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Four Card PokerLast Update: Jul 07, 2009
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| Bonus Pay Table | ||
|---|---|---|
| Hand | Table 1 | Table 2 |
| Four of a kind | 25 | 30 |
| Straight flush | 20 | 15 |
| Three of a kind | 2 | 2 |
| Aces Up Pay Table | |||||||
|---|---|---|---|---|---|---|---|
| Hand | Table 1 | Table 2 | Table 3 | Table 4 | Table 5 | Table 6 | Table 7 |
| Four of a kind | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 |
| Straight flush | 40 to 1 | 40 to 1 | 30 to 1 | 30 to 1 | 40 to 1 | 40 to 1 | 40 to 1 |
| Three of a kind | 9 to 1 | 7 to 1 | 9 to 1 | 7 to 1 | 8 to 1 | 8 to 1 | 7 to 1 |
| Flush | 6 to 1 | 6 to 1 | 6 to 1 | 6 to 1 | 5 to 1 | 6 to 1 | 5 to 1 |
| Straight | 4 to 1 | 5 to 1 | 4 to 1 | 5 to 1 | 4 to 1 | 4 to 1 | 4 to 1 |
| Two pair | 2 to 1 | 2 to 1 | 2 to 1 | 2 to 1 | 3 to 1 | 2 to 1 | 3 to 1 |
| Pair of aces or better | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 |
A simple strategy to this game, first proposed by Stanley Ko, is as follows.
According to the second edition of "Beyond Countingâ" by James Grosjean, this "simple strategy" results in a house edge of 3.396%.
In the same book, Grosjean presents a ten-step strategy, which also takes into consideration the dealer's up card, and the player's singletons. Out of respect of copyright, I will not re-publish his strategy. According to Grosjean, his ten-step strategy has a house edge of 2.840% under Bonus pay table 1, and 3.199% under pay table 2.
The next table shows the probability of each hand and the return under pay table 5 of the Aces Up side bet. I chose table 5 because that is the only one I knew to be in play at the time of this writing. The lower right cell shows a house edge of 3.89%.
| Return for Aces Up Pay Table 5 | ||||
|---|---|---|---|---|
| Hand | Combinations | Probability | Pays | Return |
| Four of a kind | 624 | 0.00024 | 50 | 0.012005 |
| Straight flush | 2072 | 0.000797 | 40 | 0.03189 |
| Three of a kind | 58656 | 0.022569 | 8 | 0.180552 |
| Flush | 114616 | 0.044101 | 5 | 0.220504 |
| Straight | 101808 | 0.039173 | 4 | 0.15669 |
| Two pair | 123552 | 0.047539 | 3 | 0.142617 |
| Pair of aces | 81096 | 0.031203 | 1 | 0.031203 |
| Nothing | 2116536 | 0.814378 | -1 | -0.814378 |
| Total | 2598960 | 1 | -0.038917 | |
The next table shows the house edge according to all four Aces Up pay tables.
| Aces Up House Edge | |
|---|---|
| Pay Table | House Edge |
| 1 | 1.98% |
| 2 | 2.58% |
| 3 | 2.78% |
| 4 | 3.37% |
| 5 | 3.89% |
| 6 | 4.24% |
| 7 | 6.15% |
Note: There is also a similar game called Crazy Four Poker.
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