dealing 3 of a kind in 5-card poker

The chances of three-of-a-kinds are:

For 100 sessions, over 100 hands dealt, each with probability 54912 in 2598960, on average there will be 211.3 three-of-a-kinds.

Over 100 hands dealt, on average there will be 2.1 three-of-a-kinds for each of the sessions.

Probability

  • 0.021128
  • As a percentage

  • 2.1128%
  • As a rounded-off proportion

  • 21 in 1000
  • As approximate fair betting odds

  • 140 : 3
  • Representative example

    For three-of-a-kinds

  • 100 sessions x 100 hands dealt = 10000 chances for three-of-a-kinds
  • Observed three-of-a-kinds: 202 = 2.020% (expected average: 211.3 = 2.113%)
  • For sessions (columns)
  • Summary for sessions: {'min': 0, 'max': 6, 'mean': 2.02, 'median': 2}
  • Counts: How many three-of-a-kinds for each of the sessions? [Click to show]
  • [1, 3, 2, 1, 0, 3, 0, 1, 2, 2, 2, 1, 3, 1, 3, 3, 6, 3, 2, 4, 2, 0, 1, 1, 2, 2, 1, 2, 2, 2, 4, 2, 4, 2, 3, 2, 4, 3, 3, 2, 2, 1, 1, 0, 3, 2, 1, 5, 1, 2, 4, 5, 3, 0, 4, 2, 2, 3, 0, 2, 6, 1, 0, 3, 1, 3, 2, 1, 0, 3, 3, 0, 1, 2, 5, 2, 1, 1, 2, 1, 3, 0, 1, 1, 2, 4, 1, 4, 2, 3, 1, 1, 1, 1, 1, 2, 2, 0, 3, 1]
  • Distribution: How many sessions for each different number of three-of-a-kinds? [Click to show]
  • 11 with 0 three-of-a-kinds; 28 with 1 three-of-a-kinds; 29 with 2 three-of-a-kinds; 19 with 3 three-of-a-kinds; 8 with 4 three-of-a-kinds; 3 with 5 three-of-a-kinds; 2 with 6 three-of-a-kinds;
    For hands dealt (rows)
  • Summary for hands dealt: {'min': 0, 'max': 6, 'mean': 2.02, 'median': 2}
  • Counts: How many three-of-a-kinds for each of the hands dealt? [Click to show]
  • [3, 3, 2, 3, 0, 4, 1, 2, 2, 4, 2, 1, 3, 3, 2, 0, 0, 5, 2, 0, 2, 4, 4, 0, 1, 2, 1, 3, 2, 1, 4, 1, 1, 3, 2, 2, 1, 4, 0, 2, 2, 2, 2, 2, 6, 1, 0, 1, 1, 1, 2, 1, 4, 2, 0, 2, 3, 3, 0, 5, 1, 2, 3, 1, 2, 1, 3, 3, 3, 2, 4, 0, 3, 0, 1, 2, 1, 2, 2, 2, 1, 1, 2, 5, 1, 2, 2, 1, 0, 3, 0, 2, 2, 1, 5, 3, 5, 3, 0, 3]
  • Distribution: How many hands dealt for each different number of three-of-a-kinds? [Click to show]
  • 14 with 0 three-of-a-kinds; 23 with 1 three-of-a-kinds; 31 with 2 three-of-a-kinds; 18 with 3 three-of-a-kinds; 8 with 4 three-of-a-kinds; 5 with 5 three-of-a-kinds; 1 with 6 three-of-a-kinds;

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