Friday, December 29, 2006

Irrational Utilities

In the meantime, while I await G-Rob's inevitable resumption of smoking, I will be reading the new book The Mathematics of Poker. I haven't began yet, but I've been reading reviews and they've for the most part been very favorable. There is some game theory in the book as well which reminds me of a recent conversation here at work.

Assume the following: Person X has $200 to give away to two people, Persons A and B. Person A gets to determine how the $200 is split among A and B (assume whole dollar increments). However, Person A can only make one offer. If Person B vetoes, nobody gets any money.

The theoretical optimal split works out to be Person A offers Person B $1 and then keeps $199. Why? Person B gets $1 and knows that either he can accept that offer, or get $0. Person B's equity is also maximized too, getting most of the $200 available.

Sounds easy, right?

In theory, yes. In practice, no. Apparently (I don't have references, but I do believe this happened), the average value of the accepted deal split was somewhere around $60. Why is that?

Here's my opinion: Assume for a minute that you're Person B. You know there is $200 to split, but Person A has only offered you $1. You think it's hardly fair, even though you'd get $0 if you refused. So you veto, depriving Person A of receiving any money because he made such a stingy offer that you considered insulting.

What you've basically done is assign value or utility where none should exist. Persons A and B are complete strangers. So what if he's only offered you $1. $1 is greater than $0. But you're human. You're insulted. Fuck the other guy. You'd gladly sacrifice that $1 for the knowledge that Person A would get $0, even though Person A was only trying to maximize his utility.

So my question, which I hope is answered in the book, is how much irrational value are you placing on negative equity situations? I think I'm seeing it all the time at the poker table. Look at G-Rob's latest post. He's taking negative equity situations and gambling it up because he's assigned future value (tilt-implied-odds) to his decision.

Famous players that are targets in tournaments face the same thing. They could be making optimal bets at all times based on every variable in their analysis, but all that goes to shit when some donkey calls off all his chips for the "value" of claiming he busted a former bracelet winner.

I'm hoping to read this book with one eye on the math and one eye on how applicable it is in various situations. I'll keep you "posted," as they say.

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