Three Card Poker @ Ocean’s 11, CA
At the Ocean’s 11 Cardroom in Oceanside, CA, they play a version of Three Card Poker, where you get to see one of the dealer’s up cards. It’s also a little different than the licensed casino game, which pays an ante bonus for 3-of-a-kind or better. The Ocean’s 11 version just pays even money on the ante for all winners, and when the dealer doesn’t qualify. And they pay off 200:1 on the Pair Plus bonus bet for royal flushes, whereas the licensed game only pays 40:1 for all straight flushes. I wanted to see how this game compared to the licensed version, so I wrote some programs to analyze basic strategy. I then simulated the game to verify my results. (The Wizard Of Odds doesn’t provide a strategy for the Ocean’s 11 version of California Three Card Poker.)
Overall, the game is actually better than the licensed version, even though you have to pay collection on each bet (at the least, collection costs 1% of your bet). The basic strategy is very simple, fold on any of the following:
- the dealer’s upcard is at least a Q, AND it beats your entire hand
- the dealer’s upcard is a Q, AND your hand is less than Q-9-garbage
- the dealer’s upcard is a K, AND your hand is less than K-9-garbage
- the dealer’s upcard is a A, AND your hand is less than A-9-garbage
This strategy yields a 1.8% house edge, which is less than the casino version of the game (3.38%). Even with the 1% house collection (by law, these California games are player-banked), the game is still better than the casino.
Even more surprising, the Pair Plus bonus bet is 3.00% better than the casino version.
| Hand | Probability | Paytable Improvement | ΔEV |
|---|---|---|---|
| Royal Flush | 4/C(52,3) | +160 | 0.028959 |
So if you play the Pair Plus bonus bet, the Three Card Poker game at Ocean’s 11 is by far better than the licensed version at the casino.
Discount Gambling 
What if you’re playing more than one hand? You get to see some cards in one hand before you get to make your decision in the next hand. Does that change the strategy on which cards to bet and which to fold?
I looked into collusion strategies for this O11 3-card poker, but the additional info of confederate cards isn’t much help. This is expected, since the dealer is already showing an upcard, and the requirements for calling is reduced. Collusion effects are probably stronger in the normal 3-card poker game, but overall, the structure of the game doesn’t provide much benefit to collusion.