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Texas Hold'em Bonus Poker Analysis

Analysis of Texas Hold'em Bonus Poker

House Advantage

The house advantage with the player using the optimal strategy is 2.036921% of the Ante bet wagered. For every $100 wagered on the Ante bet the player will lose $2.04 on average.

The house advantage was determined by exhaustive combinatorial analysis, cycling through every possible combination of two player cards, two dealer cards and five board cards with the player using optimal strategy at each decision point. This took approximately 6 hours on a 3GHz Pentium with 1GB of memory.

Optimal Strategy

A) Flop Bet
The player should make the Flop bet when the total expected value of the Ante, Flop, Turn and River bets is greater than that of folding (i.e. -1.000000). From Table 1 below it can be seen that player should make the Flop bet with all hands except for 2-3 offsuit, 2-4 offsuit, 2-5 offsuit, 2-6 offsuit and 2-7 offsuit.

B) Turn and River Bets
The player should make the Turn or River bet if the chance of winning the hand is greater than 50% given the player's two cards and the visible board cards. If the chance of winning is less than 50% the player should check instead.

Given the number of different combinations available and the fact the optimal strategy is not readily simplified it is very difficult to list the correct way to play every hand without having a extremely long list of rules and exceptions. Our online optimal strategy calculator provides the correct way to play a hand given the player's cards and visible board cards.

