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Two for the Show

Introduction



I had my first experience with 'Two for the Show' at the Excalibur Hotel in Las Vegas on August 11, 2016. At first glance, the name might suggest it’s a follow-up to another game, One for the Money Nevertheless, I find minimal similarities with that previous game. Instead, it bears a strong resemblance to Three Card Poker .

Rules



  1. The gameplay utilizes a standard deck of cards.
  2. To start the game, the player must place an Ante bet, and there’s also an optional side bet called Two Pair Plus.
  3. The dealer will distribute six cards, three to the player and three to himself.
  4. After reviewing his cards, the player is faced with a decision: either match the Ante bet with a Play bet or choose to fold.
  5. If the player folds, the dealer collects the Ante bet.
  6. When at least one player opts for the Play bet, the dealer reveals his cards and forms the best possible two-card poker hand from the six cards dealt.
  7. The ranking system for two-card hands mirrors that found in pai gow poker, where pairs are superior to two unrelated cards. For instance, the top hand is a pair of aces and the lowest is a 2-3 combination. Flushes and straights do not hold any special value and are treated as two separate cards.
  8. To qualify to open, the dealer must have at least an ace-king. If the dealer fails to open, players are paid even money on the Ante and the Play bets are considered a push.
  9. If the dealer opens, the hands of the player and dealer are compared to determine the winner.
  10. Should the player have the superior hand, they will receive a 1:1 payout on the Ante, while the Play bet payout is based on the following rules:

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

  11. If both the player and dealer hold identical poker hands, the Ante and Play bets will result in a push.
  12. Should the dealer's hand be stronger, both the Ante and Play bets will be forfeited.
  13. The payout for the Two Pair Plus bet is determined by the poker ranking of all six cards held by the player. Payouts on this bet remain active even if the player decides to fold. The payout table is as follows:

    Two for the Show Pay Table

    Player Hand Pays
    Royal flush100 to 1
    Straight flush50 to 1
    Full house9 to 1
    Flush8 to 1
    Straight6 to 1
    Three of a kind5 to 1
    Two pair2 to 1



Here’s an image of the rack card; click on it to view a larger version.



Strategy



It's advisable for players to place a Play bet whenever they hold a pair; otherwise, they should fold.

Ante and Play Analysis



The table below illustrates the probability and potential return contributions for all possible combinations of Ante and Play bets. The lower right cell indicates 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

On average, players are expected to raise 65.48% of the time, with a final average bet totaling 1.6548 units. The Element of Risk, calculated as the expected loss ratio relative to total bets, stands at 3.61% divided by 1.6548, equaling 2.18%.

Two Pair Plus Analysis



The following table details the probability and return contributions for all potential outcomes of the Two Pair Plus bet, with the lower right cell revealing 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



Elliot Frome conducted the analysis of the Ante bet on behalf of Scientific Games, the game’s owner. His findings are based on extensive random simulations.

I have also reviewed the Two Pair Plus bet independently, and my conclusions align with Elliot's analysis.

Acknowledgements



I appreciate ShuffleMaster/Scientific Games (I’m uncertain about their formal title) for providing their mathematical report by Elliot Frome, which significantly eased my task in evaluating the game.

External Links



Wizard of Vegas — Discussion about Two for the Show.