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#1
12-12-2005, 04:41 PM
 Guest Posts: n/a
Is Game Theory Applicable Here?

A friend of mine and I were discussing a fairly simple game: you are presented the opportunity to take either \$240 straight up or to play a game where 25% of the time you will win \$1,000. You may only play the game once.

My friend aruged that the expected value for the game is \$250 if you take the shot at \$1000 and only \$240 if you do not, and therefore you should take the chance. I completely understand, but...

Seeing as it is a one time event, I argued that it was not necessarily advantageous to play for the long run. Therefore, it is not unreasonable to sacrifice \$10 in expected value in order to play a game you cannot lose rather than one that you are a huge underdog to win.

I understand that one's decision might be influenced by how much money they have to start, or if the game had different values (I feel most people would rather take 240K straight up than take a 1-in-4 on \$1 million, even if it is mathematically incorrect), but in general is my logic faulty?
#2
12-12-2005, 04:57 PM
 pzhon Member Join Date: Mar 2004 Posts: 66
Re: Is Game Theory Applicable Here?

[img]/images/graemlins/diamond.gif[/img] Game theory is completely irrelevant.

[img]/images/graemlins/diamond.gif[/img] EV makes sense even for events that only happen once. Many people find this counterintuitive.

[img]/images/graemlins/diamond.gif[/img] It is ok to have a nonlinear value for money, which can lead you to being rationally risk averse. If the value you place on having \$x is log x, you should accept the the gamble if you have at least \$9038.19, and decline if you have less.

[img]/images/graemlins/diamond.gif[/img] "it is not unreasonable to sacrifice \$10 in expected value in order to play a game you cannot lose rather than one that you are a huge underdog to win" sounds overly emotional, and does not easily fit into a consistent system for analyzing gambles. Many people are willing to pay for short-term certainty. This is an easily exploited weakness in poker.
#3
12-12-2005, 05:10 PM
 Guest Posts: n/a
Re: Is Game Theory Applicable Here?

I'm not too familiar with game theory, that's just what he called it. Sorry if i erred.

Your last point about exploting my idea as a weakness in poker makes sense, but in poker you can consistently make this decision over and over again and play for the long term. I would not even bring up this question in a poker game, my question was about a one time scenario.

Thanks for the other stuff though.
#4
12-12-2005, 10:43 PM
 ThinkQuick Member Join Date: Jan 2004 Location: Alberta, Canada Posts: 97
Re: Is Game Theory Applicable Here?

pzhon's summary is great

you can use the search function to find other similar threads.. the last one I remember was 'deal or no deal' I think.

He isn't saying that you are a weak poker player. He's agreeing with you in fact that its ok to sacrifice some EV for guaranteed money if the money means something to you. I personally may not give up any EV for only 250/240 bucks, it may have to be more.
now take this lesson and ensure that you don't play above your bankroll in order to allow you to keep pushing all edges
#5
12-12-2005, 11:57 PM
 AaronBrown Senior Member Join Date: May 2005 Location: New York Posts: 505
Re: Is Game Theory Applicable Here?

In addition to phzon's excellent reply, I would add that you have to be careful once you deviate from maximizing expected value. It can be rational to deviate, but most people wander into inconsistency and error when they do. Here is one famous example known as Allais' paradox (for which Maurice Allais won the 1988 Nobel Prize). The poker adaptation in my own.

(A) You’re at the final table of a Poker tournament with two other entrants left. There is a \$2,500,000 first prize, \$500,000 second prize but no third prize. You have the middle stack, the woman on your right has ten times your stack, the guy on your left is down to a chip and a chair. You think there is a 10% chance you will win, an 89% chance you will take second and a 1% chance you will take third. The other players offer a split. You get \$500,000. The chip leader gets \$2,500,000 and will compensate the short stack out of that. Do you take the split?

(B) Same tournament and prizes, but you now have the short stack. You figure you have no chance at all to win, an 11% chance of picking up the \$500,000 and 89% chance of getting nothing. The chip leader offers to settle for second place, taking \$500,000 and her chips off the table. The middle stack says he’ll do it if you give up 10% of your chips, then play out for first place or nothing. With this deal, you figure to have a 90% chance of ending up with nothing, and a 10% chance of winning \$2,500,000.

First answer honestly what you would do in each situation, then look more closely and I'll bet you've made completely inconsistent decisions in the two cases.
#6
12-14-2005, 01:46 PM
 WhiteWolf Member Join Date: Mar 2005 Posts: 87
Re: Is Game Theory Applicable Here?

[ QUOTE ]
In addition to phzon's excellent reply, I would add that you have to be careful once you deviate from maximizing expected value. It can be rational to deviate, but most people wander into inconsistency and error when they do. Here is one famous example known as Allais' paradox (for which Maurice Allais won the 1988 Nobel Prize). The poker adaptation in my own.

(A) You’re at the final table of a Poker tournament with two other entrants left. There is a \$2,500,000 first prize, \$500,000 second prize but no third prize. You have the middle stack, the woman on your right has ten times your stack, the guy on your left is down to a chip and a chair. You think there is a 10% chance you will win, an 89% chance you will take second and a 1% chance you will take third. The other players offer a split. You get \$500,000. The chip leader gets \$2,500,000 and will compensate the short stack out of that. Do you take the split?

(B) Same tournament and prizes, but you now have the short stack. You figure you have no chance at all to win, an 11% chance of picking up the \$500,000 and 89% chance of getting nothing. The chip leader offers to settle for second place, taking \$500,000 and her chips off the table. The middle stack says he’ll do it if you give up 10% of your chips, then play out for first place or nothing. With this deal, you figure to have a 90% chance of ending up with nothing, and a 10% chance of winning \$2,500,000.

First answer honestly what you would do in each situation, then look more closely and I'll bet you've made completely inconsistent decisions in the two cases.

[/ QUOTE ]

Am I missing something - this seems trivially easy?

Situation A - no deal (EV of 695000) beats out deal (EV of 500000).

Situation B - deal (EV of 250000) beats out no deal (EV of 55000).
#7
12-14-2005, 04:35 PM
 Chipp Leider Junior Member Join Date: Nov 2004 Posts: 22
Re: Is Game Theory Applicable Here?

You might wanna look into Certainty Equivalent.
#8
12-15-2005, 01:11 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Am I missing something

Aaron, or is this simply a complex (or maybe not so complex) case of utility theory ?

I'm going to now read all the responses - both to the original thread and to your tourney settlement question - but before doing so I'll state that I've taken the worst of it many times in order to minimize the chance of disaster.

I posess the resources, albeit just barely [img]/images/graemlins/frown.gif[/img], to post a bond in lieu of paying for liability coverage on my car but I'd never entertain the thought of actually doing so.
#9
12-15-2005, 01:17 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Re: Is Game Theory Applicable Here?

It IS trivially easy unless your girlfriend/fiance/wife is standing over you with that "WTF are you thinking [img]/images/graemlins/mad.gif[/img]" look in her eye.

If you've ever seen that look you know NOTHING is trivial when facing it. [img]/images/graemlins/grin.gif[/img]
#10
12-15-2005, 01:25 AM
 ohnonotthat Senior Member Join Date: Aug 2005 Location: New Jersey - near A.C. Posts: 511
Have you

got a link to that ?

It's likely to be over my head but I can dream of the day I'll understand it. [img]/images/graemlins/confused.gif[/img]

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