Table 1: Expected Value By Hand

HandProbabilityAnte EVFlop EVTurn EVRiver EVTotal EV
2,3 unsuited0.009050-0.575363-0.7078710.0529740.074333-1.155927
2,4 unsuited0.009050-0.561881-0.6720100.0594800.082806-1.091604
2,5 unsuited0.009050-0.547147-0.6286140.0654610.090313-1.019987
2,6 unsuited0.009050-0.565779-0.6369940.0672570.088793-1.046723
2,7 unsuited0.009050-0.573922-0.6166540.0695410.089735-1.031301
2,8 unsuited0.009050-0.549834-0.5268930.0791290.101595-0.896002
2,9 unsuited0.009050-0.528389-0.4360830.0884350.112905-0.763132
2,T unsuited0.009050-0.502716-0.3332660.0975000.124502-0.613979
2,J unsuited0.009050-0.480122-0.2260610.1089990.137770-0.459414
2,Q unsuited0.009050-0.454685-0.1081830.1212350.151943-0.289690
2,K unsuited0.009050-0.4264320.0203490.1356070.167808-0.102668
2,A unsuited0.009050-0.3713370.1971420.1630640.1955040.184373
3,4 unsuited0.009050-0.526600-0.5941640.0714540.099277-0.950034
3,5 unsuited0.009050-0.510877-0.5494090.0776540.108177-0.874456
3,6 unsuited0.009050-0.529239-0.5568950.0797270.106774-0.899632
3,7 unsuited0.009050-0.537618-0.5359100.0817990.106328-0.885400
3,8 unsuited0.009050-0.542305-0.5006470.0844860.107859-0.850607
3,9 unsuited0.009050-0.515398-0.3992190.0943970.120723-0.699497
3,T unsuited0.009050-0.489684-0.2962180.1034830.132471-0.549947
3,J unsuited0.009050-0.467087-0.1889780.1150000.145858-0.395206
3,Q unsuited0.009050-0.441686-0.0712230.1272780.160068-0.225563
3,K unsuited0.009050-0.4135090.0570280.1419540.176028-0.038499
3,A unsuited0.009050-0.3578960.2337840.1729540.2055950.254437
4,5 unsuited0.009050-0.476330-0.4737890.0894280.125564-0.735126
4,6 unsuited0.009050-0.493562-0.4795800.0918680.125179-0.756096
4,7 unsuited0.009050-0.501720-0.4580070.0940600.125105-0.740561
4,8 unsuited0.009050-0.506646-0.4221280.0965060.125468-0.706800
4,9 unsuited0.009050-0.507923-0.3731580.0995020.127185-0.654394
4,T unsuited0.009050-0.476840-0.2598360.1092160.140423-0.487036
4,J unsuited0.009050-0.454234-0.1525450.1207770.153769-0.332233
4,Q unsuited0.009050-0.428865-0.0348930.1331290.168017-0.162612
4,K unsuited0.009050-0.4007570.0930990.1482820.1841750.024799
4,A unsuited0.009050-0.3451730.2691870.1824560.2151710.321642
5,6 unsuited0.009050-0.459170-0.4022280.1037660.143314-0.614318
5,7 unsuited0.009050-0.466277-0.3795210.1062750.144042-0.595481
5,8 unsuited0.009050-0.470990-0.3428990.1087920.144610-0.560487
5,9 unsuited0.009050-0.472500-0.2932340.1116490.145492-0.508593
5,T unsuited0.009050-0.468922-0.2299620.1144750.146902-0.437507
5,J unsuited0.009050-0.441070-0.1127640.1267190.161752-0.265364
5,Q unsuited0.009050-0.4157260.0048030.1392380.176043-0.095642
5,K unsuited0.009050-0.3876820.1325590.1550280.1924620.092367
5,A unsuited0.009050-0.3322750.3078610.1924850.2248220.392893
6,7 unsuited0.009050-0.437330-0.3070900.1211360.165558-0.457726
6,8 unsuited0.009050-0.441237-0.2703640.1239310.166656-0.421014
6,9 unsuited0.009050-0.442651-0.2203460.1268700.167737-0.368390
6,T unsuited0.009050-0.439328-0.1563200.1296810.168709-0.297258
6,J unsuited0.009050-0.438181-0.0862290.1349870.171449-0.217975
6,Q unsuited0.009050-0.4076790.0409620.1482450.187257-0.031216
6,K unsuited0.009050-0.3795850.1689310.1638400.2036330.156819
6,A unsuited0.009050-0.3490010.3072980.1887950.2236270.370719
7,8 unsuited0.009050-0.412493-0.1979680.1385250.187897-0.284039
7,9 unsuited0.009050-0.413180-0.1480880.1417980.189483-0.229986
7,T unsuited0.009050-0.409739-0.0836750.1449600.190685-0.157768
7,J unsuited0.009050-0.408885-0.0127230.1502070.193184-0.078216
