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Wizard of Odds Approved

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The following table shows the results when following perfect strategy (basic strategy and all of the exceptions):

Perfect Strategy Analysis
HandPayoffCombinationsProbabilityHit FrequencyVarianceReturn
Royal Flush827.71422,305,7520.00002147,200.9414.460.017536
Straight Flush77.713,175,011,9840.0001596,278.160.920.012378
Four Aces with any 2,3,4827.711,195,419,2640.00006016,674.6840.930.049639
Four 2's, 3's, 4's with any A,2,3,4427.713,352,690,9080.0001685,945.4430.540.071939
Four Aces187.712,309,102,0640.0001168,632.464.010.021745
Four 2's, 3's, 4's107.716,232,871,3280.0003133,198.083.520.033680
Four 5's through K's77.7128,448,252,3520.001427700.688.270.110906
Full House29.76212,339,551,6440.01065393.878.460.317020
Flush21.92442,427,643,6240.02219545.059.180.486525
Straight4170,510,316,6000.008554116.900.050.034216
Three of a Kind21,309,879,132,7160.06571315.220.010.131427
Two Pair12,335,208,664,4920.1171528.540.040.117152
Jacks or Better13,511,935,364,6080.1761855.680.060.176185
Nothing011,905,794,189,8640.5972841.671.490.000000
Totals19,933,230,517,2001.0000002.48121.951.580346

The following table shows the results when following basic strategy only (not its exceptions):

Basic Strategy Analysis
HandPayoffCombinationsProbabilityHit FrequencyVarianceReturn
Royal Flush827.71422,235,5760.00002147,208.7914.460.017533
Straight Flush77.713,176,827,2720.0001596,274.570.920.012385
Four Aces with any 2,3,4827.711,194,580,2480.00006016,686.3940.900.049604
Four 2's, 3's, 4's with any A,2,3,4427.713,352,619,7000.0001685,945.5730.540.071938
Four Aces187.712,306,989,5600.0001168,640.364.010.021725
Four 2's, 3's, 4's107.716,233,007,5520.0003133,198.013.520.033680
Four 5's through K's77.7128,449,283,3200.001427700.668.270.110910
Full House29.76212,335,483,5000.01065293.888.460.317014
Flush21.92442,534,026,3120.02220145.049.180.486642
Straight4170,389,474,5600.008548116.990.050.034192
Three of a Kind21,309,843,273,8120.06571215.220.010.131423
Two Pair12,335,223,553,1560.1171528.540.040.117152
Jacks or Better13,511,045,218,1680.1761405.680.060.176140
Nothing011,906,723,944,4640.5973301.671.490.000000
Totals19,933,230,517,2001.0000002.48121.921.580338

The following table shows the basic strategy:

Basic Strategy
Type of Play Play Details
Pat Hand
(more)Full House; Four 2's, 3's, 4's with any A,2,3,4; Four Aces with an...
4 of a Kind
(more)2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK...
4 to a Royal FlushTJQK
Pat HandFlush
4 to a Royal FlushTJQA; TJKA; TQKA; JQKA
3 of a Kind + 1 Kicker2223; 2224; 222A; 3332; 3334; 333A; 4442; 4443; 444A; AAA2; AAA3; AAA4
3 of a Kind222; 333; 444; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK; AAA
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...
Pat HandStraight
2 Pair
(more)2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 22JJ; 22QQ; 22KK; 22AA...
1 PairAA
3 to a Royal FlushTJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA
1 PairJJ; QQ; KK
3 to a Straight Flush345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TJ; 9TQ; 9JQ; 9JK; 9QK
1 Pair22; 33; 44
3 to a Straight Flush
(more)A23; A24; A25; A34; A35; A45; 234; 235; 236; 245; 246; 256; 346; 347...
3 to a Flush
(more)237; 238; 239; 23T; 23J; 23Q; 23K; 247; 248; 249; 24T; 24J; 24Q; 24K...
1 Pair55; 66; 77; 88; 99; TT
4 to a Straight2345; 3456; 4567; 5678; 6789; 789T; 89TJ; 9TJQ; TJQK
2 to a Royal FlushJQ; QK
2 to a Royal FlushJA; JK; KA
2 to a Royal FlushTA; TJ; TQ; QA
4 to a StraightJQKA
2 to a Straight FlushA2; A3; A4
2 to a Royal FlushTK
2 to a Straight Flush8J; 9J; 9Q
2 to a Straight FlushA5
Single Cardan Ace
4 to a Straight9JQK; TJQA; TJKA; TQKA
2 to a Straight Flush8Q; 9K
2 to a Straight Flush7J
2 to a Flush2J; 2Q; 2K; 3J; 3Q; 3K; 4J; 4Q; 4K
2 to a Flush5J; 5Q; 5K; 6J; 6Q; 6K; 7Q; 7K; 8K
3 to a StraightJQK
Single Carda Jack
Single Carda Queen
Single Carda King
2 to a Straight Flush23; 24; 34
2 to a Straight Flush9T
2 to a Straight Flush45; 67
2 to a Straight Flush56; 78; 89
2 to a Straight Flush35
2 to a Straight Flush68; 8T
2 to a Straight Flush25; 46; 57; 79
2 to a Straight Flush36; 47
2 to a Straight Flush7T
2 to a Straight Flush58; 69
2 to a Straight Flush26; 37; 48; 6T
2 to a Straight Flush59
2 to a Flush27; 28; 29; 2T; 38; 39; 3T; 49; 4T
2 to a Flush5T

