In this blog post, Stephen How described the new Shuffle Master game Raise it Up Stud (RIUS). Stephen was the mathematician for the game andstated that herecently saw it at Pala casino. As far as I know,Pala is the only casino currently hosting RIUS. It will also be shown at G2Ethis year.RIUSis yet another poker hybrid, with the familiar ante/raise/blind structure. Because the player has the opportunity to make a strategic decision as hole-cards are exposed, knowledge of a hole-card in advance will move the edge towards the player. I do not know how RIUS is dealt and therefore if the information presented here can be used in practice. But this article should underscore how quickly analysis can be done on a new game and how weaknesses, if they exist, can quickly be exploited by AP’s.

This game is based on the best five-card poker hand a player can make using five of six cards, with the hands ranked in the usual poker order. The player does not compete against the dealer. Like Caribbean Stud and Mississippi Stud, the player is playing against a pay table. Here are the rules:

  • The player makes a 1 unit ante bet and a matching blind bet.

  • The player is dealt three cards and three other cards are dealt face down (Flop, Turn, River).

  • After considering his three cards, the player can either make a raise wager of 3 units, or check.

  • The dealer then exposes the first of the three hole-cards (the Flop card).

  • The player can then either make a raise wager of 2 units, or check.

  • The dealer then exposes the second of the three hole-cards (the Turn card).

  • The player can then either make a raise wager of 1 unit, or fold.

  • The player must raise exactly one time (3x before Flop, 2x before Turn, or 1x before River), or fold.

  • The dealer then exposes the third of the three hole-cards (the River card).

  • If the player folds, he forfeits his ante and blind bets.

  • If the player made a raise bet at some point, then the player makes his best five-card hand using any five of the six exposed cards.

  • If the player has less than a pair of tens as his final hand, then he loses his ante, play and blind bets.

  • If the player has a pair of tens or higher, then the player is paid on each of his ante/play/blind bets by reference to the pay structure for that bet.

  • The ante bet is always paid 1-to-1 for a pair of tens or higher, otherwise it is lost.

Here is the pay table for the raise bet:

  • Royal Flush pays 100-to-1.

  • Straight Flush pays 20-to-1.

  • Four-of-a-Kind pays 10-to-1.

  • Full House pays 6-to-1.

  • Flush pays 5-to-1.

  • Straight pays 4-to-1.

  • Three-of-a-Kind pays 3-to-1.

  • Two Pairs pays 1.5-to-1 (3-to-2).

  • Pair of Tens through Aces pays 1-to-1.

  • All other hands lose the raise bet.

Here is the pay table for the blind bet:

  • Royal Flush pays 1000-to-1.

  • Straight Flush pays 200-to-1.

  • Four-of-a-Kind pays 30-to-1.

  • Full House pays 4-to-1.

  • Flush pays 3-to-1.

  • Straight pays 2-to-1.

  • Three-of-a-Kind pays 1-to-1.

  • Two Pairs push.

  • Pair of Tens through Aces push.

  • All other hands lose the blind bet.

There is an important way of thinking about this game that makes its analysis easier to follow. This method has to do with how many cards the player knows before making each decision. In the base game, the player makes his first wager without knowing his own cards. In other words, he knows 0 cards when he makes his ante bet. His next bet (raise 3x or check) is made after his three cards are dealt, so the player knows 3 cards. After the Flop card is exposed, the player’s next bet (2x or check) is made knowing 4 cards. After the Turn card is exposed, the player’s next bet (1x or fold) is made knowing 5 cards. We therefore refer to the base game as 0-3-4-5.

To begin with, I computed the house edge for the 0-3-4-5 game by cycling through every possible hand, determining optimal play, and recording the result. After doing this, I obtained a house edge of 3.5022%. Stephen How got the same result and gives a straightforward strategy in this blog post that he says simulates at 3.70%.