7,Q unsuited0.009050-0.4042250.0706270.1566320.1968540.019887
7,K unsuited0.009050-0.3711740.2074940.1734450.2151470.224911
7,A unsuited0.009050-0.3358210.3536480.2009860.2379860.456798
8,9 unsuited0.009050-0.384650-0.0761190.1574030.210989-0.092377
8,T unsuited0.009050-0.380172-0.0111490.1620050.212934-0.016383
8,J unsuited0.009050-0.3795170.0596070.1671630.2154560.062709
8,Q unsuited0.009050-0.3751400.1439920.1733730.2192150.161440
8,K unsuited0.009050-0.3669650.2408070.1831680.2257990.282809
8,A unsuited0.009050-0.3269120.3949040.2136970.2520270.533716
9,T unsuited0.009050-0.3507360.0612670.1809570.2355390.127027
9,J unsuited0.009050-0.3503660.1300480.1866440.2380140.204340
9,Q unsuited0.009050-0.3461640.2144170.1940720.2421390.304465
9,K unsuited0.009050-0.3382260.3124770.2044920.2494450.428187
9,A unsuited0.009050-0.3219690.4309120.2278180.2656460.602407
T,J unsuited0.009050-0.3142760.2099080.2107380.2639090.370279
T,Q unsuited0.009050-0.3104010.2916310.2216780.2687850.471694
T,K unsuited0.009050-0.3026680.3895570.2356310.2777090.600228
T,A unsuited0.009050-0.2868300.5088660.2635170.2963870.781940
J,Q unsuited0.009050-0.3060440.3253880.2340550.2821560.535555
J,K unsuited0.009050-0.2984750.4227470.2494380.2920500.665761
J,A unsuited0.009050-0.2826020.5425300.2799160.3126490.852493
Q,K unsuited0.009050-0.2935710.4582320.2635070.3072760.735444
Q,A unsuited0.009050-0.2778940.5772740.2965280.3294040.925311
K,A unsuited0.009050-0.2726590.6128030.3133300.3458420.999317
2,3 suited0.003017-0.495875-0.5606230.0666920.102820-0.886985
2,4 suited0.003017-0.483298-0.5268390.0733370.110792-0.826008
2,5 suited0.003017-0.469516-0.4860270.0795590.118004-0.757980
2,6 suited0.003017-0.486835-0.4932410.0805230.116672-0.782881
2,7 suited0.003017-0.494377-0.4737640.0824950.117570-0.768076
2,8 suited0.003017-0.471643-0.3891350.0925970.129160-0.639021
2,9 suited0.003017-0.451312-0.3033930.1043000.140255-0.510150
2,T suited0.003017-0.427016-0.2064210.1170670.151774-0.364595
2,J suited0.003017-0.405416-0.1048740.1322360.165345-0.212709
2,Q suited0.003017-0.3811050.0067610.1485970.180799-0.044946
2,K suited0.003017-0.3541050.1284690.1674250.1993520.141142
2,A suited0.003017-0.3020020.2951560.2007430.2311250.425022
3,4 suited0.003017-0.450565-0.4543220.0856680.126174-0.693044
3,5 suited0.003017-0.435876-0.4122820.0922820.134645-0.621230
3,6 suited0.003017-0.452945-0.4186580.0934640.133362-0.644776
3,7 suited0.003017-0.460712-0.3985630.0950620.133131-0.631082
3,8 suited0.003017-0.464978-0.3650600.0978550.134706-0.597478
3,9 suited0.003017-0.439566-0.2694300.1108310.147282-0.450882
3,T suited0.003017-0.415236-0.1723000.1236890.158929-0.304918
3,J suited0.003017-0.393638-0.0707350.1388870.172618-0.152868
3,Q suited0.003017-0.3693650.0407700.1552640.1882210.014889
3,K suited0.003017-0.3424410.1621990.1743680.2072490.201376
3,A suited0.003017-0.2898670.3288130.2105810.2410910.490618
4,5 suited0.003017-0.403827-0.3418630.1045690.150923-0.490199
4,6 suited0.003017-0.419851-0.3466670.1062330.150578-0.509707
4,7 suited0.003017-0.427416-0.3260280.1079860.150604-0.494853
4,8 suited0.003017-0.431911-0.2919350.1110180.151193-0.461634
4,9 suited0.003017-0.432941-0.2455210.1162540.153077-0.409130
4,T suited0.003017-0.403616-0.1387800.1301270.166162-0.246108
4,J suited0.003017-0.382016-0.0371820.1453390.179834-0.094025
4,Q suited0.003017-0.3577760.0742120.1618110.1956010.073849
4,K suited0.003017-0.3309210.1953850.1812840.2151800.260929
4,A suited0.003017-0.2783840.3613450.2199810.2506120.553554
