What are the Chances of That?

dealing a flush in 5-card poker

The chances of flushes are:

For 100 sessions, over 100 hands dealt, each with probability 5108 in 2598960, on average there will be 19.7 flushes.

Over 100 hands dealt, on average there will be 0.2 flushes for each of the sessions.

Probability

0.001965

As a percentage

0.1965%

Representative example

For flushes

100 sessions x 100 hands dealt = 10000 chances for flushes

Observed flushes: 13 = 0.130% (expected average: 19.7 = 0.197%)

For sessions (columns)

Summary for sessions: {'min': 0, 'max': 1, 'mean': 0.13, 'median': 0}

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

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

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

87 with 0 flushes; 13 with 1 flushes;

For hands dealt (rows)

Summary for hands dealt: {'min': 0, 'max': 1, 'mean': 0.13, 'median': 0}

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

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

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

87 with 0 flushes; 13 with 1 flushes;