Texas Holdem Vs Dealer Odds

  1. Texas Holdem Vs Dealer Odds 2017
  2. Texas Holdem Vs Dealer Odds Online
  3. Texas Holdem Vs Dealer Odds Game
  4. Texas Holdem Against Dealer Odds

Answers to these and similar questions about Texas Holdem poker probabilities and odds can be found here. This collection of Texas Hold'em odds also contains the probabilities for several long-shot scenarios like set over set, flush over flush and other rather unlikely scenarios. If you're missing a probability, just leave a comment below!

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On This Page

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.

Texas Hold 'Em Bonus goes by the name of Easy Poker at the Casino Bregenz in Austria.

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 rules. Despite what the rule booklet says, the Casino Bregenz in Austria follows the Atlantic City rules.

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 RulesExpand

Turn BetRiver BetOutcomeWinCombinationsProbabilityReturn
NoNoDealer wins-3161919379699880.291077-0.873232
NoNoTie012592751631760.0226380
NoNoPlayer wins with less than straight253034245372000.0953380.190676
NoNoPlayer wins with straight or higher310844712100360.0194950.058486
NoYesDealer wins-413961730007000.025099-0.100394
NoYesTie01677046055360.0030150
NoYesPlayer wins with less than straight322968670620000.041290.12387
NoYesPlayer wins with straight or higher46057301841640.0108890.043556
YesNoDealer wins-418966395093560.034095-0.136381
YesNoTie01355814452880.0024370
YesNoPlayer wins with less than straight312473818804800.0224240.067271
YesNoPlayer wins with straight or higher42521409294360.0045330.018131
YesYesDealer wins-556047088273160.100754-0.50377
YesYesTie05479434476800.009850
YesYesPlayer wins with less than straight4123726571544800.2224190.889677
YesYesPlayer wins with straight or higher527478962411640.0493980.24699
Player folds-125170868800000.045249-0.045249
Total556276200480001-0.020369

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.

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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

Texas Holdem Vs Dealer Odds 2017

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.

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Odds in texas holdem chart

Two-Card Expected Values

Initial HandLas Vegas RulesAtlantic 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 unsuited0.1843730.160096
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 unsuited0.2544370.226376
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 unsuited0.0247990.005551
4,A unsuited0.3216420.290174
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 unsuited0.0923670.069855
5,A unsuited0.3928930.358138
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 unsuited0.1568190.134306
6,A unsuited0.3707190.351472
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 unsuited0.019887-0.003259
7,K unsuited0.2249110.202399
7,A unsuited0.4567980.434885
8,9 unsuited-0.092377-0.170864
8,T unsuited-0.016383-0.08401
8,J unsuited0.0627090.011207
8,Q unsuited0.161440.125955
8,K unsuited0.2828090.262927
8,A unsuited0.5337160.511803
9,T unsuited0.1270270.046521
9,J unsuited0.204340.139978
9,Q unsuited0.3044650.256228
9,K unsuited0.4281870.395968
9,A unsuited0.6024070.583126
T,J unsuited0.3702790.288219
T,Q unsuited0.4716940.405776
T,K unsuited0.6002280.550453
T,A unsuited0.781940.745643
J,Q unsuited0.5355550.472903
J,K unsuited0.6657610.619251
J,A unsuited0.8524930.819462
Q,K unsuited0.7354440.6922
Q,A unsuited0.9253110.895545
K,A unsuited0.9993170.972816
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 suited0.1411420.129363
2,A suited0.4250220.402419
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 suited0.014889-0.002919
3,K suited0.2013760.186589
3,A suited0.4906180.464512
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 suited0.0738490.053019
4,K suited0.2609290.243121
4,A suited0.5535540.524295
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 suited0.1367450.112895
5,K suited0.3247930.303963
5,A suited0.6207670.588467
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 suited0.013273-0.011162
6,Q suited0.1976280.173777
6,K suited0.3858580.365029
6,A suited0.599820.582012
7,8 suited-0.05986-0.133104
7,9 suited-0.005551-0.067365
7,T suited0.0662870.015313
7,J suited0.1462670.110272
7,Q suited0.2460240.22461
7,K suited0.4511060.430277
7,A suited0.6829110.662637
8,9 suited0.1256480.052404
8,T suited0.2009550.13792
8,J suited0.2807950.232842
8,Q suited0.3813330.348359
8,K suited0.506560.488168
8,A suited0.7572190.736945
9,T suited0.337570.262459
9,J suited0.4162670.356253
9,Q suited0.5184070.473476
9,K suited0.6461450.616192
9,A suited0.8222760.80444
T,J suited0.5745330.497955
T,Q suited0.6770170.615537
T,K suited0.8085210.762138
T,A suited0.9902890.956538
J,Q suited0.7376660.679207
J,K suited0.8704920.82713
J,A suited1.0562111.02548
Q,K suited0.9365060.896165
Q,A suited1.1244321.096723
K,A suited1.1940241.169336
2,2 pair-0.134137-0.140431
3,3 pair0.0785840.068777
4,4 pair0.3222890.308953
5,5 pair0.5894570.572593
6,6 pair0.8374650.820601
7,7 pair1.0936691.076805
8,8 pair1.3530481.336184
9,9 pair1.6121141.59525
T,T pair1.878991.860933
J,J pair2.0974152.082887
Q,Q pair2.3158382.304838
K,K pair2.5356912.528219
A,A pair2.7888992.78206

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

EventPaysCombinationsProbabilityReturn
Player has AA, dealer has AA100060.0000040.003694
Player has AA3073440.0045210.135636
Player has AK suited2549000.0030170.075415
Player has AQ or AJ suited2098000.0060330.120664
Player has AK unsuited15147000.009050.135747
Player has KK, QQ, or JJ10220500.0135750.135747
Player has AQ or AJ unsuited5294000.01810.090498
Player has Pair 22 to 10,103661500.0407240.122172
All other-114700000.904977-0.904977
Total16243501-0.085406

Bonus Bet — Atlantic City Rules

EventPaysCombinationsProbabilityReturn
AA3073500.0045250.135747
AK suited2549000.0030170.075415
AQ or AJ suited2098000.0060330.120664
AK unsuited15147000.009050.135747
KK, QQ, or JJ10220500.0135750.135747
AQ or AJ unsuited5294000.01810.090498
Pair 22 to 10,103661500.0407240.122172
All other-114700000.904977-0.904977
Total16243501-0.088989

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.

6-Card Bonus


Some casinos add on a side bet known as the 6-Card Bonus. This side bet is found on multiple poker-derivative games, so I created a special page for it. For more information, please see my page on the 6-Card Bonus.

C5


At the Casino Bregenz in Austria, where the game goes by the title Easy Poker, they add a side bet called the C5, which is based on the poker-value of the player's seven-card hand. The following return table shows a house edge of 8.95%.

C5

EventPaysCombinationsProbabilityReturn
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

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.

Texas Holdem Vs Dealer Odds Online

Links


Texas Holdem Vs Dealer Odds Game

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

Texas Holdem Against Dealer Odds

Analysis at ReviewPokerRooms.com.