Spoiler for my guess
Generalizing to j and k,
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Posted 23 June 2012 - 01:55 AM
Spoiler for my guess
The game seems simply to determine when to say Stop.
Seems that 2 draws puts your winning chances above 50%.
So I'm stopping after my 2nd draw.
Vidi vici veni.
Posted 24 June 2012 - 02:32 AM
You and I are playing a little game (that is in no way whatsoever related to any game played on this site *cough*). There are 12 objects, 4 of which have the property M. The goal is to choose an object with the property M.
However, you and I are playing by different rules. For each round, first there is the N phase, in which you secretly choose an object (write down its number or something), then there is the D phase, during which I pick an object and it is revealed whether or not the object has property M.
If the object I pick has the property M, I win, if not we keep going. During any N phase, after you choose an object, you can call 'STOP' and the game will end. Then you reveal your choices, and if at least one has the property M, you win. If none have the property M, I win.
What is your play?
Bonus: Generalize to a case of n objects, k of which have the property M.
Edited by bushindo, 24 June 2012 - 02:41 AM.
Posted 24 June 2012 - 03:28 AM
Posted 24 June 2012 - 04:37 AM
Posted 24 June 2012 - 05:01 AM
Posted 24 June 2012 - 05:17 AM
Posted 24 June 2012 - 05:21 AM
Of course not, but it doesn't matter. If N knows what he or she draws, then the only reason to continue the game is if he or she draws not-M. Calling STOP at this point would ensure a loss. Continuing gives a chance of victory and a chance of loss. So clearly it's better to allow another round. This logic continues until k=n, at which point whoever draws next wins.
You can't say STOP after they've already won.
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