Poker Hand Probabilities
Mark Brader has provided the following tables of probabilities of the various five-card poker hands when five cards are dealt from a single 52-card deck, and also when using multiple decks.
The traditional hand types are described on the poker hand ranking page. These include one hand that belongs to two types at once - a straight flush is both a straight and a flush. With two or more decks, it is possible for other combinations to occur, such as a hand that has both a flush and a pair (such as 4-6-6-8-9 all of one suit). The left-hand tables include these composite hand types for multiple decks; in these tables "plain" means a hand that is not a flush.
The hands are listed in descending order of probability, which could be used as the basis for their ranking order in multi-deck poker variations. It can be seen that as the number of decks increases, flushes become easier to make than straights, and sets of equal cards become more common.
Here is the Perl program that produced the tables. Mark Brader has placed both the program and the tables in the public domain.
** single deck
Traditional hands
0.001539% straight flush 0.001539% straight flush
0.024010% 4 of a kind plain 0.024010% 4 of a kind
0.144058% full house plain 0.144058% full house
0.196540% nothing flush 0.196540% flush
0.392465% straight plain 0.392465% straight
2.112845% 3 of a kind plain 2.112845% 3 of a kind
4.753902% 2 pairs plain 4.753902% 2 pairs
42.256903% pair plain 42.256903% pair
50.117739% nothing plain 50.117739% nothing
** 2 decks
0.000792% 5 of a kind plain Traditional hands
0.001392% straight flush
0.007464% 2 pairs flush 0.000792% 5 of a kind
0.094995% 4 of a kind plain 0.001392% straight flush
0.099519% pair flush 0.094995% 4 of a kind
0.177742% nothing flush 0.265987% full house
0.265987% full house plain 0.284725% flush
0.354927% straight plain 0.354927% straight
3.343832% 3 of a kind plain 3.343832% 3 of a kind
5.844242% 2 pairs plain 5.844242% 2 pairs
44.484905% pair plain 44.484905% pair
45.324204% nothing plain 45.324204% nothing
** 3 decks
0.000259% full house flush Traditional hands
0.001347% straight flush
0.001427% 5 of a kind plain 0.001347% straight flush
0.004280% 3 of a kind flush 0.001427% 5 of a kind
0.012840% 2 pairs flush 0.128405% 4 of a kind
0.128405% 4 of a kind plain 0.313878% full house
0.128405% pair flush 0.317524% flush
0.171999% nothing flush 0.343460% straight
0.313618% full house plain 3.762252% 3 of a kind
0.343460% straight plain 6.201937% 2 pairs
3.762252% 3 of a kind plain 43.859790% nothing
6.201937% 2 pairs plain 45.069980% pair
43.859790% nothing plain
45.069980% pair plain
** 4 decks
0.000081% 4 of a kind flush Traditional hands
0.000484% full house flush
0.001325% straight flush 0.001325% straight flush
0.001837% 5 of a kind plain 0.001837% 5 of a kind
0.007106% 3 of a kind flush 0.146964% 4 of a kind
0.015988% 2 pairs flush 0.334432% flush
0.142119% pair flush 0.337906% straight
0.146884% 4 of a kind plain 0.339149% full house
0.169218% nothing flush 3.972239% 3 of a kind
0.337906% straight plain 6.379388% 2 pairs
0.338664% full house plain 43.150650% nothing
3.972239% 3 of a kind plain 45.336110% pair
6.379388% 2 pairs plain
43.150650% nothing plain
45.336110% pair plain
** 5 decks
0.000001% 5 of a kind flush Traditional hands
0.000164% 4 of a kind flush
0.000655% full house flush 0.001312% straight flush
0.001312% straight flush 0.002116% 5 of a kind
