idea to estimate the percentage of drawn positions in chess

[Uri Blass]

I wonder if there is an estimate for the percentage of drawn positions in chess.

My idea of getting an estimate.

Take 1000 random positions from games and let an engine to play against itself every position.
Divide the number of draws by 10 and you get an estimate for the % of the draws.

Now the question is if the estimate is going to get bigger or smaller when you use longer time control or stronger engines.

You can do the same also to estimate the percentage of drawn positions in perft(n) after n plies.

[fkarger]

I think we have to distinguish at least two meanings of "percentage of drawn positions in chess".

1) Percentage after 'normal' play from the starting position
2) Percentage after any kind of play from the starting position

Maybe the following procedure is worth considering:

Case 1: Percentage after 'normal' play from the starting position
1.1 Map SF evaluations to winning percentage (at a fixed (shallow) depth of SF)
1.2 Take all positions from a human master database (for having a decent quality)
1.3 Calculate the mean winning percentage of these positions using 1.1

Case 2: Percentage after any kind of play from the starting position
2.1 Create a database by random play from the starting position
2.2 Do the same procedure like in Case 1 but replace the human master database by the database of 2.1

Best regards

Frank

[Brunetti]

I wonder if there is an estimate for the percentage of drawn positions in chess.

Hello,
we don't know which positions are drawn, except the extremely microscopic portion included in tablebases. So you can't calc what you're asking

Alex

[Uri Blass]

I wonder if there is an estimate for the percentage of drawn positions in chess.

Hello,
we don't know which positions are drawn, except the extremely microscopic portion included in tablebases. So you can't calc what you're asking

Alex

We do not know but can get an estimate based on results of the engine against itself or based on evaluation of positions.

[Uri Blass]

I think we have to distinguish at least two meanings of "percentage of drawn positions in chess".

1) Percentage after 'normal' play from the starting position
2) Percentage after any kind of play from the starting position

Maybe the following procedure is worth considering:

Case 1: Percentage after 'normal' play from the starting position
1.1 Map SF evaluations to winning percentage (at a fixed (shallow) depth of SF)
1.2 Take all positions from a human master database (for having a decent quality)
1.3 Calculate the mean winning percentage of these positions using 1.1

Case 2: Percentage after any kind of play from the starting position
2.1 Create a database by random play from the starting position
2.2 Do the same procedure like in Case 1 but replace the human master database by the database of 2.1

Best regards

Frank

The question is if evaluation at a fixed shallow depth is a good estimate.

It is possible to test it based on games that I expect to give a better estimate.

[Brunetti]

We do not know but can get an estimate based on results of the engine against itself or based on evaluation of positions.

Ok, so what is "drawn"? Score between which values, calculated at which depth, by what engine/s? You should define everything, you can't just ask a percentage
Anyway, considering all legal positions 10^40 or what, I think it's around 1 billionth or so.

Alex

[fkarger]

I think we have to distinguish at least two meanings of "percentage of drawn positions in chess".

1) Percentage after 'normal' play from the starting position
2) Percentage after any kind of play from the starting position

Maybe the following procedure is worth considering:

Case 1: Percentage after 'normal' play from the starting position
1.1 Map SF evaluations to winning percentage (at a fixed (shallow) depth of SF)
1.2 Take all positions from a human master database (for having a decent quality)
1.3 Calculate the mean winning percentage of these positions using 1.1

Case 2: Percentage after any kind of play from the starting position
2.1 Create a database by random play from the starting position
2.2 Do the same procedure like in Case 1 but replace the human master database by the database of 2.1

Best regards

Frank

The question is if evaluation at a fixed shallow depth is a good estimate.

It is possible to test it based on games that I expect to give a better estimate.

Sure. Games or higher depth could give a better estimate because we can assume
that higher depth means 'closer to the truth'.

On the other hand there could be an interesting phenomenom called 'Wisdom of the crowd':
If the estimation error of SFs evaluations is distributed in a way (e.g. symmetric) that errors cancel out
each other, than even a shallow depth could lead to a very precise estimation.

[towforce]

We're only looking for an estimate here - not the exact proportion. I'm not going to do this, but if I were, I would do it as follows:

1. My basis: the game is drawn until a bad move is made

2. Find a statistical distribution that is a good model for how long games last - adjustable for the Elo rating of the two players

3. Find a statistical distribution that is a good model for the Elo distribution of all players of interest (you can include or exclude human players - your choice)

4. Find a statistical distribution for the likelihood of a bad move being made based on a player's Elo rating and on move number in the game (the higher the move number, the more likely a player is to make a bad move)*

5. Skilfully combine the above distributions to come up with an estimate of the percentage of positions which are drawn


*if I were writing a program to attempt to beat a top engine, I would have it play for complex positions. This would throttle off both the opposing engine's ability to recognise sufficiently useful patterns, and it would throttle off its search depth. If I could manage this, this would break the basis of step 4 above.

[petero2]

Anyway, considering all legal positions 10^40 or what, I think it's around 1 billionth or so.

I extracted the legal positions from https://raw.githubusercontent.com/tromp ... .out.95544, shuffled them and analyzed them one at a time. The 22nd position I analyzed was this:
[d]3B1k2/Q2nRN2/n3RPr1/2n2npB/1bnn2P1/1R1ppB1p/2bPN1r1/5K2 w - - 0 2

This could be a draw, although it is probably difficult to prove. Even if it is not a draw, the fact that I found a position like this after looking at only 22 random positions makes me think that far more than one in a billion random positions are drawn.

[fkarger]

Crazy position. Indeed it could be difficult to prove it is a draw.

He (Brunetti) wrote about a 'billionth' not a billion.