A simple chance calculation

Question

You own 1000 points.

Your goal is to reach 2000 points, the only way you gain points is by gambling.

You will always gamble 40 points, your chance of winning a 40 points gamble is 60%, how high is your chance to double your points?

I'm pretty sure the solution is pretty simple, but I'm breaking my head over this, god I feel stupid I'm asking for help online, if some-one can help me with this problem it'd be much appreciated!

Answer 1

You don't say anything about how many chances you have to reach 2000 points. Is there a limit or is it infinite? What happens when you "win" a 40 point gamble? Do you get 80 points? What happens when you lose the gamble? If you have a score less than 40, can you still gamble (and go negative if you lose)?

 

If you have a 60% chance of increasing your score by 40 points and a 40% chance of decreasing it by 40 points, then the expected gain for each gamble is (40 points * 0.6) + (-40 points * 0.4) = 24 - 16 = 8. So in the long run you will continue to increase your score indefinitely.

 

The only way not to ever reach 2000 would be to end the game first. For example, if the rules say you lose when you reach 0 points (or 40 points), then if that happens you will never get to 2000. If that is the question, then the probability of reaching 2000 is 1 minus the chance of ever reaching 0 (or 40). I think that's a random walk question, but I don't know a formula.