Say your roommate says that she has a dog and will make you 10:1 odds if you can guess her dog's weight to within +/- a set amount. What set amount would you ask her for to make the game fair (expected value 0). E.g. if you set the confidence interval to be 1 standard deviation you will guess correctly roughly 2/3 of the time.
2026-02-23 08:19:31.1771834771
Setting amount for a fair game
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I'm assuming the standard deviation is for the guesses around the actual weight of the dog and not a standard deviation for the weights of dogs around the mean for the breed.
With that in mind, the probability of winning has to be $\frac{1}{11}$ to make it fair which corresponds to within $.115$ standard deviations. If a retriever actually weighs $64$ lbs (average for the breed) and say one standard deviation of guesses is $6$ lbs, you would have to guess within $0.69$ lbs for an expected value of zero.