dealing two pairs in 5-card poker

The chances of two-pairs are:

For 100 sessions, over 100 hands dealt, each with probability 123552 in 2598960, on average there will be 475.4 two-pairs.

Over 100 hands dealt, on average there will be 4.8 two-pairs for each of the sessions.

Probability

  • 0.047539
  • As a percentage

  • 4.7539%
  • As a rounded-off proportion

  • 6 in 125
  • As approximate fair betting odds

  • 20 : 1
  • Representative example

    For two-pairs

  • 100 sessions x 100 hands dealt = 10000 chances for two-pairs
  • Observed two-pairs: 493 = 4.930% (expected average: 475.4 = 4.754%)
  • For sessions (columns)
  • Summary for sessions: {'min': 1, 'max': 12, 'mean': 4.93, 'median': 5}
  • Counts: How many two-pairs for each of the sessions? [Click to show]
  • [4, 5, 6, 6, 4, 4, 4, 6, 8, 6, 11, 3, 5, 2, 6, 7, 10, 7, 5, 7, 5, 6, 8, 12, 1, 4, 3, 4, 7, 5, 3, 2, 4, 7, 3, 5, 6, 1, 4, 7, 3, 7, 4, 3, 8, 2, 8, 4, 6, 5, 8, 4, 9, 5, 4, 1, 3, 3, 4, 6, 3, 5, 6, 6, 4, 6, 2, 5, 4, 6, 4, 6, 1, 1, 4, 4, 5, 5, 7, 5, 4, 9, 6, 4, 5, 7, 3, 3, 5, 4, 5, 2, 4, 4, 6, 6, 2, 5, 7, 3]
  • Distribution: How many sessions for each different number of two-pairs? [Click to show]
  • 5 with 1 two-pairs; 6 with 2 two-pairs; 12 with 3 two-pairs; 23 with 4 two-pairs; 17 with 5 two-pairs; 17 with 6 two-pairs; 10 with 7 two-pairs; 5 with 8 two-pairs; 2 with 9 two-pairs; 1 with 10 two-pairs; 1 with 11 two-pairs; 1 with 12 two-pairs;
    For hands dealt (rows)
  • Summary for hands dealt: {'min': 1, 'max': 12, 'mean': 4.93, 'median': 5}
  • Counts: How many two-pairs for each of the hands dealt? [Click to show]
  • [7, 7, 4, 9, 5, 4, 5, 3, 2, 4, 2, 7, 2, 5, 4, 5, 9, 5, 6, 3, 8, 4, 2, 6, 6, 5, 1, 6, 5, 3, 3, 1, 7, 7, 8, 6, 5, 3, 10, 3, 5, 6, 5, 9, 2, 3, 3, 8, 3, 4, 4, 6, 7, 5, 4, 5, 3, 5, 6, 1, 5, 6, 3, 12, 7, 5, 7, 3, 5, 6, 5, 3, 3, 6, 5, 8, 5, 6, 3, 2, 1, 6, 1, 7, 8, 5, 7, 4, 6, 2, 6, 5, 3, 6, 6, 3, 5, 4, 5, 7]
  • Distribution: How many hands dealt for each different number of two-pairs? [Click to show]
  • 5 with 1 two-pairs; 7 with 2 two-pairs; 17 with 3 two-pairs; 10 with 4 two-pairs; 23 with 5 two-pairs; 17 with 6 two-pairs; 11 with 7 two-pairs; 5 with 8 two-pairs; 3 with 9 two-pairs; 1 with 10 two-pairs; 1 with 12 two-pairs;

    What are the Chances of That? - The Book

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