I can't verify your script, but the probability I can walk you through.
First off, these are for each point, as you say; you need ten points to win, and there are obviously ten ways to get ten points.
10 - 0, 10 - 1, etc.
I'm assuming here that the ties give neither player a point (it has been a while since I played this battler, so I may be wrong), which makes life easier, I think.
what you have to look at is this:
to get two points, the probability (in the first round) is 0.5
AND 0.5, as you want both points. So, you have half a chance, of half a chance, and we multiply: To get the first two points, your probability is 0.5 * 0.5 = 0.25, or 25%
Doing this 10 times, gives you 0.5
10, which is
1/
1024(this is only for the 10 - 0 win though). Then you work out the probability of getting ten points, but giving away 1; this would simply be the same result as above, but multiplied by 0.25, so
1/
4096. You do this repeatedly, until you have the probabilities for all the wins 10 - 0 through to 10 - 9
Now, you can win with any of these results, so you can win with 10 - 0
OR 10 -1
OR 10 - 2, etc, so you add the probabilities together.
Assuming I've done this right (I may be wrong, it has been a while since I did probabilities), this gives you a probability of winning the first round (without any ties at all) of approximately
2289662/
1758462093 or 0.00130208209157
This does seem wrong, though, 'cause that's rather a small chance....
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