Hi there, found a situation where I'm trying to find the probability of winning a ladder type game.(adsbygoogle = window.adsbygoogle || []).push({});

There are 10 steps and the goal is to win all 10 steps without busting (i.e. a streak, given one exception below in event B). On any given step three different events can occur:

Event A: 50% chance to win, move up to next step.

Event B: 25% chance to lose but not bust, stay at same step. A "life saver" if you will.

Event C: 25% chance to lose and bust. Start over.

Think of it like flipping a coin, but with a double elimination. So on a heads you move up a step. On a tails you flip again, a heads after the tails and you reset to this level, but if you get tails again, you lose. The best way I could think of it mathematically is what is the probability that you will have 10 more heads than tails and never have two tails in a row.

For instance

HHHHHHHHHH

HHHthHHthHHHthHthH

both produce a win. But

HHHthHHtt

loses after winning 5 steps.

Any ideas? Been a few years since I've done any higher math. The 10 more heads than tails portion sounds like standard deviation, but I never used that in any class I took.

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# Ladder game based on coin flips

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