Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody

The Answer 2

Prince Blueblood should bid 29/30s of whatever he values the painting at.

Imagine an auction that was down to just him and another bidder. First obvious fact is that he should never bid more than his valuation of the painting, otherwise if he loses, he's back where he started, and if he wins, he overpays for the painting. Nor should he pay EXACTLY how much he thinks it's worth, because no matter if he wins or loses, he breaks even profit-wise. Might as well have stayed home. So he has to bid below the valuation and hope to win.

Your expected payoff is the probability you win multiplied by the profit should you win. So in this scenario where it's down to two ponies, half of the painting's value is the happiest compromise between the two values.

Using similar logic, for this auction of thirty ponies including Blueblood, he should pay 29/30s; higher bids to compensate for the increased number of rivals, in this case thirty.