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Using a standard deck of playing cards, how many ways of assembling (shuffling) them will result in a competent player always "going out" in a standard (seven initial columns, every remaining third card can be played) game of solitaire? And what proportion / percentage of the total number of ways that a deck can be assembled does that number represent?

RobPratt
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Chris Haws
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  • This is a very interesting question but I'm not sure if it's known what arangements of cards will be winable. Also there is a total of 52! ways to rearange aa deck of cards which is about 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Just to give it a little perspective – KBusc Sep 05 '14 at 20:31
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    Bill Turnball has a page devoted to an empirical analysis of the odds at winning in Solitare, along with quite a few useful links. – Semiclassical Sep 05 '14 at 20:31
  • Related: https://math.stackexchange.com/questions/121305/what-is-the-probability-that-a-solitaire-game-be-winnable – Henry Jun 10 '19 at 22:03

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To have an answer to this question you need to define exactly the strategy your "competent player" uses. This means one could write a computer program that takes in a position (including what is known about the order of the pack) and outputs the move to take. In my experience there are many positions with multiple moves available where it is not clear what the optimal one is. In theory you could then run through all $52!\approx 8\cdot 10^{67}$ possible decks and count the number that win. In practice that is far too many to do, so you would do a random sample and see how many win.

Ross Millikan
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