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Brainy Puzzles
Puzzle Solvers: Interesting brainy puzzles shared by fellow puzzlers
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IBM Puzzle [January 09] - Ponder This! (Very Tough)
Source: IBM Research | Ponder This | January 2009 challenges
Consider the following game. You have an opportunity to buy lottery tickets. Each ticket has a value t randomly and independently picked from the continuous and uniform distribution on the interval(0,1). Each ticket costs c (0
Suppose we modify the game so that you don't have to throw away any tickets. When you decide to stop buying tickets you can cash in any (but only one) of the tickets you have purchased and the game ends. Now what are your expected winnings (using the best strategy) as a function of c?
Note:
Some of the solvers are overlooking a minor point. For credit please ensure your answer is correct for the entire range of c.
Consider the following game. You have an opportunity to buy lottery tickets. Each ticket has a value t randomly and independently picked from the continuous and uniform distribution on the interval(0,1). Each ticket costs c (0
Suppose we modify the game so that you don't have to throw away any tickets. When you decide to stop buying tickets you can cash in any (but only one) of the tickets you have purchased and the game ends. Now what are your expected winnings (using the best strategy) as a function of c?
Note:
Some of the solvers are overlooking a minor point. For credit please ensure your answer is correct for the entire range of c.
Hmm. No one wants to try the tough problem? Come on folks!
answer is - expected value is 1-sqrt(2*c) for all c <0.5
if c >0.5 then the strategy is not to toss,,hence expected value 0.
if c >0.5 then the strategy is not to toss,,hence expected value 0.