The Wizard of Odds

Texas Hold’em

Last Update: Oct 07, 2004

The following table shows how often each initial hand wins, loses, and draws in a two-player game. The return is the probability of winning less the probability of losing. The probability is the probability of getting that particular hand and the additive probability is the probability of getting the particular hand or any other higher on the list.

Initial Hold'em Hands in Rank Order — 2 Player Game

CardsWinLoseDrawReturnProbabilityAdditive Probability
Pair of A's84.93%14.52%0.54%70.41%0.45%0.45%
Pair of K's82.12%17.33%0.56%64.79%0.45%0.90%
Pair of Q's79.63%19.78%0.59%59.85%0.45%1.36%
Pair of J's77.15%22.21%0.63%54.94%0.45%1.81%
Pair of T's74.66%24.64%0.70%50.02%0.45%2.26%
Pair of 9's71.67%27.55%0.78%44.11%0.45%2.71%
Pair of 8's68.72%30.39%0.89%38.33%0.45%3.17%
K/A suited66.22%32.13%1.65%34.09%0.30%3.47%
Pair of 7's65.73%33.25%1.02%32.47%0.45%3.92%
Q/A suited65.31%32.90%1.79%32.42%0.30%4.22%
J/A suited64.40%33.61%1.99%30.79%0.30%4.52%
K/A unsuited64.47%33.83%1.70%30.64%0.90%5.43%
T/A suited63.49%34.28%2.23%29.20%0.30%5.73%
Q/A unsuited63.51%34.65%1.85%28.86%0.90%6.64%
J/A unsuited62.54%35.41%2.06%27.13%0.90%7.54%
Q/K suited62.41%35.61%1.98%26.80%0.30%7.84%
Pair of 6's62.70%36.13%1.17%26.57%0.45%8.30%
9/A suited61.51%35.95%2.54%25.56%0.30%8.60%
T/A unsuited61.57%36.12%2.31%25.44%0.90%9.50%
J/K suited61.48%36.34%2.18%25.13%0.30%9.80%
8/A suited60.51%36.62%2.87%23.89%0.30%10.11%
T/K suited60.59%37.01%2.40%23.58%0.30%10.41%
Q/K unsuited60.43%37.52%2.05%22.91%0.90%11.31%
7/A suited59.39%37.42%3.19%21.97%0.30%11.61%
9/A unsuited59.45%37.90%2.65%21.55%0.90%12.52%
J/K unsuited59.44%38.30%2.25%21.14%0.90%13.42%
Pair of 5's59.64%38.99%1.37%20.65%0.45%13.88%
J/Q suited59.07%38.55%2.38%20.52%0.30%14.18%
9/K suited58.64%38.66%2.70%19.98%0.30%14.48%
5/A suited58.06%38.22%3.72%19.85%0.30%14.78%
6/A suited58.18%38.37%3.45%19.81%0.30%15.08%
8/A unsuited58.37%38.63%3%19.75%0.90%15.99%
T/K unsuited58.49%39.02%2.49%19.48%0.90%16.89%
T/Q suited58.17%39.24%2.59%18.94%0.30%17.19%
4/A suited57.14%39.07%3.79%18.07%0.30%17.50%
7/A unsuited57.17%39.49%3.34%17.68%0.90%18.40%
8/K suited56.79%40.17%3.04%16.62%0.30%18.70%
3/A suited56.34%39.89%3.77%16.44%0.30%19%
J/Q unsuited56.91%40.64%2.46%16.27%0.90%19.91%
9/K unsuited56.41%40.78%2.81%15.62%0.90%20.81%
5/A unsuited55.74%40.35%3.91%15.39%0.90%21.72%
6/A unsuited55.87%40.51%3.62%15.36%0.90%22.62%
9/Q suited56.22%40.89%2.88%15.33%0.30%22.93%
7/K suited55.85%40.77%3.38%15.08%0.30%23.23%
T/J suited56.15%41.10%2.75%15.06%0.30%23.53%
2/A suited55.51%40.75%3.75%14.76%0.30%23.83%
T/Q unsuited55.95%41.37%2.69%14.58%0.90%24.74%
Pair of 4's56.26%42.21%1.53%14.05%0.45%25.19%
4/A unsuited54.73%41.27%3.99%13.46%0.90%26.09%
6/K suited54.80%41.52%3.67%13.28%0.30%26.40%
