Brainy Puzzles
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Kaustubh Katdare • Jan 29, 2009

# 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.
Kaustubh Katdare • Jan 31, 2009
Hmm. No one wants to try the tough problem? Come on folks!
indukuri • Jun 9, 2009
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.