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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 Flush800449,265,7440.00002344,368.4614.390.018031
Four Deuces with an Ace400456,732,7680.00002343,643.093.650.009165
Four Deuces2003,428,381,3880.0001725,814.186.810.034399
Five of a Kind with one Deuce1606,818,936,2080.0003422,923.228.650.054734
Wild Royal Flush2538,635,260,0960.001938515.931.120.048456
Five of a Kind1255,186,140,0960.002769361.200.340.033223
Straight Flush985,367,381,5680.004283233.500.270.038544
Four of a Kind41,270,898,575,2840.06375815.680.580.255031
Full House3420,561,077,9760.02109847.400.090.063295
Flush2346,016,644,0560.01735957.610.020.034718
Straight21,167,166,943,9040.05855417.080.060.117108
Three of a Kind15,614,444,408,4040.2816633.550.000.281663
Nothing010,923,800,769,7080.5480201.820.540.000000
Totals19,933,230,517,2001.0000002.2136.500.988366

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

Basic Strategy Analysis
HandPayoffCombinationsProbabilityHit FrequencyVarianceReturn
Royal Flush800457,372,1160.00002343,582.0914.650.018356
Four Deuces with an Ace400457,320,9960.00002343,586.963.650.009177
Four Deuces2003,435,552,2520.0001725,802.056.830.034471
Five of a Kind with one Deuce1606,818,071,3920.0003422,923.598.650.054727
Wild Royal Flush2539,022,169,0640.001958510.821.130.048941
Five of a Kind1255,215,796,6800.002770361.010.340.033240
Straight Flush984,404,806,4760.004234236.160.270.038109
Four of a Kind41,271,032,163,7360.06376415.680.580.255058
Full House3420,389,472,8880.02109047.420.090.063270
Flush2345,444,215,5440.01733057.700.020.034660
Straight21,164,353,818,0080.05841317.120.060.116825
Three of a Kind15,610,184,687,2600.2814493.550.000.281449
Nothing010,932,015,070,7880.5484321.820.540.000000
Totals19,933,230,517,2001.0000002.2136.790.988284

The following tables show the basic strategy:

Basic Strategy — No Wilds Dealt
Type of Play Play Details
Pat HandFull House; Royal Flush
4 to a Natural Royal FlushTJQA; TJQK; TJKA; TQKA; JQKA
4 of a Kind3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK; AAAA
3 of a Kind333; 444; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK; AAA
Pat HandStraight; Flush; Straight Flush
4 to a Straight Flush
(more)A345; 3456; 3457; 3467; 3567; 4567; 4568; 4578; 4678; 5678; 5679; 5689...
3 to a Natural Royal FlushTJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA
1 Pair33; 44; 55; 66; 77; 88; 99; TT; JJ; QQ; KK; AA
4 to a Straight4567; 5678; 6789; 789T; 89TJ; 9TJQ; TJQK
4 to a Flush
(more)3458; 3459; 345T; 345J; 345Q; 345K; 346A; 3468; 3469; 346T; 346J; 346Q...
3 to a Straight Flush
(more)345; 456; 457; 467; 567; 568; 578; 589; 678; 679; 67T; 689; 68T; 69T...
2 to a Natural Royal FlushTJ
3 to a Straight Flush346; 347; 356; 357; 367; 458; 468; 478; 569; 579; 7TJ
4 to a Straight
(more)3456; 3457; 3467; 3567; 4568; 4578; 4678; 5679; 5689; 5789; 679T; 689T...
2 to a Natural Royal FlushTQ; JQ; JK; QK
4 to a Straight678T
2 to a Natural Royal FlushTK
GarbageDiscard everything

