Posted: 10/27/2008 1:25:14 AM EDT
My son (8yo) and I (29 and holding ) were playing war (card game) and we had 4 sets of matching value face up cards. The fifth set determined the winner - him. What are the odds of that happening? The deck was well shuffled. |
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There are 52 cards in the deck. The chance that any two cards on the first draw have the same face value is 3/51. Since it does not matter what the first card is, it is the chance that the second card matches: three possible matches left out of 51 cards left. The second draw leaves 3/49, the third 3/47, the fourth 3/45. We can disregard the first pair, since this will occur at some points in the game. What we are interested in is the chance that subsequent pairs will be had. (Note, the calculation disregards the slight additional chance that there will be a dupicate pair occuring, e.g., all four kings show up. Multiplying 3/49,3/47,3/45 gives 2.6E-4, or 26/100,000. The actual odds are a little bit better than this since there is the possiblity of 4 of a kind occuring. While playing war, it does not take all that long to make 10,000 hands where you would expect this 4 pairs in a row to occur 2 to 3 times. |