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Sunday, July 25, 2010

Gamed Show

Inspired by a question from Joe*.

Consider a roulette-like game show that, fluff and stuff aside, boils down to:

90% odds are you get nothing and leave the stage. 10% odds, you win $1M.

If you win, you are given an option to spin again, with 10% odds of losing the $1M and walking away empty-handed, and 90% odds of winning another $1M.

Do you risk the second spin? Assume you only get to be on this game show once, and consider what you, personally, would really choose in that scenario. (The question is not about what optimizes expected return for the average player. You are only one player, not the average of many.)

Decide before you read further.

Now consider a variation where you choose one of two games up front:

A) 90% odds you lose, 10% odds you get $1M
B) 91% odds you lose, 9% odds you get $2M

Would you rather play game A or B? Decide before you read further.

The choice you have to make in both scenarios is exactly the same. Choosing to spin again in the first scenario is the same as choosing game B in the second. Are your answers consistent?

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