Last Updated: February 19, 2012

Texas Hold’em Bonus

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Introduction

Texas Hold 'Em Bonus is a poker based table game I noticed at the Flamingo Hilton in Las Vegas in September 2005. I also hear that it can be found in Atlantic City. Like real Texas Hold 'em the player may bet his hole card, after the flop, and after the turn (but not after the river). As in one on one poker all bets pay one to one, except the ante requires a straight or flush (depending on the location) or higher to pay.

Las Vegas Rules

  1. The game is played with a single 52-card deck.
  2. The player makes an Ante wager, plus an optional Bonus bet.
  3. Two hole cards are dealt face down to the player and dealer. The player may look at his own cards.
  4. The player must either fold or make a Flop bet. The Flop bet must be two times the amount of the ante.
  5. Three community cards (the Flop) are dealt.
  6. The player may do nothing or make a Turn bet. The Turn bet must be exactly equal to the ante bet.
  7. A fourth community card is dealt (the Turn).
  8. The player may do nothing or make a River bet. The River bet must be exactly equal to the ante bet.
  9. A fifth community card is dealt (the River).
  10. The player and dealer each make the best five-card hand using any combination of the five community cards and his own two initial hole cards. The higher hand wins.
  11. If the dealer has the higher hand the player will lose all wagers, except possibly the Bonus bet.
  12. If the player has the higher hand the Flop, Turn, and River bets will pay even money. If the player has a straight or higher the Ante bet will also pay even money, otherwise it will push.
  13. If the player and dealer have hands of equal value the the Ante, Flop, Turn, and River bets will all push.
  14. The Bonus bet will pay based only the player's and dealer's initial cards, according to the pay table posted.

The Horseshoe casino in Hammond, Indiana, follows the Las Vegas pay table.

Atlantic City Rules

There are only two rule differences under the Las Vegas rules. The player needs a flush or higher to win even money on the ante. The bonus bet does not have a line item for both player and dealer having a pair of aces.

House Edge

The following table shows all the possible outcomes assuming optimal player strategy and the Las Vegas rules. An explanation of each column follows the table. The lower right cell shows a house edge of 2.04%. The standard deviation is 3.51.

Texas Hold 'em Bonus Return Table — Las Vegas Rules

Turn Bet River Bet Outcome Win Combinations Probability Return
No No Dealer wins -3 16191937969988 0.291077 -0.873232
No No Tie 0 1259275163176 0.022638 0
No No Player wins with less than straight 2 5303424537200 0.095338 0.190676
No No Player wins with straight or higher 3 1084471210036 0.019495 0.058486
No Yes Dealer wins -4 1396173000700 0.025099 -0.100394
No Yes Tie 0 167704605536 0.003015 0
No Yes Player wins with less than straight 3 2296867062000 0.04129 0.12387
No Yes Player wins with straight or higher 4 605730184164 0.010889 0.043556
Yes No Dealer wins -4 1896639509356 0.034095 -0.136381
Yes No Tie 0 135581445288 0.002437 0
Yes No Player wins with less than straight 3 1247381880480 0.022424 0.067271
Yes No Player wins with straight or higher 4 252140929436 0.004533 0.018131
Yes Yes Dealer wins -5 5604708827316 0.100754 -0.50377
Yes Yes Tie 0 547943447680 0.00985 0
Yes Yes Player wins with less than straight 4 12372657154480 0.222419 0.889677
Yes Yes Player wins with straight or higher 5 2747896241164 0.049398 0.24699
Player folds -1 2517086880000 0.045249 -0.045249
Total 55627620048000 1 -0.020369

Explanation of table

  • Column 1:Yes if player makes turn bet, no otherwise
  • Column 2:Yes if player makes river bet, no otherwise
  • Column 3:Outcome
  • Column 4: Net win
  • Column 5:Total combinations
  • Column 6:Probability
  • Column 7:Contribution to return (win*probability)

The lower right cell shows a house edge of 2.037%. However I think this makes the game look like a worse bet than it really is. What this means is that for every dollar bet on the ante the player can expect to lose 2.037 cents. However by the end of the hand the average wager will be 3.8181 times the ante. So the element of risk, or ratio of loss to total amount bet is a much lower 2.037%/3.8181=0.5335%. The standard deviation is 3.500839.

