To test this I created a very simple pgn file consisting of just 2 games. One where player A wins with white and one where player B wins with white (edit: this is just an extreme example case - but the problem happens for all possible sample sizes).

I then called Ordo as follows:

Code: Select all

```
ordo -N 0 -s 10000 -q -U "0,1,2,3,4,5,6,7,8,9,10" -w 50 -u 1 test.pgn
# PLAYER : RATING ERROR POINTS PLAYED (%) CFS(%) W D L D(%)
1 A : 2300 145 1.0 2 50.0 50 1 0 1 0.0
2 B : 2300 145 1.0 2 50.0 --- 1 0 1 0.0
White advantage = 50.01 +/- 0.01
Draw rate (equal opponents) = 50.00 % +/- 0.00
```

But, as you can see the prior standard deviation for the white advantage is 1.0 while the posterior standard deviation is 0.01.

I went one step further and calculated the posterior standard deviation for many values in the interval [0, 80] and this is the result:

Is this a bug? If this is known already, let me know.