Probability Question- could be simple/could be hard??

Suppose you have an initial balance of £50 and play £10 stakes on a coin- heads you win ( and gain £10) / tails you lose. What is the probability of doubling your initial balance assuming you play as long as you need to? Or indeed the probability of losing the balance?
How does the stake size affect the probabilities? What if you played at £5 will it make any difference? And what if i went for a target of £150


Also generalising, balance of B
Stake size - s
target - T ( 2xB or 3xB etc)
p= probability of a win on one trial?

Anyone got any ideas? Its either really simple or really complicated??
Many Thanks

Quote:

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Originally Posted by rodders

Suppose you have an initial balance of £50 and play £10 stakes on a coin- heads you win ( and gain £10) / tails you lose. What is the probability of doubling your initial balance assuming you play as long as you need to? Or indeed the probability of losing the balance?
How does the stake size affect the probabilities? What if you played at £5 will it make any difference? And what if i went for a target of £150


Also generalising, balance of B
Stake size - s
target - T ( 2xB or 3xB etc)
p= probability of a win on one trial?

Anyone got any ideas? Its either really simple or really complicated??
Many Thanks

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You might want to read up on Gambler Ruin problem - such questions are covered there