Discount Gambling

I got pretty excited last week about possibly exploiting Joker information for the new Wild 52 game at the Las Vegas Flamingo. Its a 7-card poker game with a Joker, where up to 6 players hold 5 cards each, and play against a dealer hand. There are 2 community cards, an Ante, and two 2x betting rounds. I figured it was a lock that sharing Joker Busy status with confederates, combined with an optimized strategy both, would yield at least a 5% player edge. So I worked it all out, and was shocked to find only a ~1% improvement from around a 2% house edge to a 1% house edge.

Honestly, I was thinking “Vegas trip”, and betting $25 or $100 Antes with my friends, winning thousands each until they shut us down. I thought it’d end up being obvious to everyone that knowing where the Joker would yield a huge player advantage. I figured they’d set up the game with a small house edge, and they didn’t foresee players sharing Joker information. Well, whether they looked into it or not, sharing Joker info didn’t help out much to change the overall odds 😦

Here’s how the game is played:

1. The game is played with a 52 card deck plus one completely wild Joker.
2. Each player Antes before the hand begins.
3. Each player and the dealer receives 5 cards, dealt face down.
4. The player looks at his hand, and decides to either Play it by 2x raising his Ante, or folding his hand and losing his Ante.
5. The dealer then turns up the first community card.
6. Based on his 6-card hand, each player either checks, or makes the Option bet (2x the Ante).
7. The dealer then turns up the 2nd community card.
8. Action is complete, and the dealer then turns up his 5 cards.
9. The dealer’s 7 card hand (5 hole + 2 community) qualifies with a pair of 5’s or better.
10. If the dealer does not qualify, the 2x Play and Option bets push, and the player automatically wins the Ante bet.
11. If the dealer qualifies, then the Ante, Play, and Option bet all play even-money against the dealer hand.

Here’s a simple basic strategy that yields a 2.4% house edge:
For the 2x Play bet (5 card hand):

• Play any pair or better.
• Play any flush draw or straight draw (including gutshots).
• Play A-high, if 2nd card is at least a Queen, and 4th card is at least an Eight.
• Fold all others.

For the 2x Option bet (6 card hand):

• If the community card is a Joker, only bet trip-8’s or better.
• Bet any hand with a non-community Joker.
• Bet two pairs, if the community card is below your top pair, or if your top pair are 8’s or better, or if you also have a straight or flush draw.
• Only bet a pair of Kings or better if you also have any straight or flush draw.
• Check all others.

Effect of Collusion

I looked into the advantage obtained if 6 players colluded to share “Joker busy” information. This knowledge changed the 5th and 6th street strategies, but only at the margins, which don’t happen frequently enough to significantly change the overall EV 😦

The differences on 5th street are that:

• If the Joker is busy, you can play any Ace-high, or 4 cards higher than a Six.
• Else, if the Joker is hiding, you can only play a pair or better.

The differences on 6th street are that:

• If the Joker is busy, you can bet a pair of Jacks or better (and Ten’s if the community card is below a Ten).
• Else, if the Joker is hiding, you can only bet two pairs or better (Jacks up or better, or if the community card is under your top pair).

These differences only add up to a 1.2% improvement, and the house edge is still 1.2%.

This was pretty disappointing. I called my friends back to tell them we *weren’t* headed to Vegas that weekend 😦