According to Scott McIntosh the house edge is 5.5935% under the Atlantic City rules. I trust this figure because we agree exactly on the Las Vegas rules.

Strategy

The following is when the player should fold according to the rules.

  • Las Vegas: unsuited 2/3 to 2/7.
  • Atantic City: unsuited 2/3 to 2/7, and unsuited 3/4.
  • I have not quantified the strategy past the first decision point. I can say that under the Las Vegas rules the player who made the Flop bet will make the Turn bet 43.13% of the time, and the River bet 48.46% of the time. If the player made the turn bet, then he will also make the river bet 85.76% of the time. If the player made the flop bet, but not the turn bet, he will make the river bet 15.78% of the time.

    The following table shows the expected value of all 169 possible initial hands under both the Las Vegas and Atlantic City rules.

    Two-Card Expected Values

    Initial Hand

    Las Vegas Rules

    Atlantic City Rules

    2,3 unsuited -1.155927 -1.195592
    2,4 unsuited -1.091604 -1.13521
    2,5 unsuited -1.019987 -1.067022
    2,6 unsuited -1.046723 -1.077817
    2,7 unsuited -1.031301 -1.050057
    2,8 unsuited -0.896002 -0.917393
    2,9 unsuited -0.763132 -0.784523
    2,T unsuited -0.613979 -0.636507
    2,J unsuited -0.459414 -0.478676
    2,Q unsuited -0.28969 -0.305687
    2,K unsuited -0.102668 -0.1154
    2,A unsuited 0.184373 0.160096
    3,4 unsuited -0.950034 -1.009069
    3,5 unsuited -0.874456 -0.937452
    3,6 unsuited -0.899632 -0.946711
    3,7 unsuited -0.8854 -0.919748
    3,8 unsuited -0.850607 -0.872617
    3,9 unsuited -0.699497 -0.724139
    3,T unsuited -0.549947 -0.575726
    3,J unsuited -0.395206 -0.417719
    3,Q unsuited -0.225563 -0.24481
    3,K unsuited -0.038499 -0.054482
    3,A unsuited 0.254437 0.226376
    4,5 unsuited -0.735126 -0.813569
    4,6 unsuited -0.756096 -0.819136
    4,7 unsuited -0.740561 -0.790904
    4,8 unsuited -0.7068 -0.744413
    4,9 unsuited -0.654394 -0.679669
    4,T unsuited -0.487036 -0.516079
    4,J unsuited -0.332233 -0.358011
    4,Q unsuited -0.162612 -0.185124
    4,K unsuited 0.024799 0.005551
    4,A unsuited 0.321642 0.290174
    5,6 unsuited -0.614318 -0.692805
    5,7 unsuited -0.595481 -0.661787
    5,8 unsuited -0.560487 -0.614096
    5,9 unsuited -0.508593 -0.549471
    5,T unsuited -0.437507 -0.467184
    5,J unsuited -0.265364 -0.294408
    5,Q unsuited -0.095642 -0.12142
    5,K unsuited 0.092367 0.069855
    5,A unsuited 0.392893 0.358138
    6,7 unsuited -0.457726 -0.536213
    6,8 unsuited -0.421014 -0.48732
    6,9 unsuited -0.36839 -0.421999
    6,T unsuited -0.297258 -0.339273
    6,J unsuited -0.217975 -0.244386
    6,Q unsuited -0.031216 -0.056994
    6,K unsuited 0.156819 0.134306
    6,A unsuited 0.370719 0.351472
    7,8 unsuited -0.284039 -0.362526
    7,9 unsuited -0.229986 -0.296292
    7,T unsuited -0.157768 -0.212535
    7,J unsuited -0.078216 -0.116966
    7,Q unsuited 0.019887 -0.003259
    7,K unsuited 0.224911 0.202399
    7,A unsuited 0.456798 0.434885
    8,9 unsuited -0.092377 -0.170864
    8,T unsuited -0.016383 -0.08401
    8,J unsuited 0.062709 0.011207
    8,Q unsuited 0.16144 0.125955
    8,K unsuited 0.282809 0.262927
    8,A unsuited 0.533716 0.511803
    9,T unsuited 0.127027 0.046521
    9,J unsuited 0.20434 0.139978
    9,Q unsuited 0.304465 0.256228
    9,K unsuited 0.428187 0.395968
