Yes but a seemingly non-harmful operation such as averaging the branching factors at the _root_ instead of the nodes themselves gives very bad results. This does not add skeweness although I suspect even the regular nodes count will be a little skewed due to the possiblity of being log-normal (didn't test it yet).Michel wrote:Max and min are unfortunately extremely tricky functions to treat statistically. Even if X_1,...,X_n are uniformly distributed (and independent), the distribution of max(X_1,....,X_n) and min(X_1,....,X_n) will be very skew.If it was another operation such as maximizing, minimizing or a product then it wouldn't have worked.

I made the following test keeping everything inside the tree the same. The difference is which quantity I average : EBF or nodes count. In the EBF case , I determine the nodes count by raising to 13. And in the second case I do the opposite. You can see the EBF average gives different results and I don't think it will change with more games.

Code: Select all

```
perft 13
rounds 1000000
EBFAverage 24.2935 1.02652e+018
DirectAverage 25.5528 1.9802e+018
time 51.05 sec
```