# Just for Fun

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John played a solitaire game several times. He played 9 games and won 6 out of those. His win percentage is 66.66%. How many games will he needs to wins to make his game winning percentage 99%.

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This looks very much like homework -- is it?

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The IT department removes the games from the windows install so he never finishes his game ;)

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Yeah, It is interesting :) Perhaps we could find something to learn again.

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I can't help but feel this is a trick question somehow. Can you even lose solitaire (been a long time since I played it)? Assuming it's not then I would say he now needs to win the next 291 games in a row since (6+291)/(9+291) = 0.99.

That seemed a bit easy though and since you chose 2/3rds of wins maybe you are doing something funny with the recurring numbers and maybe you meant 99.99(recurring)%. In which case it's now impossible for him to ever do it since 0.9999999 recurring is 1 and since he's already lost 3 he can never get 100%.

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What Nanoha said, but I make it that he needs to win the next 288, and I have completely forgotten the reason that it's 3 less, but its completely brilliant, and now I'm confusing myself.

Gah!!!!!

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@Nanoha: You have a good point. I never thought I believe There are many unsolvable sets of cards in a solitaire game that are having no more moved. That way a player would never be able to attain a 99% wins. Mostly only games which are possible to be won are given to player by computer I guess.
According to Wiki the number of possible hands is over 8×1067 only 79% of the games are solvable. https://en.wikipedia.org/wiki/Klondike_%28solitaire%29

@Eulagrief: I should have choosen minesweeper for this case.

The player needs 292 to win, to make it 99%. but to make 78% the player needs much less effort, only 5 moves. That this percentage goes non linear. That is why that percentage seems trivial way for game analysis. Does winning or loosing realy matter. When does it matter then.

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I once played solitare and after moving one card, an ace, to the top I riffled through deck and then lost because I had no more moves.  Epic game.  I'm still waiting for the one where I have no moves to make then riffle through the deck and lose.  That will be a very special day.

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