Q. What do you call it?

[David Weller]

There is one of many 'phenomena' that I have observed in computer chess, which I have 'called' 'parabolic terms' and am certain there is a better term, and that parabolic, is not even close. Here it is:

we all know, that a knight in the corner is generally bad and that a knight in the extended center is good. But the difference between a knight in the center and a knight in the extended center is far smaller than the difference between the rim and one-square-in-from-the-rim.

another example: mobility

It is far worse for a piece to go from 1 or 2 available moves down to 0 than it is to go from say 8 moves to 6

so what do you call this kind of curve? reciprical? eliptical?

[Dan Honeycutt]

so what do you call this kind of curve? reciprical? eliptical?

Hi David:

The general term is simply non-linear. Say 2 isolated pawns are more than twice as bad as one so you can't score it with a linear formula (number of isolated pawns times penalty each). You may be able to find a non-linear formula to give you what you want (ie penalty times number of pawns squared) but in most cases I think it is easiest to simply have a table.

Dan H.

[David Weller]

Heh, that was too easy!

but i wanted to differentiate the non-linear types of terms

some terms seem to be 'exponential' in that they just keep getting higher faster. Others get higher, but at a progressively slower rate..

One example of this is that i believe 2 rivets [in construction] are only about 60% stronger than 1

but in your example, you are saying that 2 isolated pawns are more than twice one.

both are non-linear but clearly they are different. one is 'more' than linear the other 'less'

But thanks for the heads-up about isolated pawns, I was just scoring them at about 30 centipawns each.

I guess if you make tables and tune them well, there is no need for the semantics [?] but I thought it might be interesting to someone, if they didnt already know these distinctions existed among their eval terms.

[Tord Romstad]

Heh, that was too easy!

but i wanted to differentiate the non-linear types of terms

some terms seem to be 'exponential' in that they just keep getting higher faster. Others get higher, but at a progressively slower rate..

For continuous functions, the terms 'convex function' and 'concave function' are sometimes used. A convex function is a function which 'bends upward', i.e. a function which has a positive second derivative. Similarly, a concave function is one for which the graph 'bends downward'.

A generalization to functions of several variables is the following: A multi-variable function is convex if the straight line segment between two points on the graph is always above the graph, while it is concave if the line segment is always below the graph.

I haven't heard any similar terms for discrete sequences, which is really what we are talking about in the context of chess programming.

Tord

[Dan Honeycutt]

some terms seem to be 'exponential' in that they just keep getting higher faster. Others get higher, but at a progressively slower rate..

Those are both exponential, the latter characteristic of cases where rate of change is proportional to value. Ie the rate of change of the temperature of the water in your ice cube trays is proportional to the difference in temperature between the water and the freezer. Newton's law of cooling if memory serves.

There is the classic S shaped curve which is apt for king safety. You want a function that rises slowly for few threats/defects, then rises rapidly as threats mount, then levels off again so the program doesn't do stupid things like give away pieces because its king is in danger.

You may need to invest in a math text if you want to properly name all the shapes. I just leave it at non-linear.

Best
Dan H.

[David Weller]

alright, thanks guys.


So then terms can be basically, linear, 'concave-s', or 'convex-s'?

Because I imagine most will have that 's' feature. yes/no ?

[Uri Blass]

so what do you call this kind of curve? reciprical? eliptical?

Hi David:

The general term is simply non-linear. Say 2 isolated pawns are more than twice as bad as one so you can't score it with a linear formula (number of isolated pawns times penalty each). You may be able to find a non-linear formula to give you what you want (ie penalty times number of pawns squared) but in most cases I think it is easiest to simply have a table.

Dan H.

Hi Dan,

The question if 2 isolated pawns are more than twice as bad as one isolated pawn may be dependent in your other evaluation terms.

The weakness of having many weaknesses may be evaluated by other evaluation terms(for example by mobility evaluation or by evaluating pawns that are attacked by the opponent and not only isolated pawns).

Uri

[Dan Honeycutt]

The question if 2 isolated pawns are more than twice as bad as one isolated pawn may be dependent in your other evaluation terms.

Perhaps my example was bad, though for static pawn evaluation I give 2 isolated pawns a higher penalty than twice 1 isolated pawn. My evaluation is pretty basic and I don't yet look at attacks on the isolated pawns or other factors to determine how weak they really are.

Dan H.