What are the Chances of That?

dealing one pair in 5-card poker

The chances of one-pairs are:

For 100 sessions, over 100 hands dealt, each with probability 1098240 in 2598960, on average there will be 4225.7 one-pairs.

Over 100 hands dealt, on average there will be 42.3 one-pairs for each of the sessions.

Probability

0.422569

As a percentage

42.2569%

Representative example

For one-pairs

100 sessions x 100 hands dealt = 10000 chances for one-pairs

Observed one-pairs: 4302 = 43.020% (expected average: 4225.7 = 42.257%)

For sessions (columns)

Summary for sessions: {'min': 30, 'max': 56, 'mean': 43.02, 'median': 43}

Counts: How many one-pairs for each of the sessions? [Click to show]

[41, 49, 38, 44, 39, 45, 50, 42, 42, 53, 41, 41, 46, 47, 43, 44, 45, 38, 30, 44, 44, 49, 38, 42, 38, 39, 41, 39, 44, 46, 51, 45, 44, 52, 48, 42, 43, 50, 44, 41, 46, 37, 38, 38, 38, 45, 44, 41, 38, 50, 45, 48, 40, 46, 47, 46, 44, 42, 36, 53, 45, 34, 48, 37, 40, 40, 35, 39, 35, 37, 37, 44, 48, 46, 38, 43, 35, 42, 49, 43, 45, 41, 42, 45, 48, 42, 39, 43, 56, 41, 41, 44, 37, 46, 55, 40, 48, 47, 43, 40]

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

1 with 30 one-pairs; 1 with 34 one-pairs; 3 with 35 one-pairs; 1 with 36 one-pairs; 5 with 37 one-pairs; 9 with 38 one-pairs; 5 with 39 one-pairs; 5 with 40 one-pairs; 9 with 41 one-pairs; 8 with 42 one-pairs; 6 with 43 one-pairs; 11 with 44 one-pairs; 8 with 45 one-pairs; 7 with 46 one-pairs; 3 with 47 one-pairs; 6 with 48 one-pairs; 3 with 49 one-pairs; 3 with 50 one-pairs; 1 with 51 one-pairs; 1 with 52 one-pairs; 2 with 53 one-pairs; 1 with 55 one-pairs; 1 with 56 one-pairs;

For hands dealt (rows)

Summary for hands dealt: {'min': 32, 'max': 55, 'mean': 43.02, 'median': 43.5}

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

[37, 49, 38, 40, 48, 37, 37, 38, 40, 48, 38, 49, 43, 43, 43, 44, 45, 46, 40, 41, 44, 45, 47, 47, 49, 47, 40, 46, 55, 41, 49, 43, 48, 32, 40, 36, 46, 47, 42, 51, 48, 44, 44, 37, 42, 44, 41, 39, 45, 40, 47, 46, 44, 38, 49, 38, 45, 45, 36, 47, 54, 45, 50, 44, 33, 44, 43, 43, 49, 41, 48, 48, 45, 39, 34, 43, 36, 42, 44, 34, 47, 42, 43, 44, 45, 49, 49, 41, 35, 39, 47, 50, 40, 41, 41, 40, 33, 36, 38, 45]

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

1 with 32 one-pairs; 2 with 33 one-pairs; 2 with 34 one-pairs; 1 with 35 one-pairs; 4 with 36 one-pairs; 4 with 37 one-pairs; 6 with 38 one-pairs; 3 with 39 one-pairs; 8 with 40 one-pairs; 7 with 41 one-pairs; 4 with 42 one-pairs; 8 with 43 one-pairs; 10 with 44 one-pairs; 9 with 45 one-pairs; 4 with 46 one-pairs; 8 with 47 one-pairs; 6 with 48 one-pairs; 8 with 49 one-pairs; 2 with 50 one-pairs; 1 with 51 one-pairs; 1 with 54 one-pairs; 1 with 55 one-pairs;