What are the Chances of That?

dealing no pair in 5-card poker

The chances of no-pairs are:

For 100 sessions, over 100 hands dealt, each with probability 1302540 in 2598960, on average there will be 5011.8 no-pairs.

Over 100 hands dealt, on average there will be 50.1 no-pairs for each of the sessions.

Probability

0.501177

As a percentage

50.1177%

Representative example

For no-pairs

100 sessions x 100 hands dealt = 10000 chances for no-pairs

Observed no-pairs: 5027 = 50.270% (expected average: 5011.8 = 50.118%)

For sessions (columns)

Summary for sessions: {'min': 38, 'max': 60, 'mean': 50.27, 'median': 51}

Counts: How many no-pairs for each of the sessions? [Click to show]

[46, 50, 50, 51, 49, 55, 53, 46, 52, 44, 43, 54, 57, 42, 54, 51, 48, 55, 51, 51, 49, 51, 52, 58, 55, 54, 58, 41, 44, 51, 55, 54, 47, 60, 56, 49, 53, 44, 49, 55, 58, 56, 57, 43, 50, 52, 55, 46, 39, 48, 44, 54, 46, 45, 55, 51, 50, 44, 48, 42, 53, 57, 56, 48, 49, 49, 53, 56, 54, 44, 58, 44, 51, 53, 51, 49, 51, 44, 50, 57, 52, 46, 49, 53, 52, 50, 38, 51, 56, 47, 43, 49, 49, 57, 58, 45, 44, 45, 52, 44]

Distribution: How many sessions for each different number of no-pairs? [Click to show]

1 with 38 no-pairs; 1 with 39 no-pairs; 1 with 41 no-pairs; 2 with 42 no-pairs; 3 with 43 no-pairs; 10 with 44 no-pairs; 3 with 45 no-pairs; 5 with 46 no-pairs; 2 with 47 no-pairs; 4 with 48 no-pairs; 10 with 49 no-pairs; 6 with 50 no-pairs; 11 with 51 no-pairs; 6 with 52 no-pairs; 6 with 53 no-pairs; 6 with 54 no-pairs; 7 with 55 no-pairs; 5 with 56 no-pairs; 5 with 57 no-pairs; 5 with 58 no-pairs; 1 with 60 no-pairs;

For hands dealt (rows)

Summary for hands dealt: {'min': 37, 'max': 61, 'mean': 50.27, 'median': 50.5}

Counts: How many no-pairs for each of the hands dealt? [Click to show]

[46, 50, 50, 51, 52, 51, 54, 46, 49, 52, 51, 54, 56, 45, 48, 61, 50, 46, 44, 51, 38, 51, 52, 54, 54, 51, 50, 56, 40, 47, 56, 51, 51, 56, 44, 54, 43, 59, 51, 59, 45, 49, 59, 54, 50, 54, 50, 55, 40, 53, 48, 48, 47, 52, 52, 49, 55, 50, 44, 48, 47, 47, 50, 52, 58, 49, 53, 51, 53, 50, 55, 37, 49, 52, 56, 53, 54, 57, 44, 50, 46, 48, 51, 50, 56, 49, 53, 52, 44, 47, 40, 49, 44, 47, 50, 54, 53, 50, 49, 52]

Distribution: How many hands dealt for each different number of no-pairs? [Click to show]

1 with 37 no-pairs; 1 with 38 no-pairs; 3 with 40 no-pairs; 1 with 43 no-pairs; 6 with 44 no-pairs; 2 with 45 no-pairs; 4 with 46 no-pairs; 6 with 47 no-pairs; 5 with 48 no-pairs; 8 with 49 no-pairs; 13 with 50 no-pairs; 11 with 51 no-pairs; 9 with 52 no-pairs; 6 with 53 no-pairs; 9 with 54 no-pairs; 3 with 55 no-pairs; 6 with 56 no-pairs; 1 with 57 no-pairs; 1 with 58 no-pairs; 3 with 59 no-pairs; 1 with 61 no-pairs;