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Pick a card, any card.. (Posted on 2008-03-11) Difficulty: 3 of 5
You sit down with a well mixed deck containing A cards marked "+" and B cards marked "". You may draw cards from this deck as long as you want, i.e., you can stop playing at any point. Each time you draw a + card you are given $1 and each time you draw a card you have to pay $1. Cards are not replaced after having been drawn.

What would be a fair amount to pay for the right to play (i.e., what is the expected payoff) and under what circumstance should a player cease drawing?

No Solution Yet Submitted by FrankM    
Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
What's the catch? | Comment 2 of 37 |

If you do not know the counts of A and B, you should NEVER play this game.

If you do know the counts in advance, you should play only if A is greater than B, and the cost to play is less than A$ - B$.  (It is not clear whether "the fair amount to pay for the right to play" means a fee for EACH card drawn, or for the right to play until you stop or the pack is exhausted (since cards are not replaced). It's a dumb wager in any case.

If you decide to play (i.e. A and B known and A > B), then you will know the total T number of cards involved.  You should stop whenever the remaining A cards are fewer than or equal to the remaining B cards (and you have been keeping track of the total of each type).

In either case, get a life!


  Posted by ed bottemiller on 2008-03-11 15:11:44
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