 | |
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 | 499,438,812 | 0.000025 | 39,911.26 | 16.00 | 0.016704 |
| Straight Flush | 50 | 2,061,182,688 | 0.000103 | 9,670.77 | 0.25 | 0.004309 |
| Four Aces with any 2,3,4 | 400 | 1,221,216,084 | 0.000061 | 16,322.44 | 9.75 | 0.020422 |
| Four 2's, 3's, 4's with any A,2,3,4 | 200 | 3,403,661,376 | 0.000171 | 5,856.41 | 6.76 | 0.028459 |
| Four Aces | 200 | 3,434,238,600 | 0.000172 | 5,804.26 | 6.82 | 0.028715 |
| Four 2's, 3's, 4's | 80 | 21,133,939,008 | 0.001060 | 943.19 | 6.62 | 0.070682 |
| Four 5's through K's | 50 | 96,437,014,416 | 0.004838 | 206.70 | 11.63 | 0.201583 |
| Full House | 9 | 196,536,002,760 | 0.009860 | 101.42 | 0.63 | 0.073948 |
| Flush | 5 | 205,214,190,660 | 0.010295 | 97.13 | 0.17 | 0.042896 |
| Straight | 4 | 233,326,356,228 | 0.011705 | 85.43 | 0.11 | 0.039018 |
| Three of a Kind | 3 | 1,381,861,443,768 | 0.069325 | 14.42 | 0.28 | 0.173311 |
| Two Pair | 1 | 2,451,555,352,836 | 0.122988 | 8.13 | 0.00 | 0.102490 |
| Jacks or Better | 1 | 4,231,348,777,008 | 0.212276 | 4.71 | 0.00 | 0.176897 |
| Nothing | 0 | 11,105,197,702,956 | 0.557120 | 1.79 | 0.53 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.26 | 59.56 | 0.979434 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | (more)Four 5's through K's; Four 2's, 3's, 4's with any A,2,3,4; Four Ace... |
| 4 of a Kind | (more)2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK... |
| Pat Hand | Four 2's, 3's, 4's |
| 4 to a Royal Flush | TJQA; TJQK; TJKA; TQKA; JQKA |
| 3 of a Kind + 1 Kicker | 222A; 3332; 333A; 4443; 444A |
| 3 of a Kind + 1 Kicker | 4442 |
| 3 of a Kind | 333; 444; AAA |
| Pat Hand | Straight; Flush; Full House |
| 3 of a Kind + 1 Kicker | (more)5552; 5553; 5554; 555A; 6662; 6663; 6664; 6665; 666A; 7772; 7773; 7774... |
| 3 of a Kind | 222; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK |
| 2 Pair | (more)2244; 22JJ; 22QQ; 22KK; 22AA; 3366; 33JJ; 33QQ; 33KK; 4488; 44JJ; 44QQ... |
| 4 to a Straight Flush | (more)2345; 3456; 3567; 4567; 4568; 4578; 4678; 5678; 5679; 5689; 5789; 6789... |
| 1 Pair + 2 Kickers | (more)332A; 443A; 5523; 554A; 6624; 665A; 7725; 7734; 776A; 8826; 8835; 887A... |
| 4 to a Straight Flush | A234; A235; A245; A345; 2346; 2356; 2456; 3457; 3467 |
| 1 Pair | AA |
| 2 Pair | (more)2233; 2255; 2266; 2277; 2288; 2299; 22TT; 3344; 3355; 3377; 3388; 3399... |
| 1 Pair | JJ; QQ; KK |
| 3 to a Royal Flush | TJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA |
| 1 Pair + 1 Kicker | 332; 33A; 443; 44A |
| 1 Pair | 44; TT |
| 4 to a Flush | (more)2347; 234T; 234J; 234Q; 234K; 235J; 235Q; 235K; 236J; 236Q; 236K; 237J... |
| 1 Pair | 33; 99 |
| 1 Pair + 1 Kicker | 22A |
| 4 to a Flush | (more)2349; 236A; 237A; 238A; 239A; 239J; 239Q; 239K; 23TA; 246A; 2469; 247A... |
| 1 Pair | 77; 88 |
| 4 to a Flush | (more)2348; 2458; 2478; 2479; 247T; 2489; 248T; 3468; 3478; 3489; 348T; 3578... |
| 1 Pair | 22 |
| 4 to a Flush | (more)2357; 2358; 2359; 235T; 2367; 2368; 2369; 236T; 2378; 2379; 237T; 2389... |
| 1 Pair | 55; 66 |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ; TJQK |