The following table shows the exceptions to the basic strategy:

Basic Strategy Exceptions
Right Play Wrong Play Pattern(s)
Single Card: an Ace2 to a Straight Flush: 8J
(more)5♣ 6♣ 8♦ J♦ A♥
Single Card: an Ace2 to a Straight Flush: 9Q
(more)5♣ 6♣ 9♦ Q♦ A♥
Single Card: an Ace2 to a Straight Flush: A5
(more)5♣ 6♦ 7♦ 9♥ A♣
2 to a Straight Flush: 7JSingle Card: an Ace
(more)2♣ 6♦ 7♥ J♥ A♦
2 to a Straight Flush: 8QSingle Card: an Ace
(more)2♣ 6♦ 8♥ Q♥ A♦
2 to a Straight Flush: 9KSingle Card: an Ace
(more)2♣ 6♦ 9♥ K♥ A♦
4 to a Straight: TJKASingle Card: an Ace
(more)6♣ 10♦ J♥ K♠ A♣
4 to a Straight: TQKASingle Card: an Ace
(more)6♣ 10♦ Q♥ K♠ A♣
2 to a Straight Flush: 482 to a Straight Flush: 6T
(more)2♣ 4♦ 6♥ 8♦ 10♥
4 to a Straight: TJQASingle Card: an Ace
(more)6♣ 10♦ J♥ Q♠ A♣
2 to a Straight Flush: 8T2 to a Straight Flush: 35
(more)2♣ 3♦ 5♦ 8♥ 10♥
2 to a Straight Flush: 892 to a Straight Flush: 45
(more)2♣ 4♦ 5♦ 8♥ 9♥
2 to a Straight Flush: 7T2 to a Straight Flush: 36
(more)2♣ 3♦ 6♦ 7♥ 10♥
2 to a Straight Flush: 372 to a Straight Flush: 6T
(more)2♣ 3♦ 6♥ 7♦ 10♥
2 to a Straight Flush: 9T2 to a Straight Flush: 23
(more)2♣ 3♣ 4♦ 9♥ 10♥
2 to a Straight Flush: 9T2 to a Straight Flush: 24
(more)2♣ 3♦ 4♣ 9♥ 10♥
2 to a Straight Flush: 692 to a Straight Flush: 25
(more)2♣ 3♦ 5♣ 6♥ 9♥
2 to a Straight Flush: 7T2 to a Straight Flush: 25
(more)2♣ 3♦ 5♣ 7♥ 10♥
2 to a Straight Flush: 792 to a Straight Flush: 35
(more)2♣ 3♦ 5♦ 7♥ 9♥
2 to a Straight Flush: 782 to a Straight Flush: 45
(more)2♣ 4♦ 5♦ 7♥ 8♥
2 to a Straight Flush: 592 to a Straight Flush: 26
(more)2♣ 3♦ 5♥ 6♣ 9♥
2 to a Straight Flush: 462 to a Straight Flush: 8T
(more)4♣ 6♣ 7♦ 8♥ 10♥
2 to a Straight Flush: 452 to a Straight Flush: 9T
(more)4♣ 5♣ 7♦ 9♥ 10♥
2 to a Straight Flush: 892 to a Straight Flush: 232♣ 3♣ 4♦ 8♥ 9♥
2 to a Straight Flush: 892 to a Straight Flush: 242♣ 3♦ 4♣ 8♥ 9♥
2 to a Straight Flush: 682 to a Straight Flush: 352♣ 3♦ 5♦ 6♥ 8♥
2 to a Straight Flush: 582 to a Straight Flush: 362♣ 3♦ 5♥ 6♦ 8♥
2 to a Straight Flush: 592 to a Straight Flush: 373♣ 4♦ 5♥ 7♣ 9♥
2 to a Straight Flush: 362 to a Straight Flush: 473♣ 4♦ 6♣ 7♦ 8♥
2 to a Straight Flush: 582 to a Straight Flush: 473♣ 4♦ 5♥ 7♦ 8♥
2 to a Straight Flush: 692 to a Straight Flush: 473♣ 4♦ 6♥ 7♦ 9♥
2 to a Straight Flush: 262 to a Straight Flush: 482♣ 4♦ 6♣ 7♥ 8♦
2 to a Straight Flush: 582 to a Straight Flush: 695♣ 6♦ 8♣ 9♦ 10♥
2 to a Straight Flush: 462 to a Straight Flush: 794♣ 6♣ 7♦ 9♦ 10♥
2 to a Straight Flush: 562 to a Straight Flush: 895♣ 6♣ 8♦ 9♦ 10♥
2 to a Straight Flush: 562 to a Straight Flush: 9T5♣ 6♣ 8♦ 9♥ 10♥
2 to a Straight Flush: 8J2 to a Straight Flush: 9Q8♣ 9♦ J♣ Q♦ K♥