0.002115% 5 of a kind plain 0.158695% 4 of a kind
0.009007% 3 of a kind flush 0.334631% straight
0.018015% 2 pairs flush 0.344725% flush
0.150124% pair flush 0.354730% full house
0.158531% 4 of a kind plain 4.098397% 3 of a kind
0.167578% nothing flush 6.485375% 2 pairs
0.334631% straight plain 42.732316% nothing
0.354075% full house plain 45.487703% pair
4.098397% 3 of a kind plain
6.485375% 2 pairs plain
42.732316% nothing plain
45.487703% pair plain
** 6 decks
0.000001% 5 of a kind flush Traditional hands
0.000235% 4 of a kind flush
0.000785% full house flush 0.001304% straight flush
0.001304% straight flush 0.002316% 5 of a kind
0.002315% 5 of a kind plain 0.166764% 4 of a kind
0.010358% 3 of a kind flush 0.332469% straight
0.019421% 2 pairs flush 0.351644% flush
0.155370% pair flush 0.365291% full house
0.166496% nothing flush 4.182553% 3 of a kind
0.166528% 4 of a kind plain 6.555826% 2 pairs
0.332469% straight plain 42.456354% nothing
0.364507% full house plain 45.585478% pair
4.182553% 3 of a kind plain
6.555826% 2 pairs plain
42.456354% nothing plain
45.585478% pair plain
** 7 decks
0.000002% 5 of a kind flush Traditional hands
0.000295% 4 of a kind flush
0.000885% full house flush 0.001298% straight flush
0.001298% straight flush 0.002466% 5 of a kind
0.002464% 5 of a kind plain 0.172648% 4 of a kind
0.011362% 3 of a kind flush 0.330937% straight
0.020452% 2 pairs flush 0.356615% flush
0.159072% pair flush 0.372920% full house
0.165728% nothing flush 4.242684% 3 of a kind
0.172353% 4 of a kind plain 6.606043% 2 pairs
0.330937% straight plain 42.260656% nothing
0.372034% full house plain 45.653734% pair
4.242684% 3 of a kind plain
6.606043% 2 pairs plain
42.260656% nothing plain
45.653734% pair plain
** 8 decks
0.000003% 5 of a kind flush Traditional hands
0.000345% 4 of a kind flush
0.000965% full house flush 0.001293% straight flush
0.001293% straight flush 0.002583% 5 of a kind
0.002580% 5 of a kind plain 0.177128% 4 of a kind
0.012137% 3 of a kind flush 0.329794% straight
0.021240% 2 pairs flush 0.360357% flush
0.161825% pair flush 0.378687% full house
0.165155% nothing flush 4.287791% 3 of a kind
0.176783% 4 of a kind plain 6.643648% 2 pairs
0.329794% straight plain 42.114652% nothing
0.377721% full house plain 45.704068% pair
4.287791% 3 of a kind plain
6.643648% 2 pairs plain
42.114652% nothing plain
45.704068% pair plain
** 9 decks
0.000004% 5 of a kind flush Traditional hands
0.000386% 4 of a kind flush
0.001030% full house flush 0.001290% straight flush
0.001290% straight flush 0.002676% 5 of a kind
0.002673% 5 of a kind plain 0.180651% 4 of a kind
0.012752% 3 of a kind flush 0.328908% straight
0.021860% 2 pairs flush 0.363276% flush
0.163952% pair flush 0.383200% full house
0.164712% nothing flush 4.322878% 3 of a kind
0.180265% 4 of a kind plain 6.672862% 2 pairs
0.328908% straight plain 42.001546% nothing
0.382169% full house plain 45.742713% pair
4.322878% 3 of a kind plain
6.672862% 2 pairs plain
42.001546% nothing plain
45.742713% pair plain
** 10 decks
0.000004% 5 of a kind flush Traditional hands
0.000422% 4 of a kind flush
0.001084% full house flush 0.001287% straight flush
0.001287% straight flush 0.002752% 5 of a kind
0.002748% 5 of a kind plain 0.183495% 4 of a kind
0.013252% 3 of a kind flush 0.328202% straight
0.022362% 2 pairs flush 0.365617% flush
0.164358% nothing flush 0.386827% full house
0.165645% pair flush 4.350949% 3 of a kind
