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Who wants a dollar pt. 2


Question

Suppose you and a logical but competitive friend are at a $1 auction.  The auction works as such, you each start the contest with $3 and you bid on $1 bills.  The highest bid for each round wins $1 minus the amount bid AND loses their actual bid.  So for example, if in round 1, you bid $.20 and win the $1 then your new balance would be $3 - 0.20 + (1-0.20) = 3.60.  If a tie occurs, the amount gained for each individual (i.e. 1 - bid) is divided by 2 but the full bid is still subtracted from the totals. Lastly $0 bets are not allowed.  If you are out bid then you lose your bet. 

Knowing that your friend is competitive and logical...

how much should you bid?

what would be your expected payout after five rounds?

Edited by BMAD
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