- #1

BenVitale

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There's discussion on the 'necktie paradox' on this blog, where I'm a regular visitor.

I don't agree with the perspectives of those who have responded on that blog.

In the wikipedia, The necktie paradox states that

But, I look at this problem differently:

Say, the cheaper necktie has value y, and

the other one has the value (y + z) with z > 0.

Let's assume that both men have an equal chance of being correct,

the expected value in winnings for either man is,

(0.50)(y + z) – (0.50)(y) = (0.50)z

Both men are expected to make money if they bet.

So both men are correct in choosing to bet.

Is this correct?

I don't agree with the perspectives of those who have responded on that blog.

In the wikipedia, The necktie paradox states that

__each stands to either win or lose an expensive tie, each at 50% probability, so the game has no advantage to either man.__The problem reads:

Two men are each given a necktie by their respective wives as a Christmas present. Over drinks they start arguing over who has the more expensive necktie, and agree to have a wager over it. They will consult their wives and find out which necktie is the more expensive. The terms of the bet are that the man with the more expensive necktie has to give it to the other as the prize.

The first man reasons as follows: the probability of me winning or losing is 50:50. If I lose, then I lose the value of my necktie. If I win, then I win more than the value of my necktie. In other words, I can bet x and have a 50% chance of winning more than x. Therefore it is definitely in my interest to make the wager. The second man can consider the wager in exactly the same way; therefore, paradoxically, it seems both men have the advantage in the bet.

Is there a problem here?

But, I look at this problem differently:

Say, the cheaper necktie has value y, and

the other one has the value (y + z) with z > 0.

Let's assume that both men have an equal chance of being correct,

the expected value in winnings for either man is,

(0.50)(y + z) – (0.50)(y) = (0.50)z

Both men are expected to make money if they bet.

So both men are correct in choosing to bet.

Is this correct?

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