Ply versus ELO

[fourthirty]

BillT's "Star Diamond ...(Monster)" post and Fern's reply got me thinking about the correlation of ply depth versus ELO.

I found the below paper published by Diogo Ferreira in the ICGA journal back in 2013, where he attempts to build a relationship between search depth and playing strength:

https://www.semanticscholar.org/paper/T ... a5f0f58666

https://pdfs.semanticscholar.org/047f/6 ... f58666.pdf

Unfortunately the study is limited between six (6) and twenty (20) ply. I would be very curious to see the results all the way down to one (1) ply!

The estimated strength of Houdini 1.5a 64-bit at 20 ply was 2894, and decreased to 1966 at 6 ply. I copy and pasted the ELO data into Excel to generate a graph - and the ELO decrease appears to be linear throughout the entire range.

On the lower end of the ply scale not covered in this study, it would be interesting to pit a mid-range dedicated computer playing at full strength versus a strong computer (2000+) playing at limited ply depths (starting at 1 and increasing), to see the results.

On the lower end of the ply range, would this be a true test of the dedicate's evaluation function (where processor speed and search algorithms are no longer relevant)?

What is the estimated ELO of a chess computer playing the "perfect" move at one ply depth? Is it above or below 1000?

I may try this experiment if I have time this summer.

Ply regards,
Greg

[Irrawang]

Wouldn’t other factors such capture and check extensions be involved? Also the amount of knowledge applied to the first ply.

[TracySMiller]

I found the below paper published by Diogo Ferreira in the ICGA journal back in 2013, where he attempts to build a relationship between search depth and playing strength:

https://www.semanticscholar.org/paper/T ... a5f0f58666

https://pdfs.semanticscholar.org/047f/6 ... f58666.pdf

Unfortunately the study is limited between six (6) and twenty (20) ply. I would be very curious to see the results all the way down to one (1) ply!

The estimated strength of Houdini 1.5a 64-bit at 20 ply was 2894, and decreased to 1966 at 6 ply. I copy and pasted the ELO data into Excel to generate a graph - and the ELO decrease appears to be linear throughout the entire range.

Very nice study. About 66 ELO points per ply.

[BillT]

Hi Greg
Im glad you've picked up on this topic. It sounds like you are going to go into it a lot more deeply than i would and look forward with interest to your findings.
For my part what intrigues me is that by setting my SD to 1ply with PB off all the games should be really pointless because as i see it all that SD should be calculating is its own move with no thought at all of my counter move....so really any legal move.. it could move its queen for example to a square where it can be taken without compensation without realising it ---as it will not calculate any further than its own move. Therefore even pretty low rate players like myself should get bored just taking cheaply given material and winning with simple mate in 1's.....well I really dont think that is the case.....level 2 ply should also be very straight forward for a relatively weak player......not the case.
I just wonder if the level settings are really correct or there is some sort of routine built into the program to override the ply setting sometimes...like if theres a positive tactical line to follow (which would negate the point of setting it to a specific ply ).I know nothing of programming but im fairly sure that in some of my games on 2 ply or even 3 ply there are times where the tactical line must have been deeper than the stated level of ply.
Perhaps it would be different with other brands/programmers etc, maybe someone who is a better player than I could give a game to an SD on 2ply level and give an assessment ----that is of course if theres anybody else here that still has a working SD....they seem a bit prone to problems with the sensor board.
I think i have the PGN of some games to illustrate this but I have no idea how to upload them to this board.

Bill

[mclane]

They maybe have 1 ply + extensions

[donkeylane]

Interesting topic, looking at a response from Capablanca, when asked how many moves he looked ahead, his reply was 'only one, but the best one'. Similarly, I have also seen Kasparov, when asked the same question reply'I just try to find the best move', as in move singular. The human mind is a natural pattern maker, just that some are more proficient at it than others, slightly off subject, I am a keen astronomer, I know from experience people generally speaking are baffled about what they are looking at in the night sky, it takes little familiarity with the night sky to recognise the patterns of the seasons and in no time at all those patterns stay with you, and the night sky becomes very easy to navigate whatever the season. I am not saying chess is a very easy game, it isn't, but patterns apply there I believe as well. That being said, I am aware now that the days of GMs beating the top engines are over, the sheer computational power is overwhelming, reading about the optimum values for playing strength on an engine, the advice I read was hash tables and threads, the threads should match the cores of the cpu being used. And when it comes to the most critical aspect of the strength of a program, Tord Romstad, of Stockfish, said the most important aspect of a programs playing strength is not the quality of it's best moves, or it's average moves, but the quality of it's worst moves. Steve C.

[paulwise3]

On the lower end of the ply range, would this be a true test of the dedicate's evaluation function (where processor speed and search algorithms are no longer relevant)?

What is the estimated ELO of a chess computer playing the "perfect" move at one ply depth? Is it above or below 1000?

Hi Greg,

Thanx for bringing this subject!
Of course computing more plies brings more elo, but the quality of the position evaluation function is also very important.

When judging a move at one ply depth, one needs a good definition of a one ply computation.
For instance when giving check in one ply, can the evaluation function determine if it is checkmate or not? I think not. If it does, then it is in fact already looking ahead another ply to see if the check can be defended.
But general aspects like pawn structure, development of pieces and influence at vital places on the board can be done.
And talking about attacking tables: when I tried to make a chess program, I also designed a scheme (never implemented) to statically determine attackers and defenders (and in which order) for every field on the board, so it was more or less possible to statically determine which threats (Edit: I mean threats for winning or losing material) are real and which not. Never fault-free of course, but helps a lot in many cases

I am looking forward to see your testing results!

Regards, Paul
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