An Analyzable(Though Seldom Winnable) Card Solitaire

Introduction
On the whole, standard card solitaire games notoriously resist the calculation of their winning probabilities. Yan et al. [2005] have said, in referring to what is commonly known as Klondike solitaire, "It is one of the embarrassments of applied mathematics that we cannot determine the odds of winning the common game of solitaire." However, a couple of games (see Knuth [1997, 377-378] and Harkleroad [1990]) have been found to buck the general trend and lend themselves to suitable analysis. This paper adds another card solitaire to the short list of those with probabilities amenable to evaluation.

Rules of the Game
The basic game plays out as follows:
• Start by dealing four cards face up.
• If any two of the cards belong to the same suit, deal a new card face up on each of those two.
• Continue in this fashion, covering any pair of cards matching in suit with a new pair.
- If you manage to use up the whole deck by this process, you win.
- More likely, before yourunthroughthe deck, youwill hit a roadblock, with the layout containing a single card in each suit. In this case, you lose.