Introduction

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World Poker Tour All-In Hold'em is poker based table game found at many of the MGM/Mirage casinos in Las Vegas. There are two versions, both with the same name. In one, the player can raise up to 3X his Ante, and in the other, up to 10X his Ante. In the version addressed on this page, the player can raise up to 3X his ante bet. See World Poker Tour 10X Raise Hold 'Em, for the other 10X version. The rules are very true to real poker and the Element of Risk is only 0.196%.

Rules

The game uses a single 52-card deck.
Play begins with the player making an ante bet and two optional side bets
Player gets two 'hole' cards face down, which he may examine.
Player has two choices, raise or fold.
If player folds he forfeits his ante bet.
If player raises he must make a raise bet equal to three times the ante.
If the player raised the dealer will call with any pair or a blackjack point value of 11 or higher.
If the dealer does not call then he will fold. In this case the player will win even money on the ante and the raise will push.
Five community cards will be dealt.
If both player and dealer are still in the game the higher poker hand will win. If the player has the higher hand both ante and raise will pay even money. If dealer has the higher hand the ante and raise will lose. A tie will result in a push.
The 'Player's Hole Cards Bonus Bet' is paid according to the value of the player's two hold cards. The pay table is below.
The 'Player's Final Hand Bonus Bet' is paid according to the value of the player's final seven cards hand. The pay table is below.
Even if the player folds the cards will still be played out to resolve any side bets. In the event one or more players raise and one or more go all-in the dealer will separately adjudicate each hand according to the above rules.

Player's Hole Cards Bonus Bet

Hand	Pays
Two red aces	50 to 1
Ace/king suited	25 to 1
Pair of aces	20 to 1
Pair J-K	8 to 1
Pair 6-10	3 to 1
Pair 2-5	2 to 1
Suited	1 to 1
All other	Loss

Player's Final Hand Bonus Bet

Hand	Pays
Royal flush	500 to 1
Straight flush	100 to 1
Four of a kind	40 to 1
Full house	8 to 1
Flush	6 to 1
Straight	4 to 1
Three of a kind	2 to 1
All other	Loss

Strategy

The following table shows the optimal strategy. The player will raise 91.9% of the time, in all but nine hands.

House Edge

The following table shows the probability and return for all possible outcomes, assuming optimal strategy. The lower right cell shows a house edge of 0.74%. The average wager is 3.756 units, so the Element of Risk is a very low 0.20%.

All In Hold 'Em 3X — Return Table under Optimal Strategy

Win	Combinations	Probability	Return
4	1028334618404	0.369721	1.478884
1	373453502400	0.134269	0.134269
0	82860379592	0.029791	0
-1	226537819200	0.081448	-0.081448
-4	1070194682804	0.384771	-1.539084
Total	2781381002400	1	-0.007379

The following table shows the probability and return for all possible outcomes, playing blind (always raising). The lower right cell shows a house edge of 1.35%. The average wager is 4 units, so the Element of Risk is 0.34%.

All In Hold 'Em 3X — Return Table under Playing Blind

Win	Combinations	Probability	Return
4	1089643156268	0.391763	1.567053
1	402733900800	0.144796	0.144796
0	89287177820	0.032102	0
-4	1199716767512	0.431339	-1.725354
Total	2781381002400	1	-0.013504

Expected Value Table

The following table shows the expected value by raising and going all-in for all possible hands. The probability of the 2-card hand the contribution to the total return are also indicated.

World Poker Tour All-In Hold'Em Expected Value Table

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Higher Card	Lower Card	Type	Raise	Probability	Return
A	A	Pair	2.537	0.004525	0.01148
K	K	Pair	2.322202	0.004525	0.010508
Q	Q	Pair	2.12371	0.004525	0.00961
J	J	Pair	1.926	0.004525	0.008715
10	10	Pair	1.728031	0.004525	0.007819
9	9	Pair	1.489993	0.004525	0.006742
8	8	Pair	1.266058	0.004525	0.005729
7	7	Pair	1.052931	0.004525	0.004764
6	6	Pair	0.855409	0.004525	0.003871
5	5	Pair	0.665863	0.004525	0.003013
4	4	Pair	0.460929	0.004525	0.002086
3	3	Pair	0.26773	0.004525	0.001211
2	2	Pair	0.08572	0.004525	0.000388
A	K	Suited	1.317765	0.003017	0.003975
A	Q	Suited	1.249313	0.003017	0.003769
A	J	Suited	1.182055	0.003017	0.003566
A	10	Suited	1.116615	0.003017	0.003368
A	9	Suited	0.974734	0.003017	0.00294
A	8	Suited	0.900643	0.003017	0.002717
A	7	Suited	0.821663	0.003017	0.002479
A	6	Suited	0.739532	0.003017	0.002231
A	5	Suited	0.734791	0.003017	0.002217
A	4	Suited	0.667288	0.003017	0.002013
A	3	Suited	0.609512	0.003017	0.001839
A	2	Suited	0.554117	0.003017	0.001672
K	Q	Suited	1.02153	0.003017	0.003082
K	J	Suited	0.953209	0.003017	0.002875
K	10	Suited	0.888743	0.003017	0.002681
K	9	Suited	0.74892	0.003017	0.002259
K	8	Suited	0.613747	0.003017	0.001851
K	7	Suited	0.548762	0.003017	0.001655
K	6	Suited	0.478987	0.003017	0.001445
K	5

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