Profit from a favourable stopping game
Each round you win $2 with probability and lose $1 with probability . You stop the moment you win, or after straight losses - whichever comes first. What is your expected net profit (in dollars, to four decimals)?
Show hints (2)+
- First check whether the game is fair - the martingale/optional-stopping shortcut only works if it is.
- It has positive edge, so enumerate the four stopping paths and weight their payoffs.
Answer
Reveal answer →Final answer
0.392 (± 0.0005)
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