View Full Version : Please help settle disagrement on simple game theory question

11-22-2003, 03:42 PM
I was having an discussion about an unrelated topic and I used the following as an example. It was a discussion on email, so the following is exactly what was written.

"Let's say I said that we would flip a coin and if it lands heads I pay you $100, but if if lands tails you pay me $10. Now let's say that we do the flip and it lands tails. The results are bad for you, but the decision to play the game was a good one. It will still be a good decision for you to play if I get 10 tails in a row (assuming a fair coin); i.e. the ACTUAL RESULTS ARE IRRELEVANT."

This was the reply that I got

"Your analogy about the coin flip borders along the absolutely ridculous. You use this to support the theory "results are irrelevant". You say just because I lose 10 times in a row and end up ponying up $100 that it was still a good decision to play. Are you nuts? Who in their right mind would agree with that statement?"

Am I nuts? I think that the decision for you (i.e. the person who wins $100 with heads) to have played is a good one. I thought this was obvious. What do you think?

11-22-2003, 03:52 PM
i wouldn't take this proposition. either the coin is heavily biased towards tails or the person offering this to you is mentally challenged and i would feel bad taking his money from him.

11-22-2003, 04:00 PM
2 clarifications
1. I said "assuming a fair coin"
2. Forget about the mentally challenged. This is just a hypothetical example. Obviously someone would have to be very rich and stupid to make such an offer in the real world.

11-22-2003, 05:34 PM
Of course the decision for the player who wins $100 for
heads is a good one from an EV point of view and the
offer was a bad one! Too many people are results-oriented
and neglect what the edge (or disadvantage) was. On the
other hand, the situation of getting tails ten flips in
a row would make a person have second thoughts that the
coin was truly fair!

Like Ray Zee had said in a past post, you have to be
lucky to start playing poker without running too badly
or you would have second thoughts and quit the game

11-22-2003, 06:35 PM
This illustrates the difference between game theory and life theory. From a game theory point-of-view, the question isn't even worthy of discussion. From a life theory point-of-view, you really have to take the "if it looks to good to be true" approach. Your opponent is likely a deadbeat who won't pay if he loses, or (if you believe in this sort of thing) psychic, in which case you're drawing dead regardless of the fairness of the coin.

As to the rich/crazy possibility, I'd guess the probability of that is lower than the probability of your "pidgeon" being psychic.... /images/graemlins/wink.gif


11-22-2003, 07:31 PM
I agree with your game theory/life theory distinction. In real life one would be skeptical of such an offer for the reasons you have stated and many others. But I am presenting the situation in the theoretical world. That means no deadbeats, no mentally handicapped, no psychics, etc. and a fair coin.

I also agree that in a game theory sense this "isn't even worthy of discussion". So imagine my suprise, when someone tried to refute the game theory portion of this situation.

The person with whom I have the disagreement is not making arguments about the the person making the offer being retarded, a deadbeat or a psychic. He is trying to say that if you play the game and then lose money, then that means playing the game was a bad decision.

I am trying to help him understand that this is not true.

11-22-2003, 09:37 PM
You're having a semantic difficulty. The term "bad decision" is ill-defined. Try to convince your friend that it was a rational decision; you might have more luck.

11-22-2003, 09:44 PM
Depending on how he phrased his argument, this may all just be a matter of semantics.

Obviously the coin flipping involves positive EV, and is worth making the bet(s).

However, if you somehow knew the physics of the coin flip, and the acceleration at which the coins would be, blah blah blah blah blah, you would know ahead of time that you would lose all 10 flips, and therefore it would be a bad decision.

Here's another example. You are playing a live 5/10 game, and are dealt KK utg. Obviously you should raise, right? Well you do so and end up losing a huge pot to AA. The guy unnaware of what you had tells you "You shouldn't have played that hand.". With the limited information you had, he's obviously dead wrong. There's no reason to assume your KK is beat. However, with the information he held, hes right.

Basically, it's all a matter of hindsight vs. foresight.

11-23-2003, 04:40 AM
Thanks for the suggestion. This might help me make a breakthrough.

I actually tried working on semantics earlier in our discussion. What I said was basically that if you think that the quality of a decision is based on the results, then all decisions that result in a good outcome must be considered good decisions and all decisions that result in a bad outcome are considered bad decisions.

He disagreed with this suggestion. He suggested that good decisions could have bad outcomes and vice versa. Then he proceeded to disagree with the coin flip scenario that I described. This seems like a big contradiction to me.

11-23-2003, 06:00 AM
The only time I can see this as a bad bet relates to playing tournaments. If that $10 is your money for food this week you may not want to play.

11-24-2003, 02:09 PM
Tell your friend to regard it as a simple game theory question.

11-25-2003, 03:06 PM
clearly the person you were arguing with is a complete moron. 50-50 chance, he gets paid more, the chance of him paying you 100 and you not paying anything is .000977.