Number of remaining half moves

[BeyondCritics]

http://chess.stackexchange.com/question ... -of-chess/

[sje]

My reply, posted at that link:

Code: Select all

[] rg 10000000
   Checkmate  1527544 0.152754
  FiftyMoves  2241451 0.224145
Insufficient  5358614 0.535861
  Repetition   258221 0.0258221
   Stalemate   614170 0.061417
Average ply length: 342.064
Maximum ply length: 974

[hgm]

In my experience games on the average last 60 moves. Deduced from the fact that when I run test gauntlets from well-balanced initial positions at 40 moves/min, I get about 20 games per hour. This is with non-resigning engines.

[Ajedrecista]

Hello Oliver:

Interesting article so far. I did such calculations more than three years ago with CCRL games and the result from the starting position was a little more than 60 moves for not drawn games and more moves for drawn games. Here is the thread:

Average number of plies in {1-0, ½-½, 0-1}.

I suppose that CCRL has adjudication rules so there are few games with checkmate and maybe few games with insufficient material.

Regards from Spain.

Ajedrecista.

[tpetzke]

Hi,

I'm not a statistics expert but does the number of remaining half moves (thread title) not depend on the numbers of plys already played.

The chance that a game ends at ply 50 is at the 1st ply not the same as if it is already at ply 60 (obviously).

I don't see that covered by just looking how long games usually last.

Thomas...

[hgm]

The chance that a game ends at ply 50 is at the 1st ply not the same as if it is already at ply 60 (obviously).

The expected number of remaining moves can be the same in both cases, however. Although for Chess it probably is not. But for instance when hitchhiking, if you know from experience you will be offered a ride on average every 50 minutes, after you have been waiting for 30 minutes, you should still expect to stand there 50 more minutes. Not being offered a ride, no matter for how long, will not affect your probability to find one in the future. (Known as the paradox of the hitchiking hippy.) In some situations the passage of time can even increase the remaining waiting time.

[tpetzke]

I thought it might be comparable with the life expectancy (the table that the life insurers maintain). Here your age expectancy increases the older you are, because if you are already 45 chances that you will die from sudden infant death are 0.

[hgm]

That is not entirely true. What is true is that at age 2 you might have a longer average life expectancy than at age 0. But you will definitely have a longer life expectancy at age 0 than at age 45. Even when the toll of sudden-infant-death syndrome was as high as 30%.

But the basic message is indeed that it can go both ways, and that time elapsed does not necessarily have to be deducted 1:1 from expected remaining time, and sometimes even adds to it.

[PK]

perhaps it would be more interesting to calculate the expected number of moves as a function of (a) remaining material and (b) number of pawn rams. this might even be useful for time management of an engine.

[PK]

actually "sudden infant death syndrome" is an interesting analogy of an open game with many pieces having different move expectancy than semi-closed game after two minor-piece exchanges :p