Five-Card Draw

The Five-Card Draw is a probabilistic counter-argument to various complexity arguments which demonstrates that the appearance of order in a system is not indicative of design.

The argument proposes shuffling a standard 52-card deck and dealing out a five-card hand. As there are 52 possible draws on the first card, making the odds of any particular card 1 in 52. The odds of any particular second card are 1 in 51, the odds of any particular third card are 1 in 50, the odds of any particular fourth card in 1 in 49, and the odds of any particular fifth card are 1 in 48. There are 311,875,200 possible five-card hands (52 x 51 x 50 x 49 x 48), meaning that the odds of drawing any particular five-card hand at random are 1 in 311,875,200, with a probability of 0.0000000032064.

Mathematically speaking, then, the chances of drawing a royal flush or four aces and a king, or 3♣-6♦-8♠-J♥-K♣ in a single five-card draw are identical: all are 1 in 311,875,200. Thus it is clear that a royal flush differs from a random draw only in that one is externally defined as having more value that the other.