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World Poker Tour 3X Raise Hold \"Em

Introduction

World Poker Tour All-In Hold'em is a poker-themed table game found in various MGM/Mirage casinos in Las Vegas. There are two different game formats sharing the same name. In one format, players can increase their bet up to 3X their initial ante, while in the other format, they can increase it up to 10X. This particular page discusses the version where players can raise up to 3X their ante bet. For details about the 10X variant, please refer to World Poker Tour 10X Raise Hold \"Em , which explains the other version. The gameplay is designed to closely resemble authentic poker, and the Element of Risk is only 0.196%.

Rules

  1. The game uses a single 52-card deck.
  2. The game kicks off with players making an ante bet, along with two optional side bets.
  3. Each player receives a pair of 'hole' cards facedown that they can look at privately.
  4. Player has two choices, raise or fold.
  5. If a player decides to fold, they lose their ante bet.
  6. When a player opts to raise, they must place an additional wager that is three times the initial ante.
  7. If the player raises, the dealer will call with either a pair or a blackjack point value of 11 or greater.
  8. Should the dealer not respond to the bet, they will fold. In such a case, the player will win their original ante, while the additional raise bet will not result in any change.
  9. Five community cards will be dealt.
  10. If both the player and the dealer continue in the game, the winner is determined by the higher poker hand. If the player holds the superior hand, they will receive even money on both their ante and raise. Conversely, if the dealer has the better hand, the player will lose both bets. In the event of a tie, bets will remain unchanged.
  11. The 'Player's Hole Cards Bonus Bet' pays out based on the ranks of the player’s two hidden cards, with the payout structure indicated below.
  12. The 'Player's Final Hand Bonus Bet' rewards players based on the strength of their final hand consisting of seven cards, as detailed in the payout table below.
  13. Even if the player decides to fold, the game will continue to determine the outcomes of any side bets. If multiple players choose to raise or go all-in, the dealer will evaluate each hand according to the specified rules independently.

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 table below outlines the optimal gameplay strategy, revealing that players will raise 91.9% of the time, with only nine hands prompting a different decision.

House Edge

The subsequent table provides insights into the likelihood and potential returns for various outcomes, assuming players follow the optimal strategy. Notably, the lower right corner displays a house edge of 0.74%. The average bet placed is 3.756 units, which informs 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 next table illustrates the probabilities and returns for different outcomes when playing recklessly (always opting to raise). The lower right corner indicates a house edge of 1.35%, with an average wager of 4 units, corresponding to 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 details the expected value derived from raising and going all-in for all possible hands. The associated probabilities and their contributions to the overall return are also specified.

