What are the Chances of That?

dealing a full house in 5-card poker

The chances of full houses are:

For 100 sessions, over 100 hands dealt, each with probability 3744 in 2598960, on average there will be 14.4 full houses.

Over 100 hands dealt, on average there will be 0.1 full houses for each of the sessions.

Probability

0.001441

As a percentage

0.1441%

Representative example

For full houses

100 sessions x 100 hands dealt = 10000 chances for full houses

Observed full houses: 11 = 0.110% (expected average: 14.4 = 0.144%)

For sessions (columns)

Summary for sessions: {'min': 0, 'max': 1, 'mean': 0.11, 'median': 0}

Counts: How many full houses for each of the sessions? [Click to show]

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]

Distribution: How many sessions for each different number of full houses? [Click to show]

89 with 0 full houses; 11 with 1 full houses;

For hands dealt (rows)

Summary for hands dealt: {'min': 0, 'max': 2, 'mean': 0.11, 'median': 0}

Counts: How many full houses for each of the hands dealt? [Click to show]

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]

Distribution: How many hands dealt for each different number of full houses? [Click to show]

90 with 0 full houses; 9 with 1 full houses; 1 with 2 full houses;