# Rate of Ruin & Optimal N

• Nov 24th 2011, 09:37 AM
scalpmaster
Rate of Ruin & Optimal N
For a fair coin toss game, both prob(ruin) & prob(consecutive losses) increases with no. of trials.

Is the Rate of ruin .i.e.where prob(ruin) changes fastest, affected most by the number of consecutive losses?

If so, what is optimal N, maximum no. of consecutive losses to indicate a good time to exit the game?

In a bias coin toss game where prob(head)=0.7, what is the probability 30 heads clustering
(not necessary consecutively) in the first 50 tosses out of 100 trials?

Appreciate any suggestions.
• Nov 27th 2011, 11:00 PM
scalpmaster
Re: Rate of Ruin & Optimal N
To re-phrase,
When is the probability(streak of losses just enough to ruin its bankroll B) > 50%?
i.e. Is it possible to express this prob in terms of current bankroll B,bet size b, no. of consecutive losses N, p, q, etc?
• Nov 27th 2011, 11:06 PM
scalpmaster
Re: Rate of Ruin & Optimal N
Also, How do you get prob. of at least X tails in M tosses with prob. of tail = q, out of K trials?