LogFAQs > #938646653

another way to estimate this probability is to deal out a pair randomly to the 48 slots. doing that, there's a 3/47 chance they go to the same person. if you just did that 24 times in a row without considering where the previous cards went, there's a 1-(44/47)^24 = 79.46% chance someone gets a pair. but that obviously isn't going to be completely accurate either. just the second pair dealt out is already going to be less likely to be given to the same person than the first. and say you're halfway done and everyone has 2 cards. now you're even less likely to deal out a pair.

if you're combing through all possibilities, you will come across situations where the next pair to be dealt out is more likely than the initial 3/47. but that involves stacking a few players with most of the cards while the rest have very few. those situations are less common to begin with, and become even more rare with the restriction that they can't have a pair. therefore, i'd say the actual probability is signifcantly less than that 79.46% estimate. basically, every pair that pops up increases the pair of another appearing, and it's that co-dependancy that lowers the chances of "at least one" pair.

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