8/K unsuited54.43%42.39%3.18%12.04%0.90%27.30%
8/Q suited54.42%42.38%3.20%12.04%0.30%27.60%
3/A unsuited53.86%42.17%3.98%11.69%0.90%28.51%
5/K suited53.83%42.25%3.92%11.59%0.30%28.81%
9/J suited54.11%42.79%3.10%11.32%0.30%29.11%
9/Q unsuited53.86%43.14%3%10.72%0.90%30.02%
T/J unsuited53.83%43.33%2.84%10.50%0.90%30.92%
7/K unsuited53.42%43.04%3.54%10.37%0.90%31.83%
2/A unsuited52.95%43.09%3.96%9.86%0.90%32.73%
4/K suited52.89%43.12%3.99%9.77%0.30%33.03%
7/Q suited52.52%43.92%3.56%8.60%0.30%33.33%
6/K unsuited52.30%43.85%3.85%8.45%0.90%34.24%
3/K suited52.07%43.96%3.97%8.11%0.30%34.54%
9/T suited52.38%44.32%3.30%8.06%0.30%34.84%
8/J suited52.31%44.28%3.41%8.03%0.30%35.14%
Pair of 3's52.84%45.45%1.71%7.39%0.45%35.60%
6/Q suited51.68%44.45%3.87%7.23%0.30%35.90%
8/Q unsuited51.93%44.73%3.34%7.20%0.90%36.80%
5/K unsuited51.25%44.63%4.12%6.63%0.90%37.71%
9/J unsuited51.64%45.14%3.22%6.50%0.90%38.61%
2/K suited51.24%44.82%3.94%6.42%0.30%38.91%
5/Q suited50.71%45.17%4.11%5.54%0.30%39.22%
8/T suited50.51%45.84%3.65%4.67%0.30%39.52%
4/K unsuited50.23%45.57%4.20%4.65%0.90%40.42%
7/J suited50.45%45.80%3.74%4.65%0.30%40.72%
4/Q suited49.76%46.05%4.18%3.71%0.30%41.03%
7/Q unsuited49.90%46.37%3.72%3.53%0.90%41.93%
9/T unsuited49.82%46.75%3.43%3.06%0.90%42.84%
8/J unsuited49.71%46.73%3.55%2.98%0.90%43.74%
3/K unsuited49.33%46.48%4.19%2.85%0.90%44.65%
6/Q unsuited49%46.95%4.06%2.05%0.90%45.55%
3/Q suited48.94%46.90%4.16%2.04%0.30%45.85%
8/9 suited48.86%47.25%3.89%1.60%0.30%46.15%
7/T suited48.65%47.37%3.98%1.28%0.30%46.46%
6/J suited48.57%47.36%4.06%1.21%0.30%46.76%
2/K unsuited48.42%47.41%4.17%1.02%0.90%47.66%
Pair of 2's49.39%48.72%1.90%0.67%0.45%48.11%
2/Q suited48.10%47.76%4.13%0.34%0.30%48.42%
5/Q unsuited47.96%47.72%4.32%0.24%0.90%49.32%
5/J suited47.82%47.85%4.33%-0.03%0.30%49.62%
8/T unsuited47.82%48.38%3.81%-0.56%0.90%50.53%
7/J unsuited47.73%48.36%3.91%-0.64%0.90%51.43%
4/Q unsuited46.92%48.67%4.41%-1.74%0.90%52.34%
7/9 suited46.99%48.75%4.25%-1.76%0.30%52.64%
4/J suited46.87%48.73%4.40%-1.86%0.30%52.94%
6/T suited46.80%48.92%4.28%-2.12%0.30%53.24%
3/J suited46.04%49.58%4.38%-3.54%0.30%53.54%
3/Q unsuited46.02%49.59%4.39%-3.56%0.90%54.45%
8/9 unsuited46.07%49.87%4.06%-3.81%0.90%55.35%
7/8 suited45.68%49.81%4.50%-4.13%0.30%55.66%
7/T unsuited45.83%50.01%4.16%-4.18%0.90%56.56%
6/J unsuited45.71%50.02%4.26%-4.31%0.90%57.47%
6/9 suited45.15%50.29%4.55%-5.14%0.30%57.77%
2/J suited45.20%50.45%4.35%-5.24%0.30%58.07%
2/Q unsuited45.11%50.52%4.37%-5.41%0.90%58.97%
5/T suited44.94%50.51%4.55%-5.57%0.30%59.28%
5/J unsuited44.90%50.54%4.55%-5.64%0.90%60.18%
4/T suited44.20%51.14%4.65%-6.94%0.30%60.48%
7/9 unsuited44.07%51.48%4.45%-7.40%0.90%61.39%
6/8 suited43.82%51.33%4.85%-7.51%0.30%61.69%
4/J unsuited43.87%51.50%4.64%-7.63%0.90%62.59%
