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A double or nothing machine is where you place in one token, and on your next turn you either double your token or lose it with a probability of p, you can then repeat this until your final bet is 64 tokens.
At what p is the player losing to the machine? What are the chances of winning your money back?
Hint (as you have not demonstrated efforts to solve the problem):
You have 7 plays to double your money for an assumed constant probability of winning ${p}$.
So, you want a distribution that addresses the number of trials to the first success.
The distribution in question is the Geometric Probability law.
