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