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

[spike]

From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of William Flynn Wallace
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Adrian wrote:  What do I do with my take?  Make life more awesome for many, possibly most, people permanently (or as close to permanent as we get these days).

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​Now this is a great topic.​  I sometimes daydream about having a billion dollars, or ten billion or something, and plan what to do with it.  Surely some of you have the same daydream…How about you?  bill w

 

 

OK then, the DJIA closed today at 17812.19 so the decimal .19 rounds to .2, divide by pi^2 gives us 1804.7521, throw away everything to the left of the decimal and scale up by 7 digits, the vault contains $7 521 741 which is lucky as all hell for me.  If I bid the optimum strategy for my take, I bid $3,333,333 and I get all of it.  Potter gets $4 188 408, and then of course you add it to the 8000 bucks the evil bastard stole from old Uncle Billy and sure he is still rich, but so am I.  All in all it was a good imaginary day.

 

I managed to find a closed form optimization strategy.  The Monte Carlo sim was right (Monte Carlo sims always are) when it suggested bidding one third the highest possible amount.  I did, and I get all of that today.  Woohoo!

 

When I got that closed-form solution I found something else kinda fun.  Imagine a variation on the theme, where it isn’t quite as benign as going home empty handed if you over bid.  In this diabolical variation from hell, if you bid more than the amount in the vault, you must make up the difference from your own pocket to pay Potter that amount.  If for instance the maximum amount is 10 million, you bid 1 million, then in about 1 in every 10 trials, you must dig into your own pocket to give Mr. Potter whatever is in that vault below a million bucks, owwwww.  So Potter’s minimum take is whatever you bid.  But some of it will be your own money.

 

In the variation from hell, it is still advantageous for you to play the game.  But your mathematical expectation is lower and your optimal bid strategy is different.

 

What a cool game!

 

spike

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