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Heads Up Hold 'Em Appendix 1

Introduction

This page shows the possible outcomes of certain starting hand in Heads Up Hold 'Em. Everything in this page is based on the 500-50-10-8-5 pay table for a losing Odds bet. I show the top 20 hands where the player makes a large raise and the top 12 where he doesn't. The last table shoes the expected value of all 169 possible starting hands.

The column headings should hopefully be self-explanatory, except the DQ column stands for "Dealer Qualfies."

Large Raise Starting Hands — Rank 1 to 5Expand

Hand DQ Winner Pays A-A K-K Q-Q J-J 10-10
Less than pair No Dealer -4 0 0 0 0 0
Straight flush Yes Dealer 496 53680 14080 13200 12320 11440
Four of a kind Yes Dealer 46 20400 810200 1479400 2031320 2477480
Full house Yes Dealer 6 26050080 39572160 53211840 66912960 80675520
Flush Yes Dealer 4 12175280 23523520 34451180 45187640 55733660
Straight Yes Dealer 1 33520560 20231940 22472640 24713340 26954040
Less than straight Yes Dealer -5 2974796700 3550096920 4037718540 4520696820 5001875100
Anything Y/N Push 0 114023120 116769600 122990760 132773560 147465660
Royal flush No Player 503 56700 81000 89100 90720 90720
Straight flush No Player 53 56700 56700 137700 226800 317520
Four of a kind No Player 13 0 0 0 0 0
Full house No Player 6 0 0 0 0 0
Flush No Player 4.5 51143400 51119100 51637500 52154280 52671060
Straight No Player 4 32067000 36648000 58789500 81236400 103683300
Less than straight No Player 3 3449306700 3444725700 3446452200 3447873300 3449294400
Royal flush Yes Player 504 854100 829800 821700 820080 820080
Straight flush Yes Player 54 794700 834300 1644300 2446200 3246480
Four of a kind Yes Player 14 175977840 174863320 173927800 173162200 172549240
Full house Yes Player 7 1766425440 1750481600 1734416320 1718285760 1702089920
Flush Yes Player 5.5 329888200 318564260 306247000 294122560 282188560
Straight Yes Player 5 111376440 120084060 171949740 223510020 275070300
Less than straight Yes Player 4 11897136960 11326417740 10757273580 10189467720 9618509520
Expected Value 2.926804 2.680384 2.473173 2.26713 2.060795

Large Raise Starting Hands — Rank 6 to 10

Hand DQ Winner Pays 9-9 8-8 K-A Suited Q-A Suited 77
Less than pair No Dealer -4 0 0 0 24638400 0
Straight flush Yes Dealer 496 51960 51960 34320 33880 51960
Four of a kind Yes Dealer 46 2821000 3082000 720 960 3271800
Full house Yes Dealer 6 94441560 108270840 9072510 10689690 122161560
Flush Yes Dealer 4 66096760 76308860 38898300 38733680 86366480
Straight Yes Dealer 1 42845460 42845460 47407290 50577870 42845460
Less than straight Yes Dealer -5 5572796040 6144238500 6644158950 6775494210 6720424860
Anything Y/N Push 0 164281860 186957900 346109760 375534140 214233100
Royal flush No Player 503 0 0 1449900 1611900 0
Straight flush No Player 53 362880 362880 28350 56700 362880
Four of a kind No Player 13 0 0 0 0 0
Full house No Player 6 0 0 0 0 0
Flush No Player 4.5 52473420 52473420 236933100 238727250 52473420
Straight No Player 4 91925400 91925400 114506100 137469000 91925400
Less than straight No Player 3 3451505100 3451505100 3228137550 3190215750 3451505100
Royal flush Yes Player 504 0 0 9252000 9090000 0
Straight flush Yes Player 54 4050720 4050720 397350 814500 4050720
Four of a kind Yes Player 14 172080040 171728720 25475610 25475370 171478200
Full house Yes Player 7 1685886760 1669616520 417923730 416208150 1653281000
Flush Yes Player 5.5 272042900 261774040 1065913620 1063848490 251481640
Straight Yes Player 5 261808740 261808740 403335300 443746440 261808740
Less than straight Yes Player 4 9040253400 8448722940 8386689540 8172757620 7848001680
Expected Value 1.789611 1.538711 1.353264 1.286032 1.2848


