Gambling and faith, simplistic hypothetical

[Saddlepoint]

Someone offers you 1.1:1 on a coin flip, a gamble which you are permitted to take an infinite number of times. On each coin flip, you are permitted no less and no more than 1 dollar (Let's say that after a you win x number of flips, you can begin to risk more. I'm throwing this in so that nobody can say it's not worth your time to play). Super-important note: For the purposes of this hypothetical, you somehow know with 100% certainty that the coin and the bookie are both completely honest and unbiased. Would you stop playing if you lose the first 10 times you tried? The first 100? The first 1000?

With honest self-assessment, if you somehow knew that the arrangement was completely honest and random, would you be capable of continuing to play until you could no longer afford to lose?