Probability problem looking for lowest cost.

Question

In this problem let's say you have a certain amount of coins. You are playing a game where you bet up to 5 coins every round. If you bet 1 coin you have 20% chance of winning, if you bet 2 coins you have 40% chance of winning, if you bet 3 60% chance, 4 80% chance and if you bet 5 coins you have 100% chance of winning.
The objective is to win 3 times and you can play as many rounds as you like. What strategy would statistically minimize the amount of coins that you spend?

Answer 1

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Answer 2

The mean value you want is 3, so for each situation you want to solve n*p=3, which is, how many throws on the average will get me 3 wins. It turns out the there is no difference, the number of coins thrown has to be 15.

 

If you had not made the probabilities uniform, then you would get a different answer.