#combinatorics

#combinatorics

In Texas Hold'em poker, players wager on the best five-card hand they can make among the two cards in their hand and the communal ones on the table. Hands are ranked based on their probability of occurring. A full house, for example, with three cards of the same value (fives or kings, for instance) and two cards of another, is less likely than a flush with any five cards of the same suit. A full house therefore beats a flush.

If you've ever shuffled a deck of playing cards, you've most likely created a unique deck. That is, you're probably the only person who has ever arranged the cards in precisely that order. Although this claim sounds incredible, it's a great illustration of how quickly large numbers can creep into everyday situationswith occasionally challenging consequences, as the developers of an online poker game painfully discovered in the late 1990s.