The next situation I considered was if the player sees the Flop hole-card during the deal. In this case, the player knows 4 cards for his 3x bet, 4 cards for his 2x bet and 5 cards for his 1x/fold bet. Therefore this game is 0-4-4-5. In this case, I computed a player edge of 7.6933% using perfect hole-card strategy. Note that the player will have the same information both before and after the Flop card is exposed. That is, he has the same information when he chooses to raise 3x that he has when he chooses to raise 2x. It therefore comes as no surprisethat the player never raises 2x.

The following strategy simulated (1 billion rounds) at 7.55%.

RIUS Flop Hole-Card Strategy:

Raise 3x with any of the following, otherwise check:

  • Made hand.

  • Pair of 2’s through 9’s.

  • 4 to an open-ended straight.

  • 4 to a straight with 1 gap. For example, (A,2,3,4) or (3,5,6,7).

  • 4 to a flush.

  • 3 high cards with 3 suited cards. For example, (2c, Tc, Jc, Ad).

Never raise 2x.

Raise 1x with any of the following, otherwise fold:

  • Made hand.

  • Pair of 2’s through 9’s.

  • 4 to an open-ended straight.

  • 4 to a straight with 1 gap and 1 high card. For example, (3,4,5,7,J) or (3,7,8,9,J).

  • 4 to a flush.

The next situation I considered was if the player sees the Turn hole-card during the deal. In this case, the player knows 4 cards for his 3x bet, 5 cards for his 2x bet and 5 cards for his 1x/fold bet. Therefore this game is 0-4-5-5. In this case, I computed a player edge of 18.9671% using perfect hole-card strategy. Note that the player will have the same information both before and after the Turn card is exposed. That is, he has the same information when he chooses to raise 2x that he has when he chooses to raise 1x or fold. However, to maximize return, some of these hands should have a raise of 2x, some should have a raise of 1x and some should fold.

The following strategy simulated (1 billion rounds) at 17.71%.

RIUS Turn Hole-Card Strategy:

Raise 3x with any of the following, otherwise check:

  • Made hand.

  • 4 to an open-ended straight.

  • 4 to a straight with 1 gap. For example, (A,2,3,4) or (3,5,6,7).

  • 4 to a flush.

  • 3 high cards with 3 suited cards. For example, (2c, Tc, Jc, Ad).

Raise 2x with any of the following, otherwise check:

  • Made hand.

  • 4 to an open-ended straight.

  • 4 to a flush.

Raise 1x with any of the following, otherwise fold:

  • Made hand.

  • Pair of 2’s through 9’s.

  • 4 to a straight with 1 gap and 1 high card.

Finally, I considered the situation when the player sees the River hole-card during the deal. In this case, the player knows 4 cards for his 3x bet, 5 cards for his 2x bet and 6 cards for his 1x/fold bet. Therefore this game is 0-4-5-6. In this case, I computed a player edge of 63.3031% using perfect hole-card strategy. Note that the player will have full information after the Turn card is exposed. That makes the strategy pretty obvious.

The following strategy simulated (1 billion rounds) at 62.71%.

RIUS River Hole-Card Strategy:

Raise 3x with any of the following, otherwise check:

  • Made hand.

  • 4 to an open-ended straight.

  • 4 to a flush.

Raise 2x withthe following, otherwise check:

  • Made hand.

Raise 1x with the following, otherwise fold:

  • Made hand.

I do not know if RIUSis vulnerable to advantage play. I have not seen it in person and don’t know if the specific way it is dealt makes it vulnerable. But, if hole-cards are being exposed, then this game will be thoroughly crushed. This is a perfect situation for Shuffle Master to be proactive. They should determine this type of vulnerability in advance and ensure that procedures are in place to minimize the danger that hole-card exposure could potentially cause.

Here are my recommendations:

  • Develop the physical features of the game and game procedures understanding its potential hole-card vulnerability.

  • Check the table layout and game procedures to see if game protection can be enhanced.

  • Routinely audit dealers for correct procedure and hole-card exposure.

About the Author
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received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson