Three competing patterns
  Assuming repeated independent sampling from a Bernoulli distribution with two possible outcomes S and F, there are formulas for computing the probability of one specific pattern of consecutive outcomes (such as SSFFSS) winning (i.e. being generated first) over another such pattern (e.g. SFSSFS). In this article we will extend the theory to three competing patterns. 
Rita Abraham and Jan Vrbik
math.PR