Backgammon Galaxy has the advantage that one sees which player played better. When the opponent played better I accept that and analyse my errors. But it annoys me very much when the opponent played worse and still won. Every time this happens I raise the match length to avoid that. But that doesn't work at all. Here some match scores and the corresponding PR values:

2-9 ..... 9.69-13.95
6-11 ..... 9.17-13.61
4-13 ..... 8.4-19.56
10-15 ..... 5.7-16.69
15-17 ..... 6.85-10.2

(The list above is not complete. One additional match I won and one match I lost because the opponent played better.)

When I look at the list above I could cynically say I need to increase my PR value to win.

First question: Are there any tables, websites or free programs that tell me the probability that PR 6 loses against PR 17 in a 15 point match?

Second question: Any explanation why results like above happen so often (5 out of 7 matches)?

- Is raising the match length ineffective to reduce the probability to lose against a worse player?
- Is a match length of 17 still too short?
- Was it just a wagon load of bad luck?
- Any other explanation?

A match length of 17 is not that long, statistically speaking.

I suspect your data sample size is simply not large enough.

A player who often plays with a PR of 6, for example, will definitely have an edge and win a larger percentage of the matches against a player with a PR of say, 17, no matter what the length of the match is. And yes, as you know, the longer the match, the more time for your skill to show itself and a higher percentage of those matches you will win.

But the weaker player will still win many games and many matches. Over many hundreds of matches the percentages will reveal themselves. A few dozen matches? Not necessarily.

I don't know what your data sample size is, but I do suspect you're making conclusions too early.

OK, that motivates me not to give up but to continue and make the sample size larger. Thank you!

There are also some rolls that are just easier to make the right moves for, so you always have to factor in the luck number to really see how well you did against your opponent. Of course, the whole picture will only be evident over the course of hundreds of rolls, no matter over how many games they are played.