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

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 Suited 0.419135 0.003017 0.001264
K 4 Suited 0.349045 0.003017 0.001053
K 3 Suited 0.289016 0.003017 0.000872
K 2 Suited 0.23241 0.003017 0.000701
Q J Suited 0.763087 0.003017 0.002302
Q 10 Suited 0.698167 0.003017 0.002106
Q 9 Suited 0.558269 0.003017 0.001684
Q 8 Suited 0.426298 0.003017 0.001286
Q 7 Suited 0.292091 0.003017 0.000881
Q 6 Suited 0.237735 0.003017 0.000717
Q 5 Suited 0.178256 0.003017 0.000538
Q 4 Suited 0.108002 0.003017 0.000326
Q 3 Suited 0.047817 0.003017 0.000144
Suited 2 A Suited 0.003017 A
Suited 10 A 0.53638 0.003017 0.001618
Suited 9 A 0.392804 0.003017 0.001185
Suited 8 K 0.262303 0.003017 0.000791
Q 7 Suited 0.130598 0.003017 0.000394
K 6 J 0.00073 0.003017 0.000002
Suited 5 K Suited 0.003017 K
Suited 4 K Suited 0.003017 K
Suited 3 K Suited 0.003017 K
Suited 2 K Suited 0.003017 K
10 9 Suited 0.254435 0.003017 0.000768
10 8 K 0.123236 0.003017 0.000372
10 7 Suited Q 0.003017 J
10 6 Suited Q 0.003017 Suited
10 5 Q Suited 0.003017 Q
10 4 Suited Q 0.003017 Suited
10 3 Q Suited 0.003017 Q
10 2 Suited Q 0.003017 Suited
9 8 Q Suited 0.003017 Suited
9 7 A Suited 0.003017 A
9 6 Suited A 0.003017 Suited
9 5 A Suited 0.003017 K
9 4 Q Suited 0.003017 K
9 3 J Suited 0.003017 K
9 2 Suited K 0.003017 Suited
8 7 K Suited 0.003017 K
8 6 Suited K 0.003017 Suited
8 5 K Suited 0.003017 K
8 4 Suited K 0.003017 Suited
8 3 K Suited 0.003017 Q
8 2 J Suited 0.003017 Q
7 6 Suited Q 0.003017 Suited
7 5 Q Suited 0.003017 Q
7 4 Suited Q 0.003017 Suited
7 3 Q Suited 0.003017 Q
7 2 Suited Q 0.003017 Suited
6 5 Q Suited 0.003017 Q
6 4 Suited -0.009104 0.003017 -0.000027
6 3 J Suited 0.003017 J
6 2 Suited J 0.003017 Suited
5 4 J Suited 0.003017 J
5 3 Suited J 0.003017 Suited
5 2 J Suited 0.003017 -0.042873
4 3 -0.000129 J 0.003017 Suited
4 2 -0.112919 -0.000341 0.003017 J
3 2 Suited -0.17305 0.003017 -0.000522
J Suited -0.229916 1.203263 0.00905 0.010889
-0.000694 Suited Suited 1.130459 0.00905 0.01023
Suited -0.007119 -0.000021 1.058799 0.00905 0.009582
Suited 10 -0.135128 0.988983 0.00905 0.00895
-0.000408 9 Suited 0.837117 0.00905 0.007576
-0.259173 8 -0.000782 0.756525 0.00905 0.006846
Suited 7 -0.313017 0.670661 0.00905 0.006069
-0.000944 6 Suited 0.581397 0.00905 0.005262
-0.372681 5 -0.001124 0.576203 0.00905 0.005215
Suited 4 Q 0.502534 0.00905 0.004548
Suited 3 Q 0.439167 0.00905 0.003974
Suited 2 -0.009104 0.378193 0.00905 0.003423
-0.000027 J Suited 0.889344 0.00905 0.008048
J Suited J 0.81651 0.00905 0.007389
Suited 10 J 0.747699 0.00905 0.006767
Suited 9 J 0.597983 0.00905 0.005412
Suited 8 J 0.452547 0.00905 0.004095
Suited 7 J 0.381647 0.00905 0.003454
Suited 6 -0.042873 0.305742 0.00905 0.002767
-0.000129 5 J 0.241499 0.00905 0.002186
Suited 4 -0.112919 0.165108 0.00905 0.001494
-0.000341 3 J 0.099395 0.00905 0.0009
Suited 2 -0.17305 0.037196 0.00905 0.000337
-0.000522 J Suited 0.615854 0.00905 0.005573
