The probability of a royal ush in poker is p 1 649740 Show t

The probability of a royal ?ush in poker is p =1 /649,740. Show that approximately 649,740 hands would have to be dealt in order that the probability of getting at least one royal ?ush is above 1?1/e.

Solution

This depends on the house rules. By standard rules the spades royal flush does not beat the hearts royal flush, as they have an equal value.

However some house rules state that in case of an equal hand, the suit decides the winner, in which case the spades are always higher then hearts.