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Large Raise Starting Hands — Rank 11 to 15

Hand DQ Winner Pays J-A Suited 10-A Suited Q-K Suited 66 J-K Suited
Less than pair No Dealer -4 48963600 72975600 181072800 0 204835800
Straight flush Yes Dealer 496 33440 33000 14520 51960 14080
Four of a kind Yes Dealer 46 1200 1440 715020 3401920 715260
Full house Yes Dealer 6 12309750 13932690 12348180 136113720 13968240
Flush Yes Dealer 4 38542830 38350740 48424590 96289040 48244060
Straight Yes Dealer 1 53748450 56919030 50027070 42845460 53197650
Less than straight Yes Dealer -5 6896816160 7009134420 7176352500 7299937560 7301996610
Anything Y/N Push 0 417441400 467117460 416151420 245300440 457599440
Royal flush No Player 503 1666980 1678320 1746360 0 1801440
Straight flush No Player 53 97200 141750 1397250 362880 1583550
Four of a kind No Player 13 0 0 0 0 0
Full house No Player 6 0 0 0 0 0
Flush No Player 4.5 240616170 242544780 236604240 52473420 238347360
Straight No Player 4 157937040 177095070 199224000 91925400 224199660
Less than straight No Player 3 3155102010 3121611480 2971526850 3451505100 2932467690
Royal flush Yes Player 504 9034920 9023580 8955540 0 8900460
Straight flush Yes Player 54 1219500 1620450 8849250 4050720 9108450
Four of a kind Yes Player 14 25475130 25474890 24514710 171311200 24514470
Full house Yes Player 7 414491130 412772670 414451620 1636880200 412734600
Flush Yes Player 5.5 1061714820 1059542700 1046915190 240990840 1044917000
Straight Yes Player 5 486652440 530868450 646945800 261808740 685344180
Less than straight Yes Player 4 7953859830 7734885480 7529487090 7240475400 7311234000
Expected Value 1.220822 1.158099 1.088261 1.028641 1.021471

Large Raise Starting Hands — Rank 16 to 20

Hand DQ Winner Pays 10-K Suited K-A Offsuit J-Q Suited Q-A Offsuit 10-Q Suited
Less than pair No Dealer -4 228566700 0 347195250 26974800 369946350
Straight flush Yes Dealer 496 13640 33880 14080 33440 13640
Four of a kind Yes Dealer 46 715500 600 1313580 840 1313820
Full house Yes Dealer 6 15591180 9060960 15634470 10678140 17257410
Flush Yes Dealer 4 48036450 17573880 56975760 23037710 56778470
Straight Yes Dealer 1 56368230 47411100 67464150 50354100 70634730
Less than straight Yes Dealer -5 7413813000 7021846410 7598061540 7155983330 7713990210
Anything Y/N Push 0 504043750 356878390 498521230 387233690 544076520
Royal flush No Player 503 1812780 68850 1850040 72900 1861380
Straight flush No Player 53 1678320 48600 3094200 83700 3334770
Four of a kind No Player 13 0 0 0 0 0
Full house No Player 6 0 0 0 0 0
Flush No Player 4.5 240225750 53418150 238124610 53655750 239857200
Straight No Player 4 245089350 123183900 301656960 148003500 327054270
Less than straight No Player 3 2897526600 3407437200 2721830940 3366993300 2683362030
Royal flush Yes Player 504 8889120 841950 8851860 837900 8840520
Straight flush Yes Player 54 9459180 822600 17398800 1233000 17603730
Four of a kind Yes Player 14 24514230 25475730 23717790 25475490 23717550
Full house Yes Player 7 411016140 417935280 410971770 416219700 409253310
Flush Yes Player 5.5 1042810620 322214850 1026607050 316077820 1024636150
Straight Yes Player 5 727828530 432701400 924568560 476372520 962545290
Less than straight Yes Player 4 7097724930 8738770270 6711871360 8516402370 6499646650
Expected Value 0.959674 0.892177 0.874446 0.822661 0.81138

