This shows the probabilities of drawing two specific cards (labeled A and B) in a hand of five cards, from decks of various sizes.
All numbers are percentages.
When the deck contains no 'draw' cards:
Deck size | A & B | A & !B | A ^ B | A | B |
6 | 66.7 | 16.7 | 33.3 | 100.0 |
7 | 47.6 | 23.8 | 47.6 | 95.2 |
8 | 35.7 | 26.8 | 53.6 | 89.3 |
9 | 27.8 | 27.8 | 55.6 | 83.3 |
10 | 22.2 | 27.8 | 55.6 | 77.8 |
11 | 18.2 | 27.3 | 54.5 | 72.7 |
12 | 15.2 | 26.5 | 53.0 | 68.2 |
13 | 12.8 | 25.6 | 51.3 | 64.1 |
When the 'A' card causes Draw 1:
Deck size | A & B | A & !B | A ^ B | A | B |
6 | 50.0 | 0.0 | 50.0 | 100.0 |
7 | 41.7 | 8.3 | 50.0 | 91.7 |
8 | 35.7 | 14.3 | 50.0 | 85.7 |
9 | 31.2 | 18.8 | 50.0 | 81.2 |
10 | 27.8 | 22.2 | 50.0 | 77.8 |
11 | 25.0 | 25.0 | 50.0 | 75.0 |
12 | 22.7 | 27.3 | 50.0 | 72.7 |
The probabilities of other combinations can be derived from those given in this table:
- A | !B (A or not B - possibly both conditions) is the inverse of A & !B.
- A ^ !B (A or not B but NOT both conditions) is the inverse of A ^ B.
- !A & !B (neither A nor B) is the inverse of A | B
- !A | !B (not A, or not B - possibly both conditions) is the inverse of A & B.
- !A ^ !B (not A, or not B, but NOT both conditions) is logically the same as A ^ B.