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November 27th, 2011, 09:24 PM  #1 
Newbie Joined: Sep 2011 Posts: 8 Thanks: 0  Effects of Clustering of Heads or Tails
1) How did you get prob. of at least X tails in N tosses with prob. of tail = q, out of K trials? For e.g., In a bias coin toss game where prob(head)=0.7, what is the probability of 30 tails clustering (not necessary consecutively) in the first 50 tosses out of 100 trials? 2) For a fair coin toss game played infinitely, is there any mathematical expression that describes the optimal condition to quit, as a function of the variables M,no. of consecutive losses & Cnow,current balance$ for a fixed bet size,b. i.e. The best time to stop is when the no. of consecutive losses, M, has the greatest effect on the chances of current balance going to zero.Find a mathematical expression for this N in terms of Cnow & bet size, b (as % of Cnow). Appreciate any suggestions. 
November 27th, 2011, 11:03 PM  #2 
Newbie Joined: Sep 2011 Posts: 8 Thanks: 0  Re: Effects of Clustering of Heads or Tails
To rephrase, When is this prob(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, b, M, p, q, etc? 

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