6/T unsuited43.85%51.66%4.49%-7.82%0.90%63.50%
5/9 suited43.31%51.87%4.82%-8.56%0.30%63.80%
3/T suited43.38%51.99%4.63%-8.61%0.30%64.10%
6/7 suited42.83%52.09%5.08%-9.26%0.30%64.40%
3/J unsuited42.97%52.42%4.62%-9.45%0.90%65.31%
7/8 unsuited42.69%52.59%4.72%-9.90%0.90%66.21%
2/T suited42.54%52.86%4.60%-10.32%0.30%66.52%
5/8 suited41.99%52.90%5.11%-10.91%0.30%66.82%
6/9 unsuited42.10%53.12%4.78%-11.02%0.90%67.72%
2/J unsuited42.05%53.35%4.60%-11.30%0.90%68.63%
5/T unsuited41.86%53.36%4.79%-11.50%0.90%69.53%
4/9 suited41.41%53.68%4.91%-12.28%0.30%69.83%
5/7 suited40.98%53.63%5.39%-12.65%0.30%70.14%
4/T unsuited41.06%54.05%4.90%-12.99%0.90%71.04%
3/9 suited40.81%54.28%4.91%-13.47%0.30%71.34%
6/8 unsuited40.70%54.21%5.09%-13.52%0.90%72.25%
5/6 suited40.35%54.08%5.57%-13.73%0.30%72.55%
4/8 suited40.10%54.70%5.20%-14.60%0.30%72.85%
5/9 unsuited40.14%54.80%5.06%-14.66%0.90%73.76%
3/T unsuited40.16%54.97%4.88%-14.81%0.90%74.66%
2/9 suited39.97%55.14%4.88%-15.17%0.30%74.96%
6/7 unsuited39.65%55.01%5.34%-15.35%0.90%75.87%
4/7 suited39.11%55.41%5.48%-16.30%0.30%76.17%
2/T unsuited39.24%55.90%4.86%-16.66%0.90%77.07%
4/5 suited38.53%55.63%5.84%-17.09%0.30%77.38%
5/8 unsuited38.74%55.89%5.37%-17.14%0.90%78.28%
4/6 suited38.48%55.81%5.70%-17.33%0.30%78.58%
3/8 suited38.28%56.54%5.18%-18.25%0.30%78.88%
4/9 unsuited38.09%56.74%5.17%-18.66%0.90%79.79%
5/7 unsuited37.67%56.65%5.67%-18.98%0.90%80.69%
2/8 suited37.68%57.14%5.18%-19.46%0.30%81%
3/7 suited37.30%57.23%5.46%-19.93%0.30%81.30%
3/9 unsuited37.43%57.39%5.18%-19.96%0.90%82.20%
5/6 unsuited37.01%57.12%5.86%-20.11%0.90%83.11%
3/5 suited36.76%57.37%5.87%-20.61%0.30%83.41%
3/6 suited36.69%57.62%5.70%-20.93%0.30%83.71%
4/8 unsuited36.71%57.82%5.48%-21.11%0.90%84.62%
2/9 unsuited36.52%58.32%5.16%-21.80%0.90%85.52%
3/4 suited35.73%58.44%5.83%-22.72%0.30%85.82%
4/7 unsuited35.66%58.56%5.78%-22.90%0.90%86.73%
2/7 suited35.44%59.13%5.43%-23.69%0.30%87.03%
4/5 unsuited35.07%58.76%6.16%-23.69%0.90%87.93%
4/6 unsuited35%58.98%6.01%-23.98%0.90%88.84%
2/5 suited34.93%59.23%5.84%-24.30%0.30%89.14%
2/6 suited34.84%59.50%5.66%-24.66%0.30%89.44%
3/8 unsuited34.75%59.78%5.47%-25.03%0.90%90.35%
2/4 suited33.92%60.26%5.82%-26.34%0.30%90.65%
2/8 unsuited34.09%60.43%5.48%-26.34%0.90%91.55%
3/7 unsuited33.72%60.51%5.77%-26.80%0.90%92.46%
3/5 unsuited33.16%60.64%6.20%-27.47%0.90%93.36%
3/6 unsuited33.07%60.91%6.02%-27.84%0.90%94.27%
2/3 suited33.09%61.12%5.78%-28.03%0.30%94.57%
3/4 unsuited32.07%61.77%6.16%-29.71%0.90%95.48%
2/7 unsuited31.71%62.54%5.75%-30.83%0.90%96.38%
2/5 unsuited31.19%62.62%6.18%-31.43%0.90%97.29%
2/6 unsuited31.08%62.93%5.99%-31.85%0.90%98.19%
2/4 unsuited30.12%63.72%6.16%-33.60%0.90%99.10%
2/3 unsuited29.24%64.63%6.13%-35.39%0.90%100%
Total47.97%47.97%4.07%100%