0.183073% 4 of a kind plain 6.696211% 2 pairs
0.328202% straight plain 41.911346% nothing
0.385743% full house plain 45.773314% pair
4.350949% 3 of a kind plain
6.696211% 2 pairs plain
41.911346% nothing plain
45.773314% pair plain
** 11 decks
0.000005% 5 of a kind flush Traditional hands
0.000452% 4 of a kind flush
0.001129% full house flush 0.001285% straight flush
0.001285% straight flush 0.002816% 5 of a kind
0.002811% 5 of a kind plain 0.185838% 4 of a kind
0.013666% 3 of a kind flush 0.327625% straight
0.022776% 2 pairs flush 0.367536% flush
0.164070% nothing flush 0.389806% full house
0.167025% pair flush 4.373919% 3 of a kind
0.185386% 4 of a kind plain 6.715300% 2 pairs
0.327625% straight plain 41.837733% nothing
0.388677% full house plain 45.798143% pair
4.373919% 3 of a kind plain
6.715300% 2 pairs plain
41.837733% nothing plain
45.798143% pair plain
** 12 decks
0.000005% 5 of a kind flush Traditional hands
0.000478% 4 of a kind flush
0.001168% full house flush 0.001283% straight flush
0.001283% straight flush 0.002869% 5 of a kind
0.002864% 5 of a kind plain 0.187801% 4 of a kind
0.014014% 3 of a kind flush 0.327146% straight
0.023123% 2 pairs flush 0.369137% flush
0.163829% nothing flush 0.392296% full house
0.168170% pair flush 4.393060% 3 of a kind
0.187324% 4 of a kind plain 6.731197% 2 pairs
0.327146% straight plain 41.776518% nothing
0.391129% full house plain 45.818692% pair
4.393060% 3 of a kind plain
6.731197% 2 pairs plain
41.776518% nothing plain
45.818692% pair plain
** 13 decks
0.000006% 5 of a kind flush Traditional hands
0.000500% 4 of a kind flush
0.001201% full house flush 0.001281% straight flush
0.001281% straight flush 0.002915% 5 of a kind
0.002909% 5 of a kind plain 0.189471% 4 of a kind
0.014312% 3 of a kind flush 0.326741% straight
0.023419% 2 pairs flush 0.370494% flush
0.163627% nothing flush 0.394409% full house
0.169136% pair flush 4.409257% 3 of a kind
0.188971% 4 of a kind plain 6.744641% 2 pairs
0.326741% straight plain 41.724811% nothing
0.393208% full house plain 45.835980% pair
4.409257% 3 of a kind plain
6.744641% 2 pairs plain
41.724811% nothing plain
45.835980% pair plain
** 14 decks
0.000006% 5 of a kind flush Traditional hands
0.000520% 4 of a kind flush
0.001230% full house flush 0.001280% straight flush
0.001280% straight flush 0.002955% 5 of a kind
0.002948% 5 of a kind plain 0.190908% 4 of a kind
0.014568% 3 of a kind flush 0.326394% straight
0.023673% 2 pairs flush 0.371658% flush
0.163453% nothing flush 0.396224% full house
0.169963% pair flush 4.423141% 3 of a kind
0.190388% 4 of a kind plain 6.756160% 2 pairs
0.326394% straight plain 41.680557% nothing
0.394994% full house plain 45.850724% pair
4.423141% 3 of a kind plain
6.756160% 2 pairs plain
41.680557% nothing plain
45.850724% pair plain
** 15 decks
0.000007% 5 of a kind flush Traditional hands
0.000538% 4 of a kind flush
0.001255% full house flush 0.001279% straight flush
0.001279% straight flush 0.002989% 5 of a kind
0.002983% 5 of a kind plain 0.192158% 4 of a kind
0.014792% 3 of a kind flush 0.326094% straight
0.023895% 2 pairs flush 0.372667% flush
0.163303% nothing flush 0.397800% full house
0.170677% pair flush 4.435173% 3 of a kind
0.191620% 4 of a kind plain 6.766139% 2 pairs
0.326094% straight plain 41.642252% nothing
0.396545% full house plain 45.863448% pair
4.435173% 3 of a kind plain
6.766139% 2 pairs plain
41.642252% nothing plain