Small or Medium Raise Starting Hands — Rank 1 to 4

Hand Raise DQ Winner Pays 9-J Suited 9-10 Suited 10-J Offsuit 8-J Suited
Fold -2 2808746820 4745727360 3211531290 2848610160
Less than pair 1 No Dealer -2 96813774 35285766 90152010 119940810
Straight flush 1 Yes Dealer 498 6204 5544 7524 5808
Four of a kind 1 Yes Dealer 48 1299340 1785286 1388620 1320550
Full house 1 Yes Dealer 8 6169629 7059741 6293988 6728493
Flush 1 Yes Dealer 6 16162809 19609707 23040069 16635165
Straight 1 Yes Dealer 3 35594496 44256537 32389563 37940074
Less than straight 1 Yes Dealer -3 3618659371 2414393020 3635149028 4037863447
Anything 1 Y/N Push 0 343694680 353760892 305446187 413862991
Royal flush 1 No Player 501 0 0 0 0
Straight flush 1 No Player 51 686493 930069 34911 491337
Four of a kind 1 No Player 11 0 0 0 0
Full house 1 No Player 4 0 0 0 0
Flush 1 No Player 2.5 37281447 46827207 19334514 41390847
Straight 1 No Player 2 135580932 180584184 157490431 143550396
Less than straight 1 No Player 1 816859782 661034073 804735019 896068713
Royal flush 1 Yes Player 502 0 0 0 0
Straight flush 1 Yes Player 52 2595357 3940731 345249 2092563
Four of a kind 1 Yes Player 12 1164930 980100 1247730 1183443
Full house 1 Yes Player 5 37992942 41123676 41341110 38894433
Flush 1 Yes Player 3.5 190964511 228609192 110363531 202720827
Straight 1 Yes Player 3 395112510 538081014 454958082 417530033
Less than straight 1 Yes Player 2 2086951623 1642242831 2306429874 2153570370
Less than pair 2 No Dealer -3 75720207 78770340 68016577 60745398
Straight flush 2 Yes Dealer 497 6996 7656 4356 6952
Four of a kind 2 Yes Dealer 47 507180 418434 417360 486030
Full house 2 Yes Dealer 7 14352201 15134079 12586332 15392247
Flush 2 Yes Dealer 5 48522981 52230913 27150101 48150925
Straight 2 Yes Dealer 2 51293754 56898213 48304977 37526096
Less than straight 2 Yes Dealer -4 2600089461 2514381420 2394317284 2464909143
Anything 2 Y/N Push 0 282376143 286753989 262872996 273357482
Royal flush 2 No Player 502 45360 45360 90720 45360
Straight flush 2 No Player 52 4209147 5533731 233199 2753523
Four of a kind 2 No Player 12 0 0 0 0
Full house 2 No Player 5 0 0 0 0
Flush 2 No Player 3.5 204280803 194503383 35064006 202470183
Straight 2 No Player 3 176470878 209251086 277117589 105599034
Less than straight 2 No Player 2 1507655523 1428153798 1530051287 1446655188
Royal flush 2 Yes Player 503 410040 410040 820080 410040
Straight flush 2 Yes Player 53 23694003 30581469 2505141 16492077
Four of a kind 2 Yes Player 13 21904680 21575070 21822420 21886107
Full house 2 Yes Player 6 367806708 362910264 366194130 365213667
Flush 2 Yes Player 4.5 824069169 769700318 176076659 819279173
Straight 2 Yes Player 4 551661360 647591076 831699858 339164737
Less than straight 2 Yes Dealer 3 3588309756 3334636431 3718700198 3374780178
Expected Value 0.296274 0.282556 0.169480 0.162000