Basic Strategy — One Wild Dealt
Type of Play Play Details
Pat Hand
(more)Full House; Straight Flush; Wild Royal Flush; Five of a Kind with on...
4 of a KindW333; W444; W555; W666; W777; W888; W999; WTTT; WJJJ; WQQQ; WKKK; WAAA
4 to a Wild Royal FlushWTJA; WTJQ; WTJK; WTQA; WTQK; WTKA; WJQA; WJQK; WJKA; WQKA
4 to a Straight FlushW567; W678; W789; W89T; W9TJ
Pat HandStraight; Flush
4 to a Straight Flush
(more)W345; W456; W457; W467; W568; W578; W679; W689; W78T; W79T; W89J; W8TJ...
3 of a KindW33; W44; W55; W66; W77; W88; W99; WTT; WJJ; WQQ; WKK; WAA
4 to a Straight Flush
(more)WA34; WA35; WA45; W346; W347; W356; W357; W367; W458; W468; W478; W569...
3 to a Wild Royal FlushWTJ; WTQ; WTK; WJQ; WJK; WQK
3 to a Straight FlushW67; W78; W89; W9T
3 to a Wild Royal FlushWTA; WJA; WQA; WKA
4 to a StraightW567; W678; W789; W89T; W9TJ; WTJQ
3 to a Straight FlushW8T
Wild Only

Basic Strategy — Two Wilds Dealt
Type of Play Play Details
Pat HandStraight Flush; Five of a Kind; Wild Royal Flush
4 to a Wild Royal FlushWWTJ
4 of a KindWW33; WW44; WW55; WW66; WW77; WW88; WW99; WWTT; WWJJ; WWQQ; WWKK; WWAA
4 to a Wild Royal FlushWWTA; WWTQ; WWTK; WWJA; WWJQ; WWJK; WWQA; WWQK; WWKA
4 to a Straight FlushWW67; WW78; WW89; WW9T
Wilds Only

Basic Strategy — Three Wilds Dealt
Type of Play Play Details
Pat HandWild Royal Flush
4 of a KindWWWA
Wilds Only

Basic Strategy — Four Wilds Dealt
Type of Play Play Details
Pat HandFour Deuces with an Ace
Wilds Only

The following table shows the exceptions to the basic strategy:

Basic Strategy Exceptions
Right Play Wrong Play Pattern(s)
Garbage: Discard everything2 to a Natural Royal Flush: QK
(more)3♣ 4♣ 5♦ Q♦ K♦
Garbage: Discard everything2 to a Natural Royal Flush: JK
(more)3♣ 4♣ 5♦ J♦ K♦
Garbage: Discard everything2 to a Natural Royal Flush: TK
(more)3♣ 4♣ 5♦ 10♦ K♦
Wild Only3 to a Straight Flush: W8T
(more)2♣ 3♣ 4♦ 8♣ 10♣
3 to a Straight Flush: W9JWild Only
(more)2♣ 3♣ 4♣ 9♦ J♦
3 to a Straight Flush: W79Wild Only
(more)2♣ 3♣ 4♣ 7♦ 9♦
3 to a Straight Flush: W68Wild Only
(more)2♣ 3♣ 6♦ 8♦ J♣
3 to a Straight Flush: W57Wild Only
(more)2♣ 5♣ 7♣ 9♦ 10♥
3 to a Straight Flush: W56Wild Only
(more)2♣ 5♣ 6♣ 9♦ 10♥
3 to a Straight Flush: 7TJ2 to a Natural Royal Flush: TJ
(more)3♣ 7♦ 10♦ J♦ Q♣
Wild Only3 to a Wild Royal Flush: WKA
(more)2♣ 3♣ 10♦ K♣ A♣
Wild Only3 to a Wild Royal Flush: WQA
(more)2♣ 3♣ J♦ Q♣ A♣
Wild Only3 to a Wild Royal Flush: WJA
(more)2♣ 3♣ J♣ Q♦ A♣
2 to a Natural Royal Flush: TQ4 to a Straight: 679T
(more)6♣ 7♣ 9♦ 10♥ Q♥
4 to a Straight: 678T2 to a Natural Royal Flush: TQ
(more)6♣ 7♦ 8♣ 10♦ Q♦
4 to a Straight Flush: WW8TWilds Only2♣ 2♦ 8♣ 10♣ A♦
4 to a Straight Flush: WW9JWilds Only2♣ 2♦ 9♣ J♣ A♦
Wild Only3 to a Wild Royal Flush: WTA2♣ 3♣ 10♣ K♦ A♣
4 to a Straight: W9TJ3 to a Wild Royal Flush: WJA2♣ 9♣ 10♦ J♣ A♣
4 to a Straight Flush: 8TJQ3 to a Natural Royal Flush: TJQ8♣ 10♣ J♣ Q♣ K♦