Ok...let's assume you're the world's greatest breaker. When you break you do not lose. And when you don't break you only win 50% of the time.
Would it matter whether it was winner break or alternate break?
To BJTyler’s point, I put some simple numbers together that hopefully will be clear. You have a 60% chance of winning the game when you break, and your opponent has a 50% chance of winning when he breaks. You play 3 games. Here are probabilities under different conditions:
Winner breaks, you win the lag:
You win 3 games = .6* .6 * .6 = .216
You win 2 games = (.6 * .6 * .4) + (.6 * .4 * .5) + (.4 * .5 * .6) = .144 + .12 + .12 = .384
You win 1 game = (.6 * .4 * .5) + (.4 * .5 * .4) + (.4 * .5 * .5) = .12 + .08 + .1 = .30
You win 0 games = .4 * .5 * .5 = .1
Overall chance you win 2/3 games or better to win the match: .216 + .384 = .60
Winner breaks, you lose the lag:
You win 3 games = .5 * .6 * .6 = .18
You win 2 games = (.5 * .6 * .4) + (.5 * .4 * .5) + (.5 * .5 * .6) = .12 + .1 + .15 = .37
You win 1 game = (.5 * .4 * .5) + (.5 * .5 * .4) + (.5 * .5 * .5) = .1 + .1 + .125 = .325
You win 0 games = .5 * .5 * .5 = .125
Overall chance you win 2/3 games or better to win the match: .18 + .37 = .55
Alt breaks, you win the lag
You win 3 games = .6 * .5 * .6 = .18
You win 2 games = (.6 * .5 * .4) + (.6 * .5 * .6) + (.4 * .5 * .6) = .12 + .18 + .12 = .42
You win 1 game = (.6 * .5 * .4) + (.4 * .5 * .4) + (.4 * .5 * .6) = .12 + .08 + .12 = .32
You win 0 games = .4 * .5 * .4 = .08
Overall chance you win 2/3 games or better to win the match: .18 + .42 = .60
Alt breaks, you lose the lag
You win 3 games = .5 * .6 * .5 = .15
You win 2 games = (.5 * .6 * .5) + (.5 * .4 * .5) + (.5 * .6 * .5) = .15 + .1 + .15 = .40
You win 1 game = (.5 * .4 * .5) + (.5 * .6 * .5) + (.5 * .4 * .5) = .1 + .15 + .1 = .35
You win 0 games = .5 * .4 * .5 = .1
Overall chance you win 2/3 games or better to win the match: .15 + .40 = .55
Here’s the point:
Winner breaks vs. alternate break doesn’t change the probabilities at all. What’s interesting to me is how much it matters whether you win the lag. But the lag advantage is exactly the same whether it’s winner breaks or alternate break.
That’s just for three games, and the lag would begin to have less of an effect when you extend the race, but (I think) winner breaks vs. alternate break should continue to be exactly equal for any length race.