Two equally strong teams, one having the upper hand for a long time

Question

On one of my courses (applications of probability theory) the lecturer mentioned an interesting theorem. It was something along the lines of two, equally strong teams playing against each other and generally one of them having the upper hand for a long time, as opposed to just each leading the field in rapid succession. Can someone tell me if there's a theorem like that? If there is, what's its name?

Sorry for the obscure description. I attended the lecture a couple of years ago. I suppose this theorem may be more general than what I've described.

Answer 1

I think you want

The law of long leads, more properly known as the arcsine law, says that in a coin-tossing games, a surprisingly large fraction of sample paths leave one player in the lead almost all the time.

http://www.math.unl.edu/~sdunbar1/ProbabilityTheory/Lessons/BernoulliTrials/ExcessHeads/excessheads.shtml