Acceptance restricts the value to below your bid, where a uniform variable averages half of it, and doubling half your bid returns exactly your bid. The expected profit is therefore identically zero at every bid up to 100 and 100 minus b above it, so there is no optimal bid to find. With a general multiplier the profit is b squared times k minus 2, over 200, making doubling the exact break-even multiple, and the article shows a value distribution starting at 50 where the same bidder profits.
Also asked aswinners curse · winner's curse · sealed bid auction
Read the full explanation — Zero Profit at Every Bid, Because Winning Says the Firm Was Cheap
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Both seats in the marble game average a dollar a play, and that arithmetic stays true to the last line. Seat A carries variance 3/2 against seat B's 1, and seat A's law turns out to be seat B's law with one prize smeared outward, so every concave utility prefers B without variance ever being mentioned. Once both players stop flipping coins, seat B is ahead on the average too, at 1 against 3/4.
Four settlements in five come back below the 1.50 outlay, and the average payoff is still 1.80, an edge of 0.30 a contract or twenty percent of the money at risk. The reflex is not bad arithmetic, it is the mode standing in for the mean. The article carries the tally over one full cycle, the threshold saying you need the large outcome more often than one time in eight, and the reason waiting longer can leave you less likely to be ahead.
One chance in sixteen needs fifteen to one to break even, so a ten-to-one ticket is priced as though the calls came right nine times in a hundred rather than six and a quarter. The fair payout doubles and adds one with every leg, which is why multi-leg tickets run away from any quote a seller offers. The article carries the noise that hides the loss, 2.663 of spread against 0.3125 of edge, and the five-point edge per leg that would flip the verdict.