    9,A unsuited 0.602407 0.583126
    T,J unsuited 0.370279 0.288219
    T,Q unsuited 0.471694 0.405776
    T,K unsuited 0.600228 0.550453
    T,A unsuited 0.78194 0.745643
    J,Q unsuited 0.535555 0.472903
    J,K unsuited 0.665761 0.619251
    J,A unsuited 0.852493 0.819462
    Q,K unsuited 0.735444 0.6922
    Q,A unsuited 0.925311 0.895545
    K,A unsuited 0.999317 0.972816
    2,3 suited -0.886985 -0.923987
    2,4 suited -0.826008 -0.866658
    2,5 suited -0.75798 -0.801803
    2,6 suited -0.782881 -0.811796
    2,7 suited -0.768076 -0.785429
    2,8 suited -0.639021 -0.658814
    2,9 suited -0.51015 -0.529944
    2,T suited -0.364595 -0.385438
    2,J suited -0.212709 -0.23053
    2,Q suited -0.044946 -0.059747
    2,K suited 0.141142 0.129363
    2,A suited 0.425022 0.402419
    3,4 suited -0.693044 -0.74813
    3,5 suited -0.62123 -0.679983
    3,6 suited -0.644776 -0.688639
    3,7 suited -0.631082 -0.663007
    3,8 suited -0.597478 -0.617842
    3,9 suited -0.450882 -0.473684
    3,T suited -0.304918 -0.328768
    3,J suited -0.152868 -0.173698
    3,Q suited 0.014889 -0.002919
    3,K suited 0.201376 0.186589
    3,A suited 0.490618 0.464512
    4,5 suited -0.490199 -0.563403
    4,6 suited -0.509707 -0.5685
    4,7 suited -0.494853 -0.541737
    4,8 suited -0.461634 -0.496581
    4,9 suited -0.40913 -0.432516
    4,T suited -0.246108 -0.272979
    4,J suited -0.094025 -0.117875
    4,Q suited 0.073849 0.053019
    4,K suited 0.260929 0.243121
    4,A suited 0.553554 0.524295
    5,6 suited -0.376191 -0.449435
    5,7 suited -0.357989 -0.419804
    5,8 suited -0.323018 -0.372923
    5,9 suited -0.270833 -0.308801
    5,T suited -0.199974 -0.227429
    5,J suited -0.031373 -0.058245
    5,Q suited 0.136745 0.112895
    5,K suited 0.324793 0.303963
    5,A suited 0.620767 0.588467
    6,7 suited -0.227072 -0.300316
    6,8 suited -0.190276 -0.252091
    6,9 suited -0.137464 -0.187369
    6,T suited -0.066542 -0.105559
    6,J suited 0.013273 -0.011162
    6,Q suited 0.197628 0.173777
    6,K suited 0.385858 0.365029
    6,A suited 0.59982 0.582012
    7,8 suited -0.05986 -0.133104
    7,9 suited -0.005551 -0.067365
    7,T suited 0.066287 0.015313
    7,J suited 0.146267 0.110272
    7,Q suited 0.246024 0.22461
    7,K suited 0.451106 0.430277
    7,A suited 0.682911 0.662637
    8,9 suited 0.125648 0.052404
    8,T suited 0.200955 0.13792
    8,J suited 0.280795 0.232842
    8,Q suited 0.381333 0.348359
    8,K suited 0.50656 0.488168
    8,A suited 0.757219 0.736945
    9,T suited 0.33757 0.262459
    9,J suited 0.416267 0.356253
    9,Q suited 0.518407 0.473476
    9,K suited 0.646145 0.616192
    9,A suited 0.822276 0.80444
    T,J suited 0.574533 0.497955
    T,Q suited 0.677017 0.615537
    T,K suited 0.808521 0.762138
    T,A suited 0.990289 0.956538
    J,Q suited 0.737666 0.679207
    J,K suited 0.870492 0.82713
    J,A suited 1.056211 1.02548
    Q,K suited 0.936506 0.896165
    Q,A suited 1.124432 1.096723
    K,A suited 1.194024 1.169336
    2,2 pair -0.134137 -0.140431
    3,3 pair 0.078584 0.068777
    4,4 pair 0.322289 0.308953
    5,5 pair 0.589457 0.572593
    6,6 pair 0.837465 0.820601
    7,7 pair 1.093669 1.076805
    8,8 pair 1.353048 1.336184
    9,9 pair 1.612114 1.59525
    T,T pair 1.87899 1.860933
    J,J pair 2.097415 2.082887
    Q,Q pair 2.315838 2.304838
    K,K pair 2.535691 2.528219
    A,A pair 2.788899 2.78206

