### Logarithmic Patterns In Evaluations

Posted:

**Sat Dec 09, 2017 6:05 pm**Middle game bonuses sometimes follow a linear pattern, and endgame values follow a logarithmic pattern. These patterns can be used to generate mg/eg tables with appropriate formulae. Texel's tuning method can be used to fine-tune the coefficients. My research engine demonstrated a definite strength increase.

For example, knight mobility values can be generated:

where x = the number of escape squares that a knight can move to. If x = 0 then the knight is trapped. The results are:

knm_mg(8) = { -29,-22,-16,-9,-2, 4, 11, 17, 24 }

knm_eg(8) = { -50,-44,-27,-17,-9,-4, 1, 4, 8 }

knm_eg(0) = -50, arbitrarily because ln(0) has no solution.

The first coefficient is an accurate description of the shape and proportion, but the second coefficient may have to be intuitively altered to make sense with existing known evaluations of positions. That problem may be more of an aberration of my version of Texel's tuning method which overall seems to generate extreme values that are often larger than might be expected. Further, it adds extra variation to all the other tuning values, which never seems to stabilize. Has anyone have any suggestions on how to get tuning values to "stabilize"? Those who have tried Texel's tuning method should understand what this means. To a degree, one simply has to trust the tuning method.

Good luck if you try this.

For example, knight mobility values can be generated:

Code: Select all

```
mg(x) = 6.6 x - 28.86 linear
eg(x) = 24.76 ln(x) - 43.82 logarithmic
```

knm_mg(8) = { -29,-22,-16,-9,-2, 4, 11, 17, 24 }

knm_eg(8) = { -50,-44,-27,-17,-9,-4, 1, 4, 8 }

knm_eg(0) = -50, arbitrarily because ln(0) has no solution.

The first coefficient is an accurate description of the shape and proportion, but the second coefficient may have to be intuitively altered to make sense with existing known evaluations of positions. That problem may be more of an aberration of my version of Texel's tuning method which overall seems to generate extreme values that are often larger than might be expected. Further, it adds extra variation to all the other tuning values, which never seems to stabilize. Has anyone have any suggestions on how to get tuning values to "stabilize"? Those who have tried Texel's tuning method should understand what this means. To a degree, one simply has to trust the tuning method.

Good luck if you try this.