Two for the Show

Introduction

I first saw Two for the Show at the Excalibur in Las Vegas on August 11, 2016. Based on the name, one might think it is a sequel to One for the Money. However, I see little commonality with that game. Instead, it closely follows the structure of Three Card Poker.

Rules

1. The game is played with a single deck of cards.
2. Play begins with the player making an Ante bet. There is also an optional Two Pair Plus side bet.
3. The dealer shall give the player and himself six cards.
4. After examining his cards, the player must either make a Play bet equal to his Ante wager or fold.
5. If the player folds, then his Ante bet will be collected.
6. If at least one player made the Play bet, then the dealer will turn over his cards and make the best two-card poker hand among the six cards.
7. The ranking of two-card hands is the same as in pai gow poker, where pairs beat two singletons. For example, the highest hand is a pair of aces and the lowest is 2-3. Flushes and straights carry no special significance and are scored as two singletons.
8. The dealer needs at least ace-king to open. If the dealer doesn't open, then the player will be paid even money on the Ante and the Play be will be a push.
9. If the dealer does open, then the player and dealer hands will be compared — the higher hand wins.
10. If the player has the higher hand, then the Ante shall pay 1 to 1 and the Play bet as follows:

• Pair of aces: 2 to 1
• All other: 1 to 1

11. If the player and dealer hands are of equal poker rank, then the Ante and Play bets shall push.
12. If the dealer has the higher hand, then the Ante and Play bets shall lose.
13. The Two Pair Plus shall be paid according to the poker value of all six player cards. It shall have action even if the player folds. The pay table is as follows:

Two for the Show Pay Table

Player Hand Pays
Royal flush 100 to 1
Straight flush 50 to 1
Full house 9 to 1
Flush8 to 1
Straight 6 to 1
Three of a kind 5 to 1
Two pair 2 to 1

Below is an image of the rack card. Click on it for a larger version.

Strategy

The player should make the Play bet with any pair, otherwise fold.

Ante and Play Analysis

The following table shows the probability and contribution to the return for all possible outcomes of the Ante and Play bets combined. The lower right cell shows a house edge of 3.61%.

Ante and Play Analysis

Event Pays Probability Return
Player wins with aces 3 0.041864 0.125593
Player win with kings or less 2 0.212912 0.425825
Dealer doesn't qualify 1 0.180913 0.180913
Push 0 0.007480 0.000000
Player folds -1 0.345199 -0.345199
Dealer wins -2 0.211632 -0.423265
Total 1.000000 -0.036133

The player will raise 65.48% of the time, for an average final bet of 1.6548 units. The Element of Risk, defined as the ratio of the expected loss to the total amount bet, is 3.61%/1.6548 = 2.18%.

Two Pair Plus Analysis

The following table shows the probability and contribution to the return for all possible outcomes of the Two Pair Plus bet. The lower right cell shows a house edge of 6.73%.

Two Pair Plus Analysis

Event Pays Combinations Probability Return
Royal flush 200 188 0.000009 0.001847
Straight flush 100 1,656 0.000081 0.008134
Four of a kind 50 14,664 0.000720 0.036014
Full house 9 165,984 0.008153 0.073377
Flush 8 205,792 0.010108 0.080867
Straight 6 361,620 0.017763 0.106576
Three of a kind 5 732,160 0.035963 0.179817
Two pair 2 2,532,816 0.124411 0.248821
Loser -1 16,343,640 0.802791 -0.802791
Total 20,358,520 1.000000 -0.067338

Methodology

The analysis of the Ante bet was done by Elliot Frome on behalf of Scientific Games, the game owner. His analysis is based on random simulations.

I personally analyzed the Two Pair Plus bet, which agrees with the same analysis by Elliot.

Acknowledgements

I would like to thank ShuffleMaster/Scientific Games (I'm still not sure what to call them) for sharing their math report by Elliot Frome with me, which saved me a lot of trouble analyzing the game.