Discount Gambling

Arizona Stud @ Red Wind Casino, WA

Posted in Uncategorized by stephenhow on July 30, 2014

Screen Shot 2014-07-30 at 9.21.14 PMArizona 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.

Optimal Outcomes for Arizona Stud
Outcome Combinations Frequency Net Return
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
folds 15,186,972,477,600 0.273011 -1 -0.273011
total 55,627,620,048,000 1.000000 -0.013402
expected 55,627,620,048,000

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.

Arizona Stud Basic Strategy
Decision Strategy
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
card.
4x / check 4x raise any pair, else
4x raise suited Ace and Nine or better, else
4x raise Ace and Ten or better, else
check.
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.

2 Pair Plus Paytables
Player Hand Paytable A Paytable B Paytable C Paytable D
Royal Flush 500-to-1 500-to-1 500-to-1 500-to-1
Straight Flush 200-to-1 200-to-1 200-to-1 200-to-1
Four-of-a-Kind 100-to-1 100-to-1 100-to-1 80-to-1
Full House 50-to-1 50-to-1 40-to-1 40-to-1
Flush 30-to-1 25-to-1 30-to-1 30-to-1
Straight 20-to-1 20-to-1 20-to-1 20-to-1
Three-of-a-Kind 6-to-1 6-to-1 6-to-1 6-to-1
Two Pairs 4-to-1 4-to-1 4-to-1 4-to-1
others lose lose lose lose
House Edge 3.03% 5.12% 5.53% 6.58%

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 Bad Beat Bonus
Player Beat Hand Combinations Frequency Payout Return
Straight Flush 142,560 0.000000 1000 0.000008
Full House 1,324,642,176 0.000071 500 0.035719
Flush 2,719,437,696 0.000147 300 0.043998
Staight 1,597,456,728 0.000086 200 0.017230
Three-of-a-Kind 49,285,841,520 0.002658 30 0.079740
Two Pairs 257,968,615,536 0.013912 20 0.278245
Jacks-or-Better 923,384,598,264 0.049798 8 0.398385
other 17,306,259,281,520 0.933327 -1 -0.9333273
total 18,542,540,016,000 1.000000 -0.080002

Screen Shot 2014-07-30 at 9.51.37 PM

5 Responses

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  1. Julio said, on August 8, 2014 at 7:08 am

    I played it midnight on the opening day, it was of great fun. The table was close to full all the time. One guy hit flush on Player Bad Beat for 300 to 1 with a $2 bet. Was that you Stephen? :-))) Actually, I did not see you.

    Most player did not bet 4X with high pairs; I feel sorry for them. Every player told the management, this was a game and they loved it. Will go back to play again. Red Wind is a very friendly casino.

    • stephenhow said, on August 9, 2014 at 8:08 am

      I was there opening day, but left around 6pm. I like the game too. The discard decision is fun, and I like making the 4x raises. In UTH, if you “miss” the board on a 4x raise, you’re basically screwed. In AZ Stud, you can still win the 4x raises with high cards.

  2. Julio said, on August 8, 2014 at 7:30 am

    Forgot this one: another guy hit a full house on 2PP, 50 to 1, on a $5 bet.

  3. Julio said, on August 9, 2014 at 9:29 pm

    what is your other web site on food?


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