45.863448% pair plain
** 16 decks
0.000007% 5 of a kind flush Traditional hands
0.000554% 4 of a kind flush
0.001277% full house flush 0.001278% straight flush
0.001278% straight flush 0.003020% 5 of a kind
0.003013% 5 of a kind plain 0.193254% 4 of a kind
0.014989% 3 of a kind flush 0.325832% straight
0.024089% 2 pairs flush 0.373551% flush
0.163172% nothing flush 0.399181% full house
0.171301% pair flush 4.445702% 3 of a kind
0.192701% 4 of a kind plain 6.774867% 2 pairs
0.325832% straight plain 41.608774% nothing
0.397904% full house plain 45.874541% pair
4.445702% 3 of a kind plain
6.774867% 2 pairs plain
41.608774% nothing plain
45.874541% pair plain
** 17 decks
0.000007% 5 of a kind flush Traditional hands
0.000568% 4 of a kind flush
0.001277% straight flush 0.001277% straight flush
0.001297% full house flush 0.003047% 5 of a kind
0.003039% 5 of a kind plain 0.194225% 4 of a kind
0.015163% 3 of a kind flush 0.325601% straight
0.024261% 2 pairs flush 0.374332% flush
0.163056% nothing flush 0.400402% full house
0.171851% pair flush 4.454992% 3 of a kind
0.193657% 4 of a kind plain 6.782566% 2 pairs
0.325601% straight plain 41.579263% nothing
0.399104% full house plain 45.884296% pair
4.454992% 3 of a kind plain
6.782566% 2 pairs plain
41.579263% nothing plain
45.884296% pair plain
** 18 decks
0.000008% 5 of a kind flush Traditional hands
0.000580% 4 of a kind flush
0.001276% straight flush 0.001276% straight flush
0.001315% full house flush 0.003071% 5 of a kind
0.003063% 5 of a kind plain 0.195089% 4 of a kind
0.015319% 3 of a kind flush 0.325396% straight
0.024415% 2 pairs flush 0.375026% flush
0.162953% nothing flush 0.401488% full house
0.172339% pair flush 4.463250% 3 of a kind
0.194509% 4 of a kind plain 6.789408% 2 pairs
0.325396% straight plain 41.553054% nothing
0.400173% full house plain 45.892942% pair
4.463250% 3 of a kind plain
6.789408% 2 pairs plain
41.553054% nothing plain
45.892942% pair plain
** 19 decks
0.000008% 5 of a kind flush Traditional hands
0.000592% 4 of a kind flush
0.001275% straight flush 0.001275% straight flush
0.001331% full house flush 0.003093% 5 of a kind
0.003085% 5 of a kind plain 0.195864% 4 of a kind
0.015459% 3 of a kind flush 0.325212% straight
0.024552% 2 pairs flush 0.375648% flush
0.162861% nothing flush 0.402461% full house
0.172775% pair flush 4.470639% 3 of a kind
0.195273% 4 of a kind plain 6.795528% 2 pairs
0.325212% straight plain 41.529622% nothing
0.401130% full house plain 45.900658% pair
4.470639% 3 of a kind plain
6.795528% 2 pairs plain
41.529622% nothing plain
45.900658% pair plain
** 20 decks
0.000008% 5 of a kind flush Traditional hands
0.000602% 4 of a kind flush
0.001275% straight flush 0.001275% straight flush
0.001346% full house flush 0.003112% 5 of a kind
0.003104% 5 of a kind plain 0.196563% 4 of a kind
0.015585% 3 of a kind flush 0.325047% straight
0.024676% 2 pairs flush 0.376207% flush
0.162779% nothing flush 0.403338% full house
0.173167% pair flush 4.477288% 3 of a kind
0.195961% 4 of a kind plain 6.801035% 2 pairs
0.325047% straight plain 41.508548% nothing
0.401992% full house plain 45.907586% pair
4.477288% 3 of a kind plain
6.801035% 2 pairs plain
41.508548% nothing plain
45.907586% pair plain
** 21 decks
0.000008% 5 of a kind flush Traditional hands
0.000612% 4 of a kind flush
0.001274% straight flush 0.001274% straight flush
0.001359% full house flush 0.003130% 5 of a kind
