I first came across Triple Action Hold 'Em at Binion's Horseshoe on May 1, 2009. This game can also be found at various internet casinos. Cryptologic software The game utilizes a unique 28-card deck, which includes cards ranging from eights to aces, making it quite straightforward.
Rules
Players begin the game by placing one of three types of bets: the Ante, the Flop Bet, or the Bonus Bet.
Each player, as well as the dealer, is dealt two hidden cards. Additionally, a three-card flop is dealt face down, while one of the dealer's cards is shown face up and one is kept face down.
Players must choose to either make a Raise bet that matches their Ante or fold their hand. If they fold, they forfeit their Ante bet.
Once players have made their decisions, the dealer reveals his second hole card along with the flop.
For the dealer to qualify, he needs to have a five-card poker hand consisting of at least a pair of nines.
If the dealer does not qualify, the player receives their Ante bet back with even odds, and the Raise bet is pushed.
In cases where the dealer qualifies, the player's five-card hand is compared against the dealer's to determine the winner. If the player has a stronger hand, both the Ante and Raise bets pay out at even odds. If the dealer’s hand is superior, then both bets are lost. A tie results in a push.
Should the player not fold and hold a full house or better, they will receive an Ante Bonus based on the Ante amount, without needing to surpass the dealer's hand.
Regardless of the outcome for the player versus dealer comparison, the Flop and Bonus bets pay according to established tables. It seems that even if the player folds, they can still win their Bonus bet.
The best approach for the Ante bet is to always raise it. Out of the three betting options, the Ante bet carries the least risk at 1.82%. I frequently receive inquiries regarding the best betting strategy for similar games, and in this instance, it is wise to stake fully on the Ante while avoiding the Flop and Bonus bets.
Ante Bonus Pay Table
Five-Card Hand
Pays
Royal flush
50 to 1
Straight flush
20 to 1
Flush
6 to 1
Four of a kind
4 to 1
Full house
2 to 1
All other
None
Flop Bet Pay Table
Five-Card Hand
Pays
Straight flush
10 to 1
Three of a kind
10 to 1
Flush
4 to 1
Straight
2 to 1
Jacks or better
1 to 1
All other
Loss
Bonus Bet Pay Table
Five-Card Hand
Pays
Royal flush
100 to 1
Straight flush
50 to 1
Flush
25 to 1
Four of a kind
15 to 1
Full house
8 to 1
Straight
6 to 1
Three of a kind
3 to 1
Two pair
1 to 1
All other
Loss
Strategy
The return table shared below depicts the returns before the Ante Bonus is considered.
Ante Bet Analysis
The table that follows outlines the Ante Bonus's impact on the overall return.
Ante Bet Analysis
Event
Pays
Combinations
Probability
Return
Win
2
68426184
0.275193
0.550385
Dealer doesn't qualify
1
65881200
0.264957
0.264957
Push
0
4053024
0.0163
0
Lose
-2
110287992
0.44355
-0.8871
Totals
248648400
1
-0.071758
Taking everything into account, the total return on the Ante bet stands at -0.071758 plus 0.035409, which equals -0.036349. This implies a house edge of 3.63%. Players are advised to always raise, leading to an average final stake of two units.
Ante Bonus Analysis
Event
Pays
Combinations
Probability
Return
Royal flush
50
4
0.000041
0.002035
Straight flush
20
8
0.000081
0.001628
Flush
6
72
0.000733
0.004396
Four of a kind
4
168
0.001709
0.006838
Full house
2
1008
0.010256
0.020513
All other
0
97020
0.987179
0
Total
98280
1
0.035409
A detailed table listing expected value calculations for every possible initial combination of player and dealer cards is available in my analysis. element of risk = 3.63%/2 = 1.82%.
Flop Bet Analysis
Flop Bet Analysis
Five-Card Hand
Pays
Combinations
Probability
Return
Straight flush
10
20
0.006105
0.06105
Three of a kind
10
28
0.008547
0.08547
Flush
4
120
0.03663
0.14652
Straight
2
300
0.091575
0.18315
Jacks or better
1
576
0.175824
0.175824
All other
-1
2232
0.681319
-0.681319
Total
3276
1
-0.029304
Bonus Bet Analysis
Bonus Bet Analysis
Five-Card Hand
Pays
Combinations
Probability
Return
Royal flush
100
4
0.000041
0.00407
Straight flush
50
8
0.000081
0.00407
Flush
25
72
0.000733
0.018315
Four of a kind
15
168
0.001709
0.025641
Full house
8
1008
0.010256
0.082051
Straight
6
3060
0.031136
0.186813
Three of a kind
3
6720
0.068376
0.205128
Two pair
1
15120
0.153846
0.153846
All other
-1
72120
0.733822
-0.733822
Total
98280
1
-0.053887
Appendix
There are mathematically sound strategies and insights regarding various casino games such as blackjack, craps, roulette, and many others. Triple Action Hold 'Em appendix .
Acknowledgments
My thanks to J.B. and Charles R. Mousseau Please check your inbox for an email and click on the link we’ve sent you to finalize your registration.