[ExI] bar sinister gets more than you, was:... gets more than you do

[spike]

From: spike [mailto:spike66 at att.net] 

 

 

>…We can do the same trick using more easily visualized numbers, so let’s say the vault will have between 0 and 10 million imaginary bucks, equal probability of each amount…

spike

 

 

I plan to use one of the major stock indices, closing price average on Tuesday 24 November, so I don’t know what the amount will be, but I will scale it to 10M.  I have done a Monte Carlo but I will be damned if I can find the closed form solution to explain the shape of this function.  I might be doing something wrong.

 

Intuition fails: if you bid 5 million, we know that cannot be the optimal strategy: you have a 50% chance of getting nada, and the only way you can get 5 million is the one in 10 million chance the vault contains exactly 10M.  So we know the optimal bid is below 5M.  That part is easy.  

 

The next intuition is that 2.5M is your best bet.  But… perhaps not, because you then have only a 25% chance of a goose egg but you max out at 2.5M and you know the evil Mr. Potter is probably going to feast.  If you are at 2.5, it is easy enough to show that raising your bid increases your upside without introducing much risk.  And you already know 5M is too much.

 

spike

 

 

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