0.003122% 5 of a kind plain 0.197197% 4 of a kind
0.015700% 3 of a kind flush 0.324898% straight
0.024789% 2 pairs flush 0.376714% flush
0.162704% nothing flush 0.404131% full house
0.173522% pair flush 4.483305% 3 of a kind
0.196585% 4 of a kind plain 6.806017% 2 pairs
0.324898% straight plain 41.489493% nothing
0.402772% full house plain 45.913841% pair
4.483305% 3 of a kind plain
6.806017% 2 pairs plain
41.489493% nothing plain
45.913841% pair plain
** 22 decks
0.000008% 5 of a kind flush Traditional hands
0.000620% 4 of a kind flush
0.001274% straight flush 0.001274% straight flush
0.001371% full house flush 0.003146% 5 of a kind
0.003138% 5 of a kind plain 0.197773% 4 of a kind
0.015804% 3 of a kind flush 0.324763% straight
0.024891% 2 pairs flush 0.377175% flush
0.162636% nothing flush 0.404854% full house
0.173843% pair flush 4.488774% 3 of a kind
0.197153% 4 of a kind plain 6.810545% 2 pairs
0.324763% straight plain 41.472180% nothing
0.403482% full house plain 45.919517% pair
4.488774% 3 of a kind plain
6.810545% 2 pairs plain
41.472180% nothing plain
45.919517% pair plain
** 23 decks
0.000009% 5 of a kind flush Traditional hands
0.000628% 4 of a kind flush
0.001273% straight flush 0.001273% straight flush
0.001383% full house flush 0.003161% 5 of a kind
0.003153% 5 of a kind plain 0.198301% 4 of a kind
0.015899% 3 of a kind flush 0.324639% straight
0.024985% 2 pairs flush 0.377595% flush
0.162574% nothing flush 0.405514% full house
0.174137% pair flush 4.493768% 3 of a kind
0.197672% 4 of a kind plain 6.814678% 2 pairs
0.324639% straight plain 41.456381% nothing
0.404131% full house plain 45.924690% pair
4.493768% 3 of a kind plain
6.814678% 2 pairs plain
41.456381% nothing plain
45.924690% pair plain
** 24 decks
0.000009% 5 of a kind flush Traditional hands
0.000636% 4 of a kind flush
0.001273% straight flush 0.001273% straight flush
0.001393% full house flush 0.003175% 5 of a kind
0.003166% 5 of a kind plain 0.198785% 4 of a kind
0.015987% 3 of a kind flush 0.324525% straight
0.025071% 2 pairs flush 0.377981% flush
0.162517% nothing flush 0.406119% full house
0.174406% pair flush 4.498346% 3 of a kind
0.198149% 4 of a kind plain 6.818466% 2 pairs
0.324525% straight plain 41.441905% nothing
0.404726% full house plain 45.929424% pair
4.498346% 3 of a kind plain
6.818466% 2 pairs plain
41.441905% nothing plain
45.929424% pair plain
** 25 decks
0.000009% 5 of a kind flush Traditional hands
0.000643% 4 of a kind flush
0.001272% straight flush 0.001272% straight flush
0.001402% full house flush 0.003188% 5 of a kind
0.003179% 5 of a kind plain 0.199230% 4 of a kind
0.016068% 3 of a kind flush 0.324421% straight
0.025150% 2 pairs flush 0.378336% flush
0.162465% nothing flush 0.406676% full house
0.174653% pair flush 4.502558% 3 of a kind
0.198588% 4 of a kind plain 6.821951% 2 pairs
0.324421% straight plain 41.428593% nothing
0.405274% full house plain 45.933774% pair
4.502558% 3 of a kind plain
6.821951% 2 pairs plain
41.428593% nothing plain
45.933774% pair plain
** 26 decks
0.000009% 5 of a kind flush Traditional hands
0.000649% 4 of a kind flush
0.001272% straight flush 0.001272% straight flush
0.001411% full house flush 0.003199% 5 of a kind
0.003190% 5 of a kind plain 0.199642% 4 of a kind
0.016143% 3 of a kind flush 0.324325% straight
0.025223% 2 pairs flush 0.378664% flush
0.162417% nothing flush 0.407191% full house
0.174881% pair flush 4.506445% 3 of a kind