Small or Medium Raise Starting Hands — Rank 5 to 8

Hand Raise DQ Winner Pays 8-10 Suited 8-9 Suited 9-Q Offsuit 7-Q Suited
Fold -2 4813963110 6724206720 1698641010 1573514910
Less than pair 1 No Dealer -2 51975060 0 164582418 187315692
Straight flush 1 Yes Dealer 498 5544 6177 6234 7656
Four of a kind 1 Yes Dealer 48 1818214 2130910 545856 548568
Full house 1 Yes Dealer 8 7720626 8383866 4645434 5376579
Flush 1 Yes Dealer 6 21333732 31135941 21159088 14645766
Straight 1 Yes Dealer 3 46061430 76725759 26598322 25855593
Less than straight 1 Yes Dealer -3 2768249071 1659849359 4827918429 5017235253
Anything 1 Y/N Push 0 415237831 382753001 348887172 465312648
Royal flush 1 No Player 501 0 0 9510 0
Straight flush 1 No Player 51 768492 1133046 50697 0
Four of a kind 1 No Player 11 0 0 0 0
Full house 1 No Player 4 0 0 0 0
Flush 1 No Player 2.5 52909263 79683921 18960177 40605759
Straight 1 No Player 2 189233499 223742145 107342868 86973774
Less than straight 1 No Player 1 717363243 644314302 1163382756 1109414763
Royal flush 1 Yes Player 502 0 0 45930 0
Straight flush 1 Yes Player 52 3347928 5856777 474963 0
Four of a kind 1 Yes Player 12 995793 665049 905496 969750
Full house 1 Yes Player 5 42347370 43644840 30400458 31086948
Flush 1 Yes Player 3.5 253963047 372526524 102721147 191524050
Straight 1 Yes Player 3 554489979 703782105 301154709 255836829
Less than straight 1 Yes Player 2 1685831118 1325240758 2706443436 2522932332
Less than pair 2 No Dealer -3 63170316 41832201 42408465 45431775
Straight flush 2 Yes Dealer 497 7216 57433 26346 4664
Four of a kind 2 Yes Dealer 47 385566 384690 767784 765432
Full house 2 Yes Dealer 7 16072104 17078874 14184426 16676841
Flush 2 Yes Dealer 5 50617508 47198569 28841042 42453524
Straight 2 Yes Dealer 2 43997400 56212941 44115818 10945527
Less than straight 2 Yes Dealer -4 2420556384 2196905928 2428581160 2519406417
Anything 2 Y/N Push 0 281766713 274693145 265076345 265083388
Royal flush 2 No Player 502 45360 0 29640 44550
Straight flush 2 No Player 52 4172508 5075604 184743 221940
Four of a kind 2 No Player 12 0 0 0 0
Full house 2 No Player 5 0 0 0 0
Flush 2 No Player 3.5 190592127 161088579 35264733 205590501
Straight 2 No Player 3 141554691 146712525 140629632 27043626
Less than straight 2 No Player 2 1392512124 1333453179 1533362937 1470852024
Royal flush 2 Yes Player 503 410040 0 370320 410850
Straight flush 2 Yes Player 53 23341572 29315223 2387397 2451060
Four of a kind 2 Yes Player 13 21559317 21493881 22812234 22747620
Full house 2 Yes Player 6 359995020 356935260 377186322 373092432
Flush 2 Yes Player 4.5 751430443 619857086 184528193 854993920
Straight 2 Yes Player 4 436921551 462112545 462665631 79303281
Less than straight 2 Yes Dealer 3 3149001690 2919535137 3867424722 3509047758
Expected Value 0.150184 0.143694 0.081714 0.057930