5,6 suited0.003017-0.387949-0.2746650.1188280.167595-0.376191
5,7 suited0.003017-0.394542-0.2529790.1211390.168392-0.357989
5,8 suited0.003017-0.398843-0.2182000.1249120.169113-0.323018
5,9 suited0.003017-0.400096-0.1711250.1301420.170246-0.270833
5,T suited0.003017-0.396576-0.1113500.1358860.172066-0.199974
5,J suited0.003017-0.370095-0.0005260.1520580.187190-0.031373
5,Q suited0.003017-0.3458830.1107760.1686800.2031720.136745
5,K suited0.003017-0.3190920.2317170.1887000.2234680.324793
5,A suited0.003017-0.2667290.3969170.2301010.2604770.620767
6,7 suited0.003017-0.367588-0.1851290.1368940.188752-0.227072
6,8 suited0.003017-0.371145-0.1502690.1411560.189981-0.190276
6,9 suited0.003017-0.372311-0.1028680.1464580.191257-0.137464
6,T suited0.003017-0.369033-0.0423730.1522030.192660-0.066542
6,J suited0.003017-0.3676020.0242360.1603730.1962660.013273
6,Q suited0.003017-0.3385930.1445030.1780110.2137070.197628
6,K suited0.003017-0.3117580.2656290.1979120.2340740.385858
6,A suited0.003017-0.2826270.3962330.2268200.2593940.599820
7,8 suited0.003017-0.344413-0.0825460.1569580.210141-0.059860
7,9 suited0.003017-0.344908-0.0352910.1627310.211917-0.005551
7,T suited0.003017-0.3415220.0255620.1686260.2136220.066287
7,J suited0.003017-0.3403680.0929910.1765850.2170590.146267
7,Q suited0.003017-0.3355990.1720910.1864940.2230380.246024
7,K suited0.003017-0.3041520.3015100.2080690.2456800.451106
7,A suited0.003017-0.2705930.4393580.2402480.2738970.682911
8,9 suited0.003017-0.3183870.0320300.1795580.2324470.125648
8,T suited0.003017-0.3140430.0933750.1864860.2351370.200955
8,J suited0.003017-0.3130740.1606260.1943750.2388680.280795
8,Q suited0.003017-0.3085710.2407090.2040090.2451860.381333
8,K suited0.003017-0.3004580.3324940.2181510.2563740.506560
8,A suited0.003017-0.2625250.4777520.2541330.2878590.757219
9,T suited0.003017-0.2866950.1611010.2058960.2572690.337570
9,J suited0.003017-0.2859950.2264990.2143950.2613680.416267
9,Q suited0.003017-0.2816550.3065730.2252010.2682890.518407
9,K suited0.003017-0.2737650.3995390.2401970.2801750.646145
9,A suited0.003017-0.2581520.5112490.2681260.3010530.822276
T,J suited0.003017-0.2524720.3011140.2387380.2871540.574533
T,Q suited0.003017-0.2484410.3787020.2521540.2946020.677017
T,K suited0.003017-0.2407440.4715420.2699580.3077640.808521
T,A suited0.003017-0.2255270.5840950.3012410.3304790.990289
J,Q suited0.003017-0.2445600.4103680.2642310.3076270.737666
J,K suited0.003017-0.2370130.5026940.2832660.3215450.870492
J,A suited0.003017-0.2217570.6157070.3165380.3457221.056211
Q,K suited0.003017-0.2326190.5360160.2970050.3361030.936506
Q,A suited0.003017-0.2175430.6483540.3321550.3614661.124432
K,A suited0.003017-0.2128340.6817850.3479880.3770851.194024
2,2 pair0.004525-0.3860100.0133610.1018120.136700-0.134137
3,3 pair0.004525-0.3483930.1477230.1236060.1556490.078584
4,4 pair0.004525-0.3110380.2809130.1630530.1893600.322289
5,5 pair0.004525-0.2739430.4129970.2158480.2345540.589457
6,6 pair0.004525-0.2440360.5313900.2692620.2808490.837465
7,7 pair0.004525-0.2139740.6494410.3257080.3324941.093669
8,8 pair0.004525-0.1840730.7665210.3834770.3871231.353048
9,9 pair0.004525-0.1543890.8822900.4412000.4430131.612114
T,T pair0.004525-0.1227611.0004710.5002360.5010441.878990
J,J pair0.004525-0.1007591.0987790.5493890.5500062.097415
Q,Q pair0.004525-0.0786471.1970070.5985030.5989762.315838
K,K pair0.004525-0.0562881.2958270.6479140.6482392.535691
A,A pair0.004525-0.0275551.4081490.7040740.7042302.788899

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