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Jonny_trigonometry

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what is the probability of winning a game of solitaire?

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- Thread starter Jonny_trigonometry
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- #1

Jonny_trigonometry

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what is the probability of winning a game of solitaire?

- #2

Tide

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That depends on which variant of the game you are playing.

- #3

Jonny_trigonometry

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HallsofIvy

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shmoe

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- #6

robert Ihnot

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This very detailed mathematical analysis definitively depends upon computers, and before computers these things could not be figured. First of all, you must discover what is for the bettor perfect play. By simple computation it was often possible to get general figures about what to hold and discard, but to get an exact analysis is another matter and depends upon a computer.

Double Bonus, 10/7, has a supposed payout of 100.1725% with perfect play-- which, of course, assumes truly random dealing. This was certainly not known before computers, because the best strategy for the player was unknown. In fact, in Georgia, for example, it is illegal to have a offer an electronic game that pays back over 100%. Double Bonus was offered because its theoretical payout with perfect play was incorrectly estimated.

This is something like camera lenses, where before computers they would stumble on a formula for a lens, but after computers they really got going and discovered how to make a lot of new camera lenses.

Of course, Video Poker is a paying game, unlike solitaire, and, maybe no one has really put that much effort into discovering the best strategy.

- #7

Jonny_trigonometry

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HallsofIvy said:

Because I'm pretty sure that not all solitaire games are winnable.

- #8

Jonny_trigonometry

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for the first 7 face up cards, you have

2, 2, 2, 2, k, k, k

where under each face up card you have 0,1,2,3,4,5,6 face down cards respectively.

So you have 31 cards left over, and you flip them every three. Then there are 10 cards that you will never be able to use in the rest of the deck if you can't use any of the 21 cards that you will cycle through in a period 2 limit cycle. Just imagine grouping the 31 cards in 10 groups of three, and one extra, you will cycle through, seeing all of the first cards of each group, then you'll see the last card, then you'll cycle through seeing the 3rd card of each group, then the last card, then you will repeat the cycle. if all these 21 cards are the three's, fours, fives, sixes, sevens, and one eight of any suit, then you can't play anything to begin with.

In some cases, you can make many moves, but you will end up on some periodic cycle.

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