coin-flip odds (tennis match)

I've been watching the Mahut/Isner match this afternoon on ESPNU. It is currently tied at 55 in the 5th set. This is mind-boggling to me. All that has to happen for one of them to win is for one of them to get up by 2 games. Assume they have equal skill. Each game is then the equivalent of a coin flip. If I flip a coin 110 times, what are the odds that I never see two heads or two tails in a row?

I haven't even tried to play tennis in years and was never any good at it. On the other hand, the Wizard plays tennis, so this could be a interesting question for him.

My thinking is that you can't really compare it to flipping a coin. Even if the players have equal skill, the game is such that the server has a (perhaps slight) advantage. Thus, it is more like alternately flipping two biased coins -- one tending to give heads, one tails -- then trying to figure out the likelihood of neither getting a lead of 2. Also, it isn't a matter of getting two in a row. If "heads" has the lead by 1, getting two straight tails does not end the game.

The server definitely tends to have an advantage in Tennis. I haven't played since high school, but I do remember several matches in which my ability to ace an opponent was the difference in the game.

I think the original poster's reference to flipping a coin was based upon the server having an advantage. If, at tie score, Player A gets to serve twice in a row, then he will most likely in. But, if Player A only serves once, and then Player B gets to serve, then it's bake to tie score. Thus, from the tie point, one player needs to receive the serve twice in a row, somewhat equal to a coin flip being heads twice or tails twice.

Again, it's more than simply two heads or two tails in a row, since if the heads has an advantage, the tails would actually need three in a row to win.

As you guys are alluding to, the server has an 80% chance of winning the point. Here is a link to the math of today's match.

Quote: am19psu

As you guys are alluding to, the server has an 80% chance of winning the point. Here is a link to the math of today's match.

Because a strong serve is what makes both of these players viable (at the expense of their weaker return game), it probably is more like 90%+ that they win their service games. In fact, I believe there were absolutely zero breaks during the 5th set, each player won their service. So it actually WAS Head, Tail, Head, Tail...Considering the first 2 sets didn't even go to the 6-6 tiebreaker, it is remarkable that both players were able to step up their game for the 5th, and neither tired to the point of a slippage during their service game. The French player double faulted a Deuce, but then won three straight points.

I'm not sure anything at this point is an advantage. There's an added preciseness of serving, increased speed of delivery and probably more pressure to put it in an exact point on the court, and when you consider how tired they should be by now....