I just finished a phone call with a potential internship opportunity and can't help but think I messed up on (what should've been) an extremely easy question.
Here is the scenario:
You have the opportunity to play a game. This game involves a fair coin. Every time I flip the coin and you call it correctly, you win 10% of your previous amount. Every time you incorrectly guess, you lose 10%. You start with $10 dollars.
Question 1: Would you play me if I flipped the coin once?
My response: There are two outcomes for this scenario: 11 and 9. Since each have the same probablity, my expected value is 10. I'm indifferent as to whether I play.
Question 2: Would you play me if I flipped the coin twice?
My response: There are four outcomes (three results) to this scenario: 12.1, 9.9, 9.9, and 8.1. Expected value is still 10, but we are only playing this game once. Three of the four outcomes result in my total wealth being less than my original wealth and only 1/4 chance I gain wealth. Therefore, do not play two games.
What do you all think? I can't imagine a different scenario, but I feel this couldn't have been the correct answer.
Who cares. You gave a good thought process. Won't make you/break you. Don't sweat it
I don't like your answer myself. I would say that I wouldn't play either of the two games since expectation is 10 (read: no edge) but you're exposed to risk. The probability of downside risk has little to do with it - would you play a game where you lost everything with probability 1/3 and got 15 with probability 2/3?
@euroazn I was thinking the same thing myself when I first began answering the problem, but I got caught up with the fact that we were only playing the game one time, meaning the only actual outcomes possible were 11 or 9. Agree with you after looking at your other example.
Not sure I understand where you are coming from. Nowhere does the first situation imply a risk reward as you've characterized it in your last sentence. Moreover he is equally exposed to upside risk as downside risk in the case of a single flip.
OP's answer is fine.
^ with euroazn, however your answer seems pretty good IMHO.
how long did you take on it answering? just curious?
I spent probably 10 seconds doing the first one. Based mostly on intuition.
The second one took longer. Maybe 20 seconds as I calculated all of the scenarios and another 10 to recognize the 3 losses and 1 gain situation. Followed by a conversation with why I'm changing my strategy even though the expected value is the same.
Ask to borrow $200, throw in your $10, play the game, take a management fee and 20% of the upside.
lol, would be amazing if you responded that...
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