Imagine that you're playing a game of poker, five card draw. The dealer issues each player five cards, one at a time. He deals fairly, taking the top card from the shuffled deck and tossing them face down to each player in a counter-clockwise rotation as he goes around the table in order. You look at your cards and discover that you've been dealt a royal straight flush: the ace, king, queen, jack, and ten of hearts. You don't even need to discard and draw another card. You struggle to hide your excitement, knowing that the odds of drawing such a lucky hand are roughly 649, 740 to 1. This translates to a probability of success of 0.00000154, a mere fraction of one percent. Naturally, you should expect to win this hand. Even a royal straight won't be good enough to beat you. It doesn't beat the royal straight flush. Nothing does. The best another player could have done would be to draw a second royal straight flush in either diamonds, clubs or spades, splitting the jackpot with you. But the odds of two events with a probability of 0.00000154 percent occurring in the same hand of cards is considerably worse than the single rare occurrence, because the number of cards and possible winning combinations have been reduced. Furthermore, if two players in the same game drew a royal straight flush from the same deck of cards in the same hand, somebody somewhere would naturally certainly be accused of cheating. One royal flush is highly improbable; twice in the same hand absurdly so. The cards would be checked for signs of marking or tampering, and the dealer … [Read more...]