-0.229916 10 -0.000694 0.546529 0.00905 0.004946
Suited 9 Suited 0.396735 0.00905 0.00359
Suited 8 -0.007119 0.254682 0.00905 0.002305
-0.000021 7 Suited 0.110169 0.00905 0.000997
-0.135128 6 -0.000408 0.050779 0.00905 0.00046
Suited 5 -0.259173 -0.000782 0.00905 Suited
-0.313017 4 -0.000944 Suited 0.00905 -0.372681
-0.001124 3 Suited Q 0.00905 Suited
Q 2 Suited -0.009104 0.00905 -0.000027
J 10 Suited 0.375919 0.00905 0.003402
J 9 Suited 0.222222 0.00905 0.002011
J 8 Suited 0.081718 0.00905 0.00074
J 7 Suited J 0.00905 Suited
J 6 Suited J 0.00905 Suited
-0.042873 5 -0.000129 J 0.00905 Suited
-0.112919 4 -0.000341 J 0.00905 Suited
-0.17305 3 -0.000522 J 0.00905 Suited
-0.229916 2 -0.000694 Suited 0.00905 Suited
10 9 Suited 0.076457 0.00905 0.000692
10 8 -0.007119 -0.000021 0.00905 Suited
10 7 -0.135128 -0.000408 0.00905 Suited
10 6 -0.259173 -0.000782 0.00905 Suited
10 5 -0.313017 -0.000944 0.00905 Suited
10 4 -0.372681 -0.001124 0.00905 Suited
10 3 -0.429102 -0.001294 0.00905 Suited
10 2 -0.004189 -0.000013 0.00905 Suited
9 8 -0.130669 -0.000394 0.00905 Suited
9 7 -0.257263 -0.000776 0.00905 Suited
9 6 -0.380598 -0.001148 0.00905 Suited
9 5 -0.517201 -0.00156 0.00905 Suited
9 4 -0.560079 -0.00169 0.00905 Suited
9 3 -0.615748 -0.001857 0.00905 Suited
9 2 -0.224752 -0.000678 0.00905 Suited
8 7 -0.34629 -0.001045 0.00905 Suited
8 6 -0.467037 -0.001409 0.00905 Suited
8 5 -0.601872 -0.001816 0.00905 Suited
8 4 -0.730323 -0.002203 0.00905 Suited
8 3 -0.762681 -0.002301 0.00905 Suited
8 2 -0.391098 -0.00118 0.00905 Suited
7 6 -0.507268 -0.00153 0.00905 Suited
7 5 -0.639444 -0.001929 0.00905 Suited
7 4 -0.762109 -0.002299 0.00905 Suited
7 3 -0.87979 -0.002654 0.00905 Suited
7 2 -0.509758 -0.001538 0.00905 Suited
6 5 -0.631583 -0.001905 0.00905 Suited
6 4 -0.750146 -0.002263 0.00905 Suited
6 3 -0.868137 -0.002619 0.00905 Suited
6 2 -0.582347 -0.001757 0.00905 Suited
5 4 -0.696386 -0.002101 0.00905 Suited
5 3 -0.813149 -0.002453 0.00905 Suited
5 2 -0.752076 -0.002269 0.00905 Suited
4 3 -0.867297 -0.002616 0.00905 Suited
4 2 -0.920104 -0.002776 0.00905 A
3 2 K Unsuited 0.00905 A
Q 1 Unsuited

A

The next table outlines the potential results of the Player Hole Cards side bet. The lower right corner indicates a house edge of 7.24%.

J

Unsuited A Unsuited A Unsuited
A 50 1 0.000754 0.037707
Unsuited 25 4 0.003017 0.075415
A 20 5 0.003771 0.075415
Unsuited 8 18 0.013575 0.108597
A 3 30 0.022624 0.067873
Unsuited 2 24 0.0181 0.036199
A 1 308 0.232278 0.232278
Unsuited A 936 0.705882 Unsuited
A 1326 1 Unsuited

A

The subsequent table illustrates the potential outcomes of the Final Hand side bet, with a noted house edge of 6.55%.

Unsuited

K Q Unsuited K J
Unsuited 500 4324 0.000032 0.01616
K 100 37260 0.000279 0.027851
Unsuited 40 224848 0.001681 0.067227
K 8 3473184 0.025961 0.207688
Unsuited 6 4047644 0.030255 0.18153
K 4 6180020 0.046194 0.184775
Unsuited 2 6461620 0.048299 0.096597
K Unsuited 113355660 0.8473 K
Unsuited 133784560 1 K

Unsuited

K .