0.198993% 4 of a kind plain 6.825168% 2 pairs
0.324325% straight plain 41.416310% nothing
0.405780% full house plain 45.937783% pair
4.506445% 3 of a kind plain
6.825168% 2 pairs plain
41.416310% nothing plain
45.937783% pair plain
** 27 decks
0.000009% 5 of a kind flush Traditional hands
0.000655% 4 of a kind flush
0.001272% straight flush 0.001272% straight flush
0.001419% full house flush 0.003210% 5 of a kind
0.003201% 5 of a kind plain 0.200024% 4 of a kind
0.016212% 3 of a kind flush 0.324236% straight
0.025291% 2 pairs flush 0.378968% flush
0.162372% nothing flush 0.407668% full house
0.175092% pair flush 4.510045% 3 of a kind
0.199369% 4 of a kind plain 6.828146% 2 pairs
0.324236% straight plain 41.404941% nothing
0.406249% full house plain 45.941491% pair
4.510045% 3 of a kind plain
6.828146% 2 pairs plain
41.404941% nothing plain
45.941491% pair plain
** 28 decks
0.000009% 5 of a kind flush Traditional hands
0.000661% 4 of a kind flush
0.001271% straight flush 0.001271% straight flush
0.001427% full house flush 0.003220% 5 of a kind
0.003211% 5 of a kind plain 0.200379% 4 of a kind
0.016277% 3 of a kind flush 0.324153% straight
0.025354% 2 pairs flush 0.379250% flush
0.162331% nothing flush 0.408111% full house
0.175288% pair flush 4.513387% 3 of a kind
0.199718% 4 of a kind plain 6.830910% 2 pairs
0.324153% straight plain 41.394388% nothing
0.406684% full house plain 45.944930% pair
4.513387% 3 of a kind plain
6.830910% 2 pairs plain
41.394388% nothing plain
45.944930% pair plain
** 29 decks
0.000010% 5 of a kind flush Traditional hands
0.000666% 4 of a kind flush
0.001271% straight flush 0.001271% straight flush
0.001434% full house flush 0.003230% 5 of a kind
0.003220% 5 of a kind plain 0.200709% 4 of a kind
0.016337% 3 of a kind flush 0.324076% straight
0.025413% 2 pairs flush 0.379512% flush
0.162292% nothing flush 0.408524% full house
0.175470% pair flush 4.516499% 3 of a kind
0.200044% 4 of a kind plain 6.833484% 2 pairs
0.324076% straight plain 41.384566% nothing
0.407090% full house plain 45.948128% pair
4.516499% 3 of a kind plain
6.833484% 2 pairs plain
41.384566% nothing plain
45.948128% pair plain
** 30 decks
0.000010% 5 of a kind flush Traditional hands
0.000671% 4 of a kind flush
0.001271% straight flush 0.001271% straight flush
0.001441% full house flush 0.003239% 5 of a kind
0.003229% 5 of a kind plain 0.201018% 4 of a kind
0.016393% 3 of a kind flush 0.324005% straight
0.025468% 2 pairs flush 0.379758% flush
0.162256% nothing flush 0.408909% full house
0.175640% pair flush 4.519404% 3 of a kind
0.200348% 4 of a kind plain 6.835886% 2 pairs
0.324005% straight plain 41.375401% nothing
0.407468% full house plain 45.951110% pair
4.519404% 3 of a kind plain
6.835886% 2 pairs plain
41.375401% nothing plain
45.951110% pair plain
** infinite decks
0.000014% 5 of a kind flush Traditional hands
0.000821% 4 of a kind flush
0.001262% straight flush 0.001262% straight flush
0.001641% full house flush 0.003501% 5 of a kind
0.003488% 5 of a kind plain 0.210077% 4 of a kind
0.018053% 3 of a kind flush 0.321932% straight
0.027080% 2 pairs flush 0.386887% flush
0.161219% nothing flush 0.420153% full house
0.180535% pair flush 4.603633% 3 of a kind
0.209256% 4 of a kind plain 6.905450% 2 pairs
0.321932% straight plain 41.110769% nothing
0.418512% full house plain 46.036335% pair
4.603633% 3 of a kind plain
6.905450% 2 pairs plain
41.110769% nothing plain
46.036335% pair plain