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Here are the numbers for each case

I wonder if are misunderstanding this a little?

Yes, the win chance stopping at 3 is better than the win chance of stopping at 4. But when you have 3, you don't know for certain that you will be stopping at 4. So the win probs when you have 3 points look like this:

lose next point = 1 in 3.69 (27.07%)

win next point = 1 in 2.99 (33.41%)

So it is not better to stop at 3 unless you know that the 6 is likely to seat you. (Hello Douglas, Arregui, Aritz, Goiko, Bolivar, et al, depending on era and fronton)

Now, here are the cases for all the stopping points for posts 1 or 2, including cases where the key post is dominant at a 60% point-winning rate.

stop at 50% 60%
----------------------
3 3.69 2.69
4 4.09 2.96
5 2.42 2.05
6 2.67 2.26
7 ask ron d



I think we all know that for any of the posts, in the first round, stopping at an even score does not get you any closer to winning than if you had stopped at odd, but does push you one position back in the lineup. These figures reflect that.

One other thing which I find interesting about this.

If all the posts were approx equal strength, then when 1 or 2 stops at 3, at that exact moment, the post position advantage for the other low posts is gone. assuming 1 is our key, let's look at 2-3-4 vs 5-6-7.

2 - 9.35 5 - 7.27
3 - 10.02 6 - 10.09
4 - 11.77 7 - 11.79

or the whole list

1 3.69
2 9.35
3 10.02
4 11.77
5 7.27
6 10.09
7 11.79
8 8.62


That is the impact of the low posts not winning their first point, and is something I had never considered, FWIW.

















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