Small or Medium Raise Starting Hands — Rank 9 to 12

Hand Raise DQ Winner Pays 7-8 Suited 7-J Suited 6-Q Suited 9-J Offsuit
Fold -2 7766802450 2967125040 1659419190 3194142930
Less than pair 1 No Dealer -2 0 131956374 183662442 115334325
Straight flush 1 Yes Dealer 498 11460 5940 7920 7674
Four of a kind 1 Yes Dealer 48 2419541 1366207 619654 1410292
Full house 1 Yes Dealer 8 9743550 7560762 5930244 6998917
Flush 1 Yes Dealer 6 45856935 17174952 14756304 27062241
Straight 1 Yes Dealer 3 81265932 37427283 39334035 34235126
Less than straight 1 Yes Dealer -3 1324952819 4318828099 5011321105 4220686587
Anything 1 Y/N Push 0 376235795 492240979 503070943 396293289
Royal flush 1 No Player 501 0 0 0 12312
Straight flush 1 No Player 51 1441044 235980 0 55170
Four of a kind 1 No Player 11 0 0 0 0
Full house 1 No Player 4 0 0 0 0
Flush 1 No Player 2.5 114733476 43425126 40601007 22045626
Straight 1 No Player 2 240373515 134278083 95649546 154698138
Less than straight 1 No Player 1 650792775 908067000 1059234609 948545697
Royal flush 1 Yes Player 502 0 0 0 73818
Straight flush 1 Yes Player 52 8172210 1281690 0 558810
Four of a kind 1 Yes Player 12 431316 1228785 1099167 1275414
Full house 1 Yes Player 5 45881010 40912461 32516553 43001789
Flush 1 Yes Player 3.5 537839910 210705141 193074084 121137511
Straight 1 Yes Player 3 762260322 402478923 295839309 451442148
Less than straight 1 Yes Player 2 1144894200 2181003405 2469004248 2426902106
Less than pair 2 No Dealer -3 18984231 54200031 46111422 46143144
Straight flush 2 Yes Dealer 497 52150 6380 24660 24466
Four of a kind 2 Yes Dealer 47 332979 440433 694406 395868
Full house 2 Yes Dealer 7 18993870 16161768 17753496 13488503
Flush 2 Yes Dealer 5 38341555 47842808 42288076 28307799
Straight 2 Yes Dealer 2 51672768 24442677 12887115 50151274
Less than straight 2 Yes Dealer -4 2060099481 2417878494 2559655625 2187489737
Anything 2 Y/N Push 0 263584225 258035680 278576207 251633406
Royal flush 2 No Player 502 0 45360 44550 27378
Straight flush 2 No Player 52 4767606 1395360 250290 230220
Four of a kind 2 No Player 12 0 0 0 0
Full house 2 No Player 5 0 0 0 0
Flush 2 No Player 3.5 126039024 202697424 205242903 32351544
Straight 2 No Player 3 130081155 53068347 29276664 180703002
Less than straight 2 No Player 2 1275701820 1426698444 1463661891 1464522945
Royal flush 2 Yes Player 503 0 410040 410850 341892
Straight flush 2 Yes Player 53 26999790 9560970 2847510 2699100
Four of a kind 2 Yes Player 13 21434094 21840705 22618143 21794556
Full house 2 Yes Player 6 351242370 361502649 369942747 362832271
Flush 2 Yes Player 4.5 448660800 818167069 853415546 160134059
Straight 2 Yes Player 4 403634328 165211497 79516581 563209512
Less than straight 2 Yes Dealer 3 2620993494 3198815634 3385364958 3443323404
Expected Value 0.044680 0.028277 0.027687 0.025250

Finally, because the tables above were too tedious to make, here is the expected value, in order of all 169 possible starting hands.

