Ok. I had a little time and decided to actually simulate it. Obviously this is using math only and assuming that the chance of winning doesn't change based on psychology, fatigue, "hot hand" effect, etc.
https://go.dev/play/p/gtA_WdyXWu5
If you want to run some simulations, just press the run button and it will spit out results. You can adjust the variables of the program; some notes about that:
1. The lag advantage statistics are only valid when the simulation is run with the default lag chance of 0.5 (coin flip). I might some day calculate this in a different way
2. If you adjust the variables and the program completes without producing output, that means you're running too many simulations and the Go playground is shutting it off early. Dial back the number of simulations. The default of 20,000 is a lot already.
Some observations:
- When looking at only match wins, format between winner break, alternate break, and loser break is produces THE SAME RESULTS regardless of how unequal the opponents are and how long the race is.
- As pointed out above, the longer the race, the more likely the better player is to win in the end.
- Although the match win % is the same, alternate break results in closer overall scores, and loser break creates the closest overall scores.
- Winning the lag has a significant impact improving the underdog's chances of winning the match by somewhere around 15%. for a race to 10 with the better player winning the match at ~70/30 clip.