Probability Distributions of Swishes in the Game of Swish

Abstract

We examine the game of Swish, where we look at the probability of certain events occurring on the first deal of n cards. We are interested in two specific cases, namely a swishless case, where no two cards form a swish, and the general case, where we iterate through all possible deals of n cards with k swishes. We obtain a closed-form series for both the swishless case and the general case. Our series also agree with our computer simulations found in the appendix to this paper. We found that the quantity of swishless deals reaches its’ peak when dealing 19 cards, and we have found all the expected number of swishes given there n cards dealt.