Bol Baby Bol
Source: P. Winkler
You have an opportunity to make one bid on an object, whose value to its owner is, as far as you know, uniformly random between $0 and $100. What you do know is that you are so much better at operating the widget than he is, that its value to you is 80% greater than its value to him.
If you offer more than the widget is worth to the owner, he will sell it. But you get only one shot. How much should you bid?
Solution: (First solved by Jaadu)
Highlight the part between the * symbols for the answer.
* He should not bid (or bid 0$) !! Explanation in comments!! :) *