# Ping Pong First Serve Theory

#### ldv1452

There is a very intense debate on another forum (a poker site actually) on whether or not there is any advantage to serving first in table tennis (premise is that the server is more likely to win the point). There have been many good responses, but this deserves the attention of a probability expert.

Serving first in Table Tennis - Science, Math and Philosophy Forum

The first page will give the initial scenario. Later pages offer simpler scenarios to illustrate the point. Feel free to use either scenario to illustrate the answer to this very active debate.

Any insight would be greatly appreciated.

#### matheagle

MHF Hall of Honor
It's not that hard to compute the probability either wins by any possible score.

Player one can win 11-0 by the probability $$\displaystyle p^6(1-p)^5$$
where p is the probability that the server wins.

Then it gets a bit more complicated when it's 11-1, but I'm sure Sorobanned would have fun with that.
You have two choices of when that one point was won by player 2.
But that's not too rough.