World Poker Tour All-In 3x (+EV)
World Poker Tour (WPT) All-In 3x is a house game based on the popular Texas Hold’em poker game. Up to 6 players may be seated at the table, and each play separately against a single house hand. For complete rules and basic strategy, read the Wizard’s description. Of course, I analyzed the game to try to extract some advantage out of sharing hole card information with other players at the table.
Playing basic strategy (no info sharing) yields the house a 0.74% edge against the player. However, a modified strategy for 3 players sharing info yields the player an overall +0.05% return on the ante bet. It’s really easy in practice to share hole card info, and the house doesn’t really care much, so it’s not a problem. Of course, you’re not going to get rich doing this. But, I thought there might be a huge advantage to collusion, so I looked into it.
With all six players colluding, it’s possible to achieve an overall +1.25% edge over the house. However, I never formalized a strategy, because it didn’t seem worth it. I wanted to play the game with 2 other friends, so I tabulated a 3-player strategy (+0.05% net) as follows. The first table lists the hands you should raise with the colluding strategy, that are normally folds under basic strategy. The second table lists the hands you should fold under the colluding strategy, that are normally raised under the basic strategy.
| Hand | Raising Rule | ΔEV |
|---|---|---|
| 32o | No copies, and 4 out of 4 cards are higher than 6. | 1.0% |
| 42o | No copies, and 4 out of 4 cards are higher. | 2.6% |
| 52o | No copies, and at least 3 of the 4 cards are higher. | 5.4% |
| 62o | No copies, and at least 3 of the 4 cards are higher. | 2.7% |
| 72o | No copies, and at least 3 of the 4 cards are higher. | 1.7% |
| 82o | No copies, and at least 1 of the 4 cards are higher. | 7.6% |
| 43o | No copies, and at least 3 of the 4 cards are higher. | 8.3% |
| 63o | No copies, and at least 2 of the 4 cards are higher. | 8.0% |
| 73o | No copies, and at least 2 of the 4 cards are higher. | 7.6% |
| Hand | Folding Rule | ΔEV |
|---|---|---|
| 53o | Any copy, unless 3 or more cards higher than 6. | 5.8% |
| 54o | Any copy, unless 2 or more cards higher than 7. | 2.7% |
| 83o | Any copy. | 6.7% |
| 74o | Any copy, unless 3 or more higher cards. | 4.0% |
| 84o | Any copy, unless 2 or more higher cards. | 2.4% |
| 92o | Any copy, unless 2 or more higher cards. | 2.7% |
| 93o | Any copy, unless 1 or more higher cards. | 1.9% |
| 32s | Any copy, unless no suit cards AND 3 overs, or 1 suit card AND 3 over 8. |
5.3% |
| 42s | Any copy, unless no cards of suit seen, or 1 suit seen and 3 overs. | 3.4% |
| 52s | Any copy, unless no cards of suit seen, or 1 suit seen and 3 overs. | 2.3% |
| 62s | Any copy, unless no cards of suit seen, or 1 suit seen and 3 overs. | 3.6% |
So while the ΔEV may be good for a given case in the above tables, these opportunities don’t come up often enough to make a significant overall difference.
