Arizona Stud is a new poker-based table game debuting at the Red Wind Casino in Olympia, WA next week (6 Aug 2014). In this game, both the Dealer and the player each receive three hole cards. The player must discard one of his hole cards before the flop, while the Dealer must use exactly two hole cards to make a hand. After the player discards, he may wager a Play bet of 2x-4x the Ante, or check pre-flop. The two card flop is then revealed, as well as one of the Dealer’s hole cards. If the player checked pre-flop, he must then make a 1x Play bet, or fold. Finally, the community river card and all Dealer hole cards are revealed. The Dealer qualifies with a hand of AK-high or better. The Ante pushes if the Dealer doesn’t qualify. The Play bet always receives even-money action against the Dealer hand.
The set of all possible outcomes for the optimal player is listed in the table below. The total in the lower right corner shows a house edge of 1.34% of the Ante. Note that you should either 4x bet pre-flop, or check. You should never only bet 2x.
|Win 4x Play w/ ROYAL_FLUSH against qualified dealer||59,240,916||0.000001||5||0.000005|
|Win 4x Play w/ FULL_HOUSE against qualified dealer||89,284,476,240||0.001605||5||0.008025|
|Win 4x Play w/ FLUSH against qualified dealer||10,295,059,284||0.000185||5||0.000925|
|Win 4x Play w/ STRAIGHT against qualified dealer||13,761,723,420||0.000247||5||0.001237|
|Win 4x Play w/ THREE_OF_A_KIND against qualified dealer||674,048,087,712||0.012117||5||0.060586|
|Win 4x Play w/ TWO_PAIRS against qualified dealer||1,233,004,030,272||0.022165||5||0.110827|
|Win 4x Play w/ ONE_PAIR against qualified dealer||3,533,244,131,304||0.063516||5||0.317580|
|Win 4x Play w/ HIGH_CARD against qualified dealer||44,095,696,596||0.000793||5||0.003963|
|Lose 4x Play against qualified dealer||5,323,636,585,296||0.095701||-5||-0.478507|
|Push 4x Play against qualified dealer||90,869,346,720||0.001634||0||0.000000|
|Win 4x Play w/ ROYAL_FLUSH against unqualified dealer||20,545,164||0.000000||4||0.000001|
|Win 4x Play w/ FLUSH against unqualified dealer||4,736,232,972||0.000085||4||0.000341|
|Win 4x Play w/ STRAIGHT against unqualified dealer||5,959,832,148||0.000107||4||0.000429|
|Win 4x Play w/ THREE_OF_A_KIND against unqualified dealer||350,836,147,584||0.006307||4||0.025227|
|Win 4x Play w/ TWO_PAIRS against unqualified dealer||28,557,204,480||0.000513||4||0.002053|
|Win 4x Play w/ ONE_PAIR against unqualified dealer||2,530,675,447,344||0.045493||4||0.181973|
|Win 4x Play w/ HIGH_CARD against unqualified dealer||1,146,771,919,728||0.020615||4||0.082461|
|Lose 4x Play against unqualified dealer||25,248,339,684||0.000454||-4||-0.001816|
|Push 4x Play against unqualified dealer||25,026,495,696||0.000450||0||0.000000|
|Win 1x Play w/ ROYAL_FLUSH against qualified dealer||94,841,496||0.000002||2||0.000003|
|Win 1x Play w/ STRAIGHT_FLUSH against qualified dealer||541,732,152||0.000010||2||0.000019|
|Win 1x Play w/ FOUR_OF_A_KIND against qualified dealer||6,309,658,080||0.000113||2||0.000227|
|Win 1x Play w/ FULL_HOUSE against qualified dealer||45,729,841,680||0.000822||2||0.001644|
|Win 1x Play w/ FLUSH against qualified dealer||51,704,956,552||0.000929||2||0.001859|
|Win 1x Play w/ STRAIGHT against qualified dealer||90,255,233,808||0.001622||2||0.003245|
|Win 1x Play w/ THREE_OF_A_KIND against qualified dealer||591,850,723,248||0.010640||2||0.021279|
|Win 1x Play w/ TWO_PAIRS against qualified dealer||1,068,681,540,840||0.019211||2||0.038423|
|Win 1x Play w/ ONE_PAIR against qualified dealer||4,443,972,518,832||0.079888||2||0.159776|
|Win 1x Play w/ HIGH_CARD against qualified dealer||188,023,085,280||0.003380||2||0.006760|
|Lose 1x Play against qualified dealer||10,848,202,319,420||0.195015||-2||-0.390029|
|Push 1x Play against qualified dealer||161,798,077,992||0.002909||0||0.000000|
|Win 1x Play w/ ROYAL_FLUSH against unqualified dealer||14,941,584||0.000000||1||0.000000|
|Win 1x Play w/ STRAIGHT_FLUSH against unqualified dealer||220,863,744||0.000004||1||0.000004|
|Win 1x Play w/ FLUSH against unqualified dealer||23,880,526,848||0.000429||1||0.000429|
|Win 1x Play w/ STRAIGHT against unqualified dealer||48,873,031,380||0.000879||1||0.000879|
|Win 1x Play w/ THREE_OF_A_KIND against unqualified dealer||34,291,273,536||0.000616||1||0.000616|
|Win 1x Play w/ TWO_PAIRS against unqualified dealer||301,557,935,124||0.005421||1||0.005421|
|Win 1x Play w/ ONE_PAIR against unqualified dealer||3,348,961,937,952||0.060203||1||0.060203|
|Win 1x Play w/ HIGH_CARD against unqualified dealer||2,842,212,690,936||0.051094||1||0.051094|
|Lose 1x Play against unqualified dealer||1,090,180,312,308||0.019598||-1||-0.019598|
|Push 1x Play against unqualified dealer||100,426,510,008||0.001805||0||0.000000|
The basic strategy for the game is listed in the table below, which returns a 1.70% house edge. The player should 4x his hand about 27% of the time, 1x call about 46% of the time, and fold the remaining 27% of the time.
The game looks like fun. The strategy is actually pretty simple, but you get to make the occasional decision. I’ll actually be in Seattle next week (my first time), so I’ll try to check out the game. Maybe I could hit a nice bad beat for once.
|discard||Hold pair, else
hold two highest cards.
Advanced exception: hold highest and lowest cards when suited, AND
highest two cards aren’t suited, AND highest card is Eight or better, AND
middle card is Six or lower, AND lowest card is only one rank below middle
|4x / check||4x raise any pair, else
4x raise suited Ace and Nine or better, else
4x raise Ace and Ten or better, else
|1x / fold||1x call three-of-a-kind, else
1x call any pair beating the dealer by more than a kicker, else
1x call same pair as dealer plus Ten or better kicker, else
1x call open-ended straight flush draw, else
1x call flush draw or any straight draw when beating the dealer, else
1x call flush draw or open-ended straight draw when dealer has no pair, else
1x call with higher hand (Jack or better kicker), else
fold all others.
The optional 2 Pair Plus Bonus bet pays for the final hand made by the player. The house edges for the various offered paytables are listed below.
|Player Hand||Paytable A||Paytable B||Paytable C||Paytable D|
The Player Bad Beat Bonus bet pays when a player’s Jacks-or-Better hand is beat by the Dealer. The following table shows the optimal outcomes for the strategy maximizing the Bad Beat Bonus return. The house edge for the optimal Bad Beat Bonus strategy is 8.00%.
|Player Beat Hand||Combinations||Frequency||Payout||Return|