Maverick Solitaire

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).  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 percent (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 1000 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.

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 (see Bibliography) 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 is not found very often in computer implementations, but there is a version in Solitaire Virtuoso.  Any two cards can be swapped by clicking on them in succession; the program automatically detects when the cards are arranged to that the five cards in each row form a pat hand.  We hope to eventually incorporate Mark Masten's solver into the program, which might allow it to provide deals of selected difficulty.  Another method, not implemented yet, might be to allow the player to select from various suit patterns (for example 7-6-6-6 for easy deals, 7-7-7-4 for harder ones).   We will also eventually implement other forms of Poker solitaire.

Brown, Douglas -- The Key to Solitaire, Ottenheimer, 1966 (later reprinted as 150 Solitaire Games)
   pp. 14-17 describe Maverick under the name Poker Solitaire
Gardner, Martin -- Mathematical Magic Show, Vintage, 1978, (Knopf, 1977),  ISBN 0-394-72623-5
   Chapter 7, "Playing Cards", pp.94-104
Maverick, Bret -- Maverick's Guide to Poker, Tuttle, 1994, ISBN 0-8048-3032-0
   pp. 131-132 discuss Maverick Poker

Copyright 2011 by Michael Keller. All rights reserved.  This file was revised on July 11, 2011.