Starting Hands

Hand Expected
Value
A-A 2.926804
K-K 2.680384
Q-Q 2.473173
J-J 2.267130
10-10 2.060795
9-9 1.789611
8-8 1.538711
K-A Suited 1.353264
Q-A Suited 1.286032
7-7 1.284800
J-A Suited 1.220822
10-A Suited 1.158099
Q-K Suited 1.088261
6-6 1.028641
J-K Suited 1.021471
10-K Suited 0.959674
K-A Offsuit 0.892177
J-Q Suited 0.874446
Q-A Offsuit 0.822661
10-Q Suited 0.811380
5-5 0.771912
J-A Offsuit 0.755175
9-A Suited 0.736266
10-J Suited 0.694981
10-A Offsuit 0.690257
8-A Suited 0.674073
7-A Suited 0.592664
Q-K Offsuit 0.588447
9-K Suited 0.542352
5-A Suited 0.541945
J-K Offsuit 0.519223
6-A Suited 0.492238
9-A Offsuit 0.491376
4-4 0.479014
4-A Suited 0.459781
10-K Offsuit 0.455257
8-A Offsuit 0.424685
9-Q Suited 0.394332
4-5 Suited 0.383517
8-K Suited 0.357536
J-Q Offsuit 0.340062
7-A Offsuit 0.339006
2-A Suited 0.307063
7-K Suited 0.301041
9-J Suited 0.296274
9-10 Suited 0.282556
10-Q Offsuit 0.274700
5-A Offsuit 0.264119
9-K Offsuit 0.261093
6-A Offsuit 0.234489
6-K Suited 0.225093
8-Q Suited 0.213985
3-3 0.183504
4-A Offsuit 0.176621
10-J Offsuit 0.169480
8-J Suited 0.162000
5-K Suited 0.153455
8-10 Suited 0.150184
8-9 Suited 0.143694
4-5 Offsuit 0.095360
8-K Offsuit 0.088989
9-Q Offsuit 0.081714
4-K Suited 0.069536
7-Q Suited 0.057930
7-8 Suited 0.044680
7-K Offsuit 0.028395
7-J Suited 0.028277
6-Q Suited 0.027687
9-J Offsuit 0.025250
3-A Suited 0.020068
7-10 Suited 0.018994
7-9 Suited 0.014128
2-A Offsuit 0.013144
2-2 0.000179
9-10 Offsuit -0.007760
5-Q Suited -0.017258
2-K Suited -0.029687
8-Q Offsuit -0.037723
6-7 Suited -0.039140
6-K Offsuit -0.049218
4-Q Suited -0.067182
6-8 Suited -0.084301
8-J Offsuit -0.091179
5-K Offsuit -0.093825
6-J Suited -0.106196
6-10 Suited -0.111437
6-9 Suited -0.114002
3-Q Suited -0.114791
5-6 Suited -0.120550
8-10 Offsuit -0.121697
5-J Suited -0.130351
4-K Offsuit -0.146560
8-9 Offsuit -0.147223
7-Q Offsuit -0.157752
2-Q Suited -0.163139
5-7 Suited -0.168520
4-J Suited -0.178754
4-5 Suited -0.188199
6-Q Offsuit -0.189467
3-A Offsuit -0.196730
7-J Offsuit -0.206783
5-8 Suited -0.212710
3-J Suited -0.225261
7-10 Offsuit -0.234146
5-Q Offsuit -0.234759
5-10 Suited -0.243169
5-9 Suited -0.243346
7-8 Offsuit -0.244668
2-K Offsuit -0.247724
4-6 Suited -0.252965
7-9 Offsuit -0.257213
4-10 Suited -0.269631
2-J Suited -0.272401
4-Q Offsuit -0.285398
4-7 Suited -0.300381
3-10 Suited -0.314427
3-5 Suited -0.320283
6-J Offsuit -0.323081
6-7 Offsuit -0.328974
3-Q Offsuit -0.333806
4-8 Suited -0.345220
6-10 Offsuit -0.345776
5-J Offsuit -0.347894
6-8 Offsuit -0.354910
2-10 Suited -0.360027
3-4 Suited -0.362988
6-9 Offsuit -0.366367
4-9 Suited -0.378309
2-Q Offsuit -0.383155
3-6 Suited -0.384819
4-J Offsuit -0.396883
3-9 Suited -0.403419
5-6 Offsuit -0.411851
3-7 Suited -0.432839
5-7 Offsuit -0.440321
3-J Offsuit -0.444439
2-9 Suited -0.448824
2-5 Suited -0.452865
5-10 Offsuit -0.459018
5-8 Offsuit -0.465370
5-9 Offsuit -0.477216
3-8 Suited -0.479409
4-5 Offsuit -0.482027
4-10 Offsuit -0.486588
2-J Offsuit -0.492958
2-4 Suited -0.496856
2-8 Suited -0.505504
2-6 Suited -0.518374
4-6 Offsuit -0.527402
3-10 Offsuit -0.532819
2-3 Suited -0.541231
4-7 Offsuit -0.555790
2-7 Suited -0.568270
2-10 Offsuit -0.580273
4-8 Offsuit -0.581392
4-9 Offsuit -0.595406
3-5 Offsuit -0.597683
3-9 Offsuit -0.622618
3-4 Offsuit -0.642952
3-6 Offsuit -0.643338
2-9 Offsuit -0.670178
3-7 Offsuit -0.672341
3-8 Offsuit -0.699871
2-5 Offsuit -0.714659
2-8 Offsuit -0.728399
2-4 Offsuit -0.760644
2-6 Offsuit -0.761401
2-7 Offsuit -0.792329
2-3 Offsuit -0.807696

Written by: Michael Shackleford