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Texas Hold'em Bonus

Introduction

Texas Hold 'Em Bonus, a poker variant, caught my attention during my visit to the Flamingo Hilton in Las Vegas back in September 2005. I have also learned that it is available in Atlantic City. Similar to traditional Texas Hold 'Em, players can wager on their hole cards at various stages: after the flop and the turn, but not after the river. Additionally, in head-to-head poker, all betting outcomes pay out at one-to-one, except that the ante requires a straight or flush or better to qualify for a payout, depending on where you're playing.

In Austria, Texas Hold 'Em Bonus is known as Easy Poker at Casino Bregenz.

Las Vegas Rules

  1. This game utilizes a standard deck of 52 playing cards.
  2. Players begin by placing an Ante wager along with an optional Bonus bet.
  3. Each player and dealer receive two hole cards that remain face down. The player has the option to view their own cards.
  4. At this point, the player can either choose to fold or place a Flop bet, which must be double the ante.
  5. The Flop introduces three community cards to the table.
  6. Following the Flop, the player may choose to pass or make a Turn bet, which equals the ante.
  7. A fourth community card, known as the Turn, is then revealed.
  8. The player has the option to either take no action or place a River bet, which must also match the ante.
  9. The final community card, called the River, is dealt.
  10. Both the player and dealer create the strongest five-card hand they can, combining their hole cards with the community cards. The person with the higher hand claims victory.
  11. If the dealer ends up with a superior hand, the player forfeits all bets, except possibly the Bonus wager.
  12. When the player has the higher hand, the bets on the Flop, Turn, and River will return even money. Should the player achieve a straight or better, the Ante bet will also yield even money; otherwise, it remains unresolved.
  13. In cases where the player and dealer's hands are of equal strength, all bets placed on the Ante, Flop, Turn, and River will remain unchanged.
  14. The Bonus bet payout is contingent solely on the initial cards of the player and dealer, according to the established payout schedule.

At the Horseshoe Casino located in Hammond, Indiana, the game adheres to the same rules as found in Las Vegas. Contrarily, the Casino Bregenz in Austria opts for regulations akin to those in Atlantic City."); "Under the Las Vegas rules, there are just two notable differences. To receive even payouts on the ante, the player must have at least a flush or better. Additionally, the bonus bet does not cover scenarios where both the player and dealer show a pair of aces.

Atlantic City Rules

The subsequent chart outlines all feasible outcomes, assuming optimal gameplay based on the Las Vegas regulations. A detailed explanation of each column is provided after the chart. Interestingly, the table's bottom right cell reveals a house edge of 2.04%, while the standard deviation is computed at 3.51.

House Edge

Return Table for Texas Hold 'Em Bonus under Las Vegas Rules

Column 1: Displays 'Yes' if the player proceeds with the turn bet; otherwise, it shows 'No'Expand

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 2: Shows 'Yes' if the player opts for the river bet; otherwise, it displays 'No'
  • Column 7: This column represents the contribution to the total return (win multiplied by probability)
  • Column 3:Outcome
  • Column 4: Net win
  • Column 5:Total combinations
  • Column 6:Probability
  • The 2.037% figure might suggest a less favorable betting outlook; however, it indicates that for every dollar wagered on the ante, a player can anticipate a loss of 2.037 cents. By hand's end, the average amount risked will be approximately 3.8181 times the ante, resulting in a lower loss ratio of 2.037% divided by 3.8181, yielding 0.5335%. The standard deviation remains close to 3.500839.

The lower right cell shows a house edge Scott McIntosh states that under the Atlantic City rules, the house edge stands at 5.5935%. I have confidence in this data as we have aligned perfectly on the Las Vegas figures. element of risk The following conditions represent instances when a player should choose to fold their initial two-card hand, as per the game regulations.

In Atlantic City: fold unsuited hands ranging from 2/3 to 2/7, as well as unsuited combinations of 3/4.

Strategy

I haven't analyzed the strategic decisions beyond the initial choice. However, under Las Vegas guidelines, players who place a Flop bet proceed to make the Turn bet 43.13% of the time and the River bet 48.46% of the time. If a player engages in the Turn bet, they are likely to pursue the River bet 85.76% of the time. Conversely, should a player place a Flop bet without moving to the Turn bet, they are likely to proceed with the River bet only 15.78% of the time.

  • Las Vegas: unsuited 2/3 to 2/7.
  • James Grosjean's work in Beyond Counting Exhibition CAA (pages 367-371) outlines a sophisticated and ongoing strategy for play after the Flop.

The following table illustrates the expected value for all 169 possible starting hands, analyzed under both the Las Vegas and Atlantic City gaming rules.

Payouts for the bonus bet hinge solely on the player's hole cards and, in some scenarios, the dealer's two hole cards. The outcome of the hand does not influence who wins. It appears there are two variations of the payout table for bonus bets. From what I've gathered, the Atlantic City payout table is similarly applied in Missouri and Indiana.

In the lower right sections, a house edge on the bonus bet is indicated at 8.5406% for Las Vegas rules and 8.8989% for 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

Certain casinos introduce an additional wager known as the 6-Card Bonus. This side wager is available in various poker-related games, prompting me to create a dedicated page for further details.

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

At Casino Bregenz in Austria, where the game is marketed as Easy Poker, they feature a side wager called C5, which depends on the value of the player's seven-card hand. The associated payout table reveals an 8.95% house edge.

6-Card Bonus

Some establishments offer a side wager simply titled the 'side bet,' which pays out based on the poker value of the player's hand. This bet adheres to a payout structure of 2-4-6-10-20-50-250, leading to a house edge of 6.92%. 6-Card Bonus .

C5

A thorough approach was employed to analyze all potential card combinations. In total, a staggering 7,089,794,712,000 hands were simulated, requiring 72 continuous days of computing power to process them.

C5

Event Pays Combinations Probability Return
Royal flush 100 4,324 0.000032 0.003232
Straight flush 60 37,260 0.000279 0.016710
Four of a kind 40 224,848 0.001681 0.067227
Full house 8 3,473,184 0.025961 0.207688
Flush 6 4,047,644 0.030255 0.181530
Straight 4 6,180,020 0.046194 0.184775
Three of a kind 2 6,461,620 0.048299 0.096597
All other -1 113,355,660 0.847300 -0.847300
Total   133,784,560 1.000000 -0.089540

Internet casinos using software by OneTouch I extend my gratitude to Scott McIntosh for his valuable contributions to this page.

Methodology

His validation of my findings for Las Vegas and the Atlantic City house edge, along with expected values, has been instrumental. Remarkably, his computational program accomplishes tasks in six hours compared to the 72 days required by mine, making it a privilege to incorporate his figures. For insightful reviews and strategies about playing poker online, I highly recommend visiting his website.

Acknowledgements

For mathematically sound strategies and insights into casino games such as blackjack, craps, roulette, and many more options, please explore further. Online Poker Room Reviews Kindly check your email and follow the link provided to finalize your registration process.

Links

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

Analysis at ReviewPokerRooms.com.