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Введение
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 | 487,639,416 | 0.000024 | 40,876.99 | 15.62 | 0.019571 |
| Straight Flush | 80 | 2,243,107,716 | 0.000113 | 8,886.43 | 0.70 | 0.009002 |
| Four Aces | 160 | 4,396,057,872 | 0.000221 | 4,534.34 | 5.58 | 0.035286 |
| Four J's, Q's, K's | 120 | 12,962,879,244 | 0.000650 | 1,537.72 | 9.21 | 0.078038 |
| Four 2's, 3's, 4's | 80 | 10,783,085,232 | 0.000541 | 1,848.56 | 3.38 | 0.043277 |
| Four 5's through 10's | 50 | 20,912,185,872 | 0.001049 | 953.19 | 2.52 | 0.052456 |
| Full House | 6 | 176,171,458,716 | 0.008838 | 113.15 | 0.22 | 0.053028 |
| Flush | 5 | 217,056,265,668 | 0.010889 | 91.83 | 0.18 | 0.054446 |
| Straight | 4 | 259,516,100,772 | 0.013019 | 76.81 | 0.12 | 0.052077 |
| Three of a Kind | 3 | 1,546,294,531,428 | 0.077574 | 12.89 | 0.32 | 0.232721 |
| Two Pair | 1 | 2,170,809,072,756 | 0.108904 | 9.18 | 0.00 | 0.108904 |
| Jacks or Better | 1 | 4,582,730,832,804 | 0.229904 | 4.35 | 0.00 | 0.229904 |
| Nothing | 0 | 10,928,867,299,704 | 0.548274 | 1.82 | 0.51 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.21 | 38.37 | 0.968710 | |
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 | 488,329,824 | 0.000024 | 40,819.20 | 15.64 | 0.019599 |
| Straight Flush | 80 | 2,243,240,844 | 0.000113 | 8,885.91 | 0.70 | 0.009003 |
| Four Aces | 160 | 4,390,746,684 | 0.000220 | 4,539.83 | 5.57 | 0.035244 |
| Four J's, Q's, K's | 120 | 12,958,984,476 | 0.000650 | 1,538.18 | 9.21 | 0.078014 |
| Four 2's, 3's, 4's | 80 | 10,782,180,168 | 0.000541 | 1,848.72 | 3.38 | 0.043273 |
| Four 5's through 10's | 50 | 20,911,315,380 | 0.001049 | 953.23 | 2.52 | 0.052453 |
| Full House | 6 | 176,144,235,588 | 0.008837 | 113.16 | 0.22 | 0.053020 |
| Flush | 5 | 216,959,729,292 | 0.010884 | 91.88 | 0.18 | 0.054422 |
| Straight | 4 | 258,979,093,380 | 0.012992 | 76.97 | 0.12 | 0.051969 |
| Three of a Kind | 3 | 1,546,023,996,756 | 0.077560 | 12.89 | 0.32 | 0.232680 |
| Two Pair | 1 | 2,170,722,248,532 | 0.108900 | 9.18 | 0.00 | 0.108900 |
| Jacks or Better | 1 | 4,587,120,090,828 | 0.230124 | 4.35 | 0.00 | 0.230124 |
| Nothing | 0 | 10,925,506,325,448 | 0.548105 | 1.82 | 0.51 | 0.000000 |
| Totals | 19,933,230,517,200 | 1.000000 | 2.21 | 38.38 | 0.968702 | |
The following table shows the basic strategy:
| Basic Strategy | |
|---|---|
| Type of Play | Play Details |
| Pat Hand | Four J's, Q's, K's; Straight Flush; Royal Flush |
| 4 of a Kind | 2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; AAAA |
| 4 to a Royal Flush | TJQA; TJQK; TJKA; TQKA; JQKA |
| 3 of a Kind | 222; 333; 444; JJJ; QQQ; KKK; AAA |
| Pat Hand | Flush; Full House |
| 3 of a Kind | 555; 666; 777; 888; 999; TTT |
| 4 to a Straight Flush | 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ |
| Pat Hand | Straight |
| 4 to a Straight Flush | (more)A234; A235; A245; A345; 2346; 2356; 2456; 3457; 3467; 3567; 4568; 4578... |
| 1 Pair | AA |
| 1 Pair | JJ; QQ; KK |
| 2 Pair | (more)2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 3344; 3355; 3366; 3377... |
| 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 | 89TJ; 9TJQ; TJQK |
| 1 Pair | 22; 33; 44; 88 |
| 3 to a Straight Flush | 9TJ; 9JQ |
| 1 Pair | 55; 66; 77; 99; TT |
| 4 to a Straight | 2345; 3456; 4567; 5678; 6789; 789T; JQKA |
| 3 to a Straight Flush | 345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TQ; 9JK; 9QK |
| 2 to a Royal Flush | JQ; JK; QK |
| 4 to a Straight | 9JQK; TJQA; TJKA; TQKA |
| 2 to a Royal Flush | JA; QA; KA |
| 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 |
| 4 to a Straight | 89JQ; 8TJQ; 9TJK; 9TQK |
| 2 to a Straight | JQ; JK; QK |
| 2 to a Straight | QA; KA |
| 2 to a Royal Flush | TJ |
| 2 to a Straight | JA |
| Single Card | a Jack |
| Single Card | an Ace |
| 2 to a Royal Flush | TQ |
| Single Card | a Queen; a King |
| 3 to a Straight Flush | 236; 246; 256; 347; 357; 367; 458; 468; 478; 569; 579; 589; 67T; 68T; 69T |
| 4 to a Straight | (more)2346; 2356; 2456; 3457; 3467; 3567; 4568; 4578; 4678; 5679; 5689; 5789... |
| 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 | |
| Single Card: a Queen | 2 to a Royal Flush: TQ | |
| Single Card: an Ace | 2 to a Straight: KA | |
| Single Card: an Ace | 2 to a Straight: QA | |
| 2 to a Royal Flush: TJ | 2 to a Straight: JK | |
| Single Card: an Ace | 2 to a Straight: JA | |
| 2 to a Straight: JA | 2 to a Royal Flush: TJ | |
| 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 | 2 to a Royal Flush: TJ | |
| 3 to a Straight Flush: 8JQ | 4 to a Straight: JQKA | |