The following chart illustrates the value of each in a two-player game, based on the expected value numbers above. Remember that this is based on a two-player game. As the number of players increase the value of suited and connected cards increase, while the value of pairs and high rank decrease.


Image courtesy of Lewis.

The next table shows the exact number of combinations for each type of hand and outcome.

Initial Hold'em Hands in Rank Order - 2 Player Game

CardsWinLoseDraw
Pair of A's10689050508182797002068413872
Pair of K's10334823348218054929270061760
Pair of Q's10022031864248960808073794456
Pair of J's9710037624279573264079664136
Pair of T's9396318660310063634488479396
Pair of 9's9019433616346743166898569116
Pair of 8's86483810883824878572112174740
K/A suited55560168602695828836138443904
Pair of 7's82718212684185073272128539860
Q/A suited54800084682760067476150213656
J/A suited54031468682820166172166976560
K/A unsuited162275025368515112196428254068
T/A suited53269038482876538768186846984
Q/A unsuited159857135408720474832464680428
J/A unsuited157406468768912667168517554756
Q/K suited52362471602987581872166460568
Pair of 6's78910703404547183796147180264
9/A suited51608397603016078036213371804
T/A unsuited154972217049092919708580727388
J/K suited51580611443049188680183039776
8/A suited50767804203072539816240969364
T/K suited50834302203105241880201617500
Q/K unsuited152113230609444274260515271480
7/A suited49827138003139541936268033864
9/A unsuited149640163929540798468666053940
J/K unsuited149618748369641415084567578880
Pair of 5's75059575324907085336172391532
J/Q suited49562175763234663532199408492
9/K suited49199097163243785672226594212
5/A suited48717477723206623380311918448
6/A suited48813780243219122704289788872
8/A unsuited146932821009723241152754345548
T/K unsuited147235195089820780404626568888
T/Q suited48806851403291973852217630608
4/A suited47940268323278130392318132376
7/A unsuited143900637129939252312841552776
8/K suited47648798723370019408255390320
3/A suited47266741443347256736316358720
J/Q unsuited1432379290810228648776618427116
9/K unsuited1419829395610265635344706939500
5/A unsuited1403081968810156250556983798556
6/A unsuited1406304132010195561344912266136
9/Q suited47172554323431137856241896312
7/K suited46856680563420792044283829500
T/J suited47115487443448330720230410136
2/A suited46571360043418914204314239392
T/Q unsuited1408244403610412137392676287372
Pair of 4's70801266605312421552192886188
4/A unsuited13776739008103889023561005227436
6/K suited45982706483483916764308102188
8/K unsuited1370091506410670255592799698144
8/Q suited45657454563555935008268609136
3/A unsuited13555849932106135755601001443308
5/K suited45168160963544730964328742540
9/J suited45401522043589956848260180548
9/Q unsuited1355753433610858998252754336212
T/J unsuited1354847313610906688220715707444
7/K unsuited1344560557210834203360891059868
2/A unsuited1332729679210846174716997397292
4/K suited44375271363617856828334905636
7/Q suited44068726243684927940298489036
6/K unsuited1316363958011037567576969661644
3/K suited43688344523688385916333069232
9/T suited43945713683718728732276989500
8/J suited43890991883715250836285939576
Pair of 3's66500474645720468052214918884
6/Q suited43360382483729828676324422676
8/Q unsuited1307136354011259165660840339600
5/K unsuited12901056312112327448041037067684
9/J unsuited1299808077611361371772811416252
2/K suited42991803803760233764330875456
5/Q suited42550053363790282148345002116
8/T suited42378637723846142844306282984
4/K unsuited12642107712114704178121058343276
7/J suited42332751403843163392313851068
4/Q suited41752629403863932512351094148
7/Q unsuited1256136213611672495220937011444
9/T unsuited1253904338411767972884863852532
8/J unsuited1251335948411763185532894323784
3/K unsuited12417107796116993908561054370148
6/Q unsuited12332844936118173192121020704652
3/Q suited41060742683935038804349176528
8/9 suited40991828763964811484326295240
