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| Ante Pay Table | ||||
| Hand | Pays | Combinations | Probability | Return |
| Player wins with royal flush | 102 | 736259040 | 0.000026 | 0.0027 |
| Player has royal flush, dealer doesn't qualify | 100 | 119892960 | 0.000004 | 0.000431 |
| Player wins with straight flush | 22 | 6001122284 | 0.000216 | 0.004747 |
| Player has straight flush, dealer doesn't qualify | 20 | 1089672828 | 0.000039 | 0.000784 |
| Player wins with four of a kind | 12 | 41419896552 | 0.001489 | 0.01787 |
| Player has four of a kind, dealer doesn't qualify | 10 | 909499320 | 0.000033 | 0.000327 |
| Player wins with full house | 5 | 589505037660 | 0.021195 | 0.105973 |
| Player wins with flush | 4 | 505131419580 | 0.018161 | 0.072645 |
| Player wins with straight or less | 3 | 6426670016572 | 0.23106 | 0.693181 |
| Player has full house, dealer doesn't qualify | 3 | 24601676832 | 0.000885 | 0.002654 |
| Player has flush, dealer doesn't qualify | 2 | 168883536432 | 0.006072 | 0.012144 |
| Player has straight or less, dealer doesn't qualify | 1 | 5521376219148 | 0.198512 | 0.198512 |
| Tie | 0 | 678596916580 | 0.024398 | 0 |
| Player folds | -1 | 5009067102600 | 0.180093 | -0.180093 |
| Player loses | -3 | 8839701755612 | 0.317817 | -0.953451 |
| Total | 27813810024000 | 1 | -0.021576 | |
The only pay table fully analyzed is pay table 3, because it takes my computer about a month to cycle through all possible combinations. However, assuming the player was following optimal strategy under pay table 3 but playing under pay table 1 or 2 then the house edge under pay table 1 would be 2.40%, and under pay table 2 would be 1.96%. The actual house edge under pay tables 1 and 2 would be slightly less or equal to these figures.
Unfortunately there is no easy way to quantify optimal strategy for this game. I can say the optimal strategy player will raise 82% of the time. So only in the worst 18% of hands should the player fold. In general these are when the player has two singletons in the hole that are low compared to the flop, with little or no chance for a straight or flush.
I am aware of two side bets, known as the AA+ as follows. Both are based on the poker value of the player's two cards and the three flop cards.
In version 1 a flush or higher pays 25 to 1 and a pair of aces to a straight pays 7 to 1. Following is the return table. The lower right cell shows a house edge of 6.40%.
| AA+ Side Bet, version 1 | ||||
| Hand | Pays | Combinations | Probability | Return |
| Royal Flush | 25 | 4 | 0.000002 | 0.000038 |
| Straight flush | 25 | 36 | 0.000014 | 0.000346 |
| 4 of a kind | 25 | 624 | 0.00024 | 0.006002 |
| Full house | 25 | 3744 | 0.001441 | 0.036014 |
| Flush | 25 | 5108 | 0.001965 | 0.049135 |
| Straight | 7 | 10200 | 0.003925 | 0.027473 |
| Three of a kind | 7 | 54912 | 0.021128 | 0.147899 |
| Two pair | 7 | 123552 | 0.047539 | 0.332773 |
| Pair of aces | 7 | 84480 | 0.032505 | 0.227537 |
| Other | -1 | 2316300 | 0.891241 | -0.891241 |
| Total | 2598960 | 1 | -0.064023 | |
Version 2 has the following return table. The lower right cell shows a house edge of 6.26%.
| AA+ Side Bet, version 2 | ||||
| Hand | Pays | Combinations | Probability | Return |
| Royal Flush | 100 | 4 | 0.000002 | 0.000154 |
| Straight flush | 50 | 36 | 0.000014 | 0.000693 |
| 4 of a kind | 40 | 624 | 0.00024 | 0.009604 |
| Full house | 30 | 3744 | 0.001441 | 0.043217 |
| Flush | 20 | 5108 | 0.001965 | 0.039308 |
| Straight | 7 | 10200 | 0.003925 | 0.027473 |
| Three of a kind | 7 | 54912 | 0.021128 | 0.147899 |
| Two pair | 7 | 123552 | 0.047539 | 0.332773 |
| Pair of aces | 7 | 84480 | 0.032505 | 0.227537 |
| Other | -1 | 2316300 | 0.891241 | -0.891241 |
| Total | 2598960 | 1 | -0.062583 | |
The above analysis was performed using a brute force combinatorial program that analyzed all 27,813,810,024,000 possible outcomes, and played every hand according to optimal player strategy. It took my computers about a month to crank though the 27.8 trillion hands.
The web site for Casino Hold'em, as well as other games, is www.casinopokergames.com.
There is a good Casino Hold 'Em calculator at beatingbonuses.com.
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