An early form of Poker solitaire is actually a puzzle of sorts, one which has been called Maverick solitaire (after its appearance on the 1950’s/1960’s Western T.V. show Maverick, in the first season episode Rope of Cards).
Twenty five cards are dealt from a shuffled 52-card deck. The object is to divide the 25 cards into five groups of five cards so that each is a pat hand in draw poker (a hand which does not need to be drawn to).
The pat hands we need to consider are four of a kind, full house, flush, and straight. The best place to start in solving a problem in Maverick solitaire is to divide the cards into suits, checking to see which suits have five or more cards, enough to make a flush. When each suit has five or more cards (which should happen in slightly over 50 percent of deals), it is often possible to make four flushes, and then a fifth hand using the excess cards over five in each suit. For example, if the suit distribution is 7-6-6-6, any two cards from the long suit and one card from each other suit can be selected in an attempt to make a full house or straight. A card can be matched in six ways: as part of a flush, as part of a straight, in a pair combined with another three-of-a-kind, in three-of-a-kind combined with another pair, in four-of-a-kind, or as the fifth card added to another four-of-a-kind. Martin Gardner discussed the game and showed an example of an unmatchable card, but such cards are rare. The most common type of unsolvable deal seems to be a hand with one or two four-card suits, with cards widely spread to make straights difficult.
Maverick Solitaire is well-known as a sucker bet, as the probability of success with a random group of 25 cards would seem low, but is actually quite high: the eponymous author of Maverick’s Guide to Poker estimates the odds to be at least 98% (he disallows four of a kind). This is remarkably accurate: Mark Masten’s computer solver, allowing four of a kind, solved about 98.1 percent of a random set of 1,000 deals. Deals with unique solutions are even less common than impossible ones: the sample above had 19 impossible deals and only 8 with unique solutions.