7/T suited40819793923974745192333565016
6/J suited40755198043973845076340924720
2/K unsuited12188434992119323346041050099204
Pair of 2's62153389326131263428238832040
2/Q suited40358816564007516560346891384
5/Q unsuited12071696952120112451881087926660
5/J suited40123157444014522472363451384
8/T unsuited1203623248812176548164958088148
7/J unsuited1201308171612173201868984585216
4/Q unsuited11811371136122505101161108987548
7/9 suited39426213924090671224356996984
4/J suited39324169724088400276369472352
6/T suited39266721084104432864359184628
3/J suited38630361764159779908367473516
3/Q unsuited11584866456124812333001104769044
8/9 unsuited11595799440125537862121021283148
7/8 suited38330289484179323008377937644
7/T unsuited11535749664125888305921046288544
6/J unsuited11506494924125917253281072648548
6/9 suited37883136644219861368382114568
2/J suited37926156924232576904365097004
2/Q unsuited11354561340127160854081100222052
5/T suited37705143684237642236382132996
5/J unsuited11302890012127220798641145898924
4/T suited37088494364291052704390387460
7/9 unsuited11093320344129570689281120479528
6/8 suited36764999884306901164406888448
4/J unsuited11042141700129619819921166745108
6/T unsuited11036953920130043073721129607508
5/9 suited36340615884351955816404272196
3/T suited36395803804362401812388307408
6/7 suited35935171204370161484426610996
3/J unsuited10815107388131934801841162281228
7/8 unsuited10746273060132377801641186815576
2/T suited35692426924435207380385839528
5/8 suited35231211844438503004428665412
6/9 unsuited10597789824133709423401202136636
2/J unsuited10584165504134292451081157458188
5/T unsuited10535890248134300621401204916412
4/9 suited34741775084504174356411937736
5/7 suited34382572004499538784452493616
4/T unsuited10333998000136041429001232727900
3/9 suited34238077964554104352412377452
6/8 unsuited10243683888136463313361280853576
5/6 suited33853297804537587344467372476
4/8 suited33647392524589448464436101884
5/9 unsuited10102761228137932421161274865456
3/T unsuited10107409188138354409681228018644
2/9 suited33538466524626624744409818204
6/7 unsuited9981208956138460715761343588268
4/7 suited32813506844649083360459855556
2/T unsuited9876826080140711231641222919556
4/5 suited32329909924667156556490142052
5/8 unsuited9751514484140670468601352307456
4/6 suited32286654404682984704478639456
3/8 suited32120178604743496732434775008
4/9 unsuited9586525644142828794001301463756
5/7 unsuited9483045336142594850761428338388
2/8 suited31613958564793871944435021800
3/7 suited31298764164801904088458509096
3/9 unsuited9420931080144452809801304656740
5/6 unsuited9316432056143786450041475791740
3/5 suited30841594284813740036492390136
3/6 suited30780137964834343060477932744
4/8 unsuited9240017508145526860561378165236
2/9 unsuited9191649444146799377521299281604
3/4 suited29976288124903575660489085128
4/7 unsuited8976366960147405825841453919256
2/7 suited29735050284961014704455769868
4/5 unsuited8828636988147914712841550760528
4/6 unsuited8810556372148462849201514027508
2/5 suited29306891644969642304489958132
2/6 suited29229711444992190388475128068
3/8 unsuited8746838952150477051721376324676
2/4 suited28458137605055981376488494464
2/8 unsuited8579951172152111289121379788716
3/7 unsuited8487091056152317476841452030060
3/5 unsuited8347913928152624668081560488064
3/6 unsuited8323953276153327157681514199756
2/3 suited27765122525128405976485371372
3/4 unsuited8071367556155491829281550318316
2/7 unsuited7981752972157426127881446503040
2/5 unsuited7851752316157631348401555981644
2/6 unsuited7822767648158396197201508481432
2/4 unsuited7580812908160383506161551705276
2/3 unsuited7359823500162686859601542359340
Total13341253692921334125369292113130263816

Methodology: The 2-player program considered all combin(52,2)*combin(50,2)*combin(48,5)=2,781,381,002,400 possible outcomes in a 2-player game of Texas Hold'em.

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