| 3 to a Straight Flush | A23; A34; A45; 235; 89T; 89J; 8TJ; 9TJ; 9TQ; 9JQ |
| 4 to a Straight | JQKA |
| 3 to a Straight Flush | 8JQ; 9JK; 9QK |
| 2 to a Royal Flush | JQ; JK |
| 3 to a Straight Flush | 345; 456; 567; 678; 789 |
| 2 to a Royal Flush | QK |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 2 to a Royal Flush | JA; QA; KA |
| 3 to a Flush | 56A; 67A; 78A; 89A; 9TA |
| 3 to a Straight Flush | 246; 347 |
| Single Card | an Ace |
| 3 to a Straight | JQK |
| 4 to a Straight | 89JQ; 8TJQ; 9TJK; 9TQK |
| 3 to a Straight Flush | 568; 578; 679; 689; 78T; 78J; 79T; 79J; 7TJ; 89Q; 8TQ; 9TK |
| 2 to a Straight | JQ |
| 3 to a Straight Flush | 234; 245; 346; 356; 457; 467 |
| 2 to a Straight | JK; QK |
| 2 to a Royal Flush | TJ; TQ; TK |
| Single Card | a Jack; a Queen; a King |
| 3 to a Flush | 257; 268; 279; 28T; 358; 369; 37T; 459; 46T |
| 3 to a Straight Flush | 236; 256; 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) |
| Single Card: a King | 2 to a Royal Flush: TK | |
| 2 to a Royal Flush: TJ | 2 to a Straight: JK | |
| 2 to a Straight Flush: 34 | Garbage: Discard everything | |
| 2 to a Royal Flush: JA | 4 to a Straight: TJKA | |
| 2 to a Royal Flush: QA | 4 to a Straight: TQKA | |
| 2 to a Royal Flush: KA | 4 to a Straight: TQKA | |
| 2 to a Royal Flush: KA | 4 to a Straight: TJKA | |
| 2 to a Royal Flush: JA | 4 to a Straight: TJQA | |
| 2 to a Royal Flush: QA | 4 to a Straight: TJQA | |
| 4 to a Straight: 9JQK | 2 to a Royal Flush: JK | |
| 4 to a Straight: TJKA | 2 to a Royal Flush: JK | |
| 4 to a Straight: 9JQK | 2 to a Royal Flush: QK | |
| 4 to a Straight: TQKA | 2 to a Royal Flush: QK | |
| Single Card: an Ace | 3 to a Straight Flush: 246 | |
| Single Card: an Ace | 3 to a Straight Flush: 347 | |
| 3 of a Kind + 1 Kicker: 6662 | 3 of a Kind + 1 Kicker: 6663 | |
| Pat Hand: Full House | 3 of a Kind: 333 | |
| 3 to a Straight Flush: 689 | 4 to a Straight: 89JQ | 6♣ 8♣ 9♣ J♦ Q♥ |
| 3 to a Straight Flush: 79T | 4 to a Straight: 9TQK | 7♣ 9♣ 10♣ Q♦ K♥ |
| 3 to a Straight Flush: 345 | 2 to a Royal Flush: JK | 3♣ 4♣ 5♣ J♦ K♦ |
| 3 to a Straight Flush: 456 | 2 to a Royal Flush: JK | 4♣ 5♣ 6♣ J♦ K♦ |
| 3 to a Straight Flush: 567 | 2 to a Royal Flush: JK | 5♣ 6♣ 7♣ J♦ K♦ |
| 3 to a Straight Flush: 678 | 2 to a Royal Flush: JK | 6♣ 7♣ 8♣ J♦ K♦ |
| 4 to a Flush: 2367 | 1 Pair: 77 | 7♣ 7♦ 2♣ 3♣ 6♣ |
| 1 Pair + 1 Kicker: 33A | 3 to a Royal Flush: TJA | 3♣ 3♦ 10♣ J♣ A♣ |
| 1 Pair + 1 Kicker: 44A | 3 to a Royal Flush: TJA | 4♣ 4♦ 10♣ J♣ A♣ |
| 1 Pair + 1 Kicker: 33A | 3 to a Royal Flush: TQA | 3♣ 3♦ 10♣ Q♣ A♣ |
| 1 Pair + 1 Kicker: 44A | 3 to a Royal Flush: TQA | 4♣ 4♦ 10♣ Q♣ A♣ |
| 1 Pair + 1 Kicker: 33A | 3 to a Royal Flush: TKA | 3♣ 3♦ 10♣ K♣ A♣ |
| 1 Pair + 1 Kicker: 44A | 3 to a Royal Flush: TKA | 4♣ 4♦ 10♣ K♣ A♣ |
| 3 of a Kind + 1 Kicker: 6664 | 3 of a Kind + 1 Kicker: 6663 | 6♦ 6♥ 6♣ 3♠ 4♣ |
| 3 of a Kind + 1 Kicker: 6665 | 3 of a Kind + 1 Kicker: 6663 | 6♦ 6♥ 6♣ 3♠ 5♣ |
| 3 of a Kind + 1 Kicker: 666A | 3 of a Kind + 1 Kicker: 6663 | 6♦ 6♥ 6♣ 3♠ A♣ |