“necktie paradox” - -KINGDOM OF JOGA-

-as of [31 JANUARY 2024]–

(2 men are each given a necktie by their respective wives as a ‘christmas present’)

over drinks they start arguing over who has the cheaper necktie.

they agree to have a wager over it.

they will consult their wives and find out which necktie is 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.

this is obviously not possible

the paradox is solved because the men’s reasoning is flawed

each is considering his tie to be both the more expensive tie and the less expensive tie at the same time, while it can only be one or the other

(the 2 outcomes of the game each should consider are…)

* if I have the more expensive tie, and i make the bet, i lose my more expensive tie

* if I have the less expensive tie, and i make the bet, I win a more expensive tie.

(thus each stands to either win or lose an expensive tie, each at 50% probability, so the game has no advantage to either man)

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