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Greatest Loser Prop

Posted By: Steve Mellen
Date: Wednesday, 26 March 2008, at 11:11 p.m.

In Response To: Greatest Loser Prop (Chuck Bower)

There's a lot of stuff we don't know, most notably this person's overall chances, and their likelihood of winning an elimination vote if it comes down to it. But for the sake of argument, let's assume that the 5 players who survive this week have an equal chance of winning the $250,000, and the elimination vote is a straight 50/50 proposal.

That means the EV of making this week's cut (becoming "safe") is $50,000, and the EV of missing the cut is (50% * $50,000 + 50% * 0) = $25,000. There's a $25,000 difference between the two cases.

If you would make the cut whether you took the extra pound or not, it obviously doesn't help (and you would have rather had the cash). Likewise if you would have missed the cut either way. So the relevant question is how often you make the cut with the extra pound when you would have missed it otherwise; let's call this "x". Multiplying x by $25,000 tells us the value of taking the extra pound.

Thus, for the extra pound to be worth more than $10,000 cash, x would have to be greater than 40%. Without ever having watched the show, it sounds very, very unlikely from your description that 1 extra pound could mean a 40% greater chance of making the cut, which would make the cash option superior. But maybe you'll disagree with me on this.

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