    Bonus Bet

    The bonus bet pays based only on the players hole cards, and in some cases the dealer's two hole cards. Who wins the hand does not matter. There seem to be two pay tables available for the bonus bet as follows. From what I hear the Atlantic City pay table is also used in Missouri and Indiana.

    Bonus Bet — Las Vegas Rules

    Event Pays Combinations Probability Return
    Player has AA, dealer has AA 1000 6 0.000004 0.003694
    Player has AA 30 7344 0.004521 0.135636
    Player has AK suited 25 4900 0.003017 0.075415
    Player has AQ or AJ suited 20 9800 0.006033 0.120664
    Player has AK unsuited 15 14700 0.00905 0.135747
    Player has KK, QQ, or JJ 10 22050 0.013575 0.135747
    Player has AQ or AJ unsuited 5 29400 0.0181 0.090498
    Player has Pair 22 to 10,10 3 66150 0.040724 0.122172
    All other -1 1470000 0.904977 -0.904977
    Total 1624350 1 -0.085406

    Bonus Bet — Atlantic City Rules

    Event Pays Combinations Probability Return
    AA 30 7350 0.004525 0.135747
    AK suited 25 4900 0.003017 0.075415
    AQ or AJ suited 20 9800 0.006033 0.120664
    AK unsuited 15 14700 0.00905 0.135747
    KK, QQ, or JJ 10 22050 0.013575 0.135747
    AQ or AJ unsuited 5 29400 0.0181 0.090498
    Pair 22 to 10,10 3 66150 0.040724 0.122172
    All other -1 1470000 0.904977 -0.904977
    Total 1624350 1 -0.088989

    The lower right cells show a house edge on the bonus bet of 8.5406% under the Las Vegas rules and 8.8989% under the Atlantic City rules.

    Methodology

    A brute force approach was used to cycle through all possible cominations of cards. In total 7,089,794,712,000 hands were played out, requiring 72 days of computer time to loop through them all.

    Acknowledgements

    I would like to thank Scott McIntosh of Online Poker Room Reviews for his contributions to this page. He confirmed my Las Vegas results and provided the Atlantic City house edge and expected values. His program runs in six hours compared to the 72 days mine takes, so I was happy to use his numbers. For reviews and advice on playing poker online I encourage you to visit his web site.

    There is a good Texas Hold 'Em Bonus calculator at beatingbonuses.com.

    Analysis at ReviewPokerRooms.com.

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