Elo Increase per Doubling

[Don]

What is the conclusion of this discussion? Were the previous results of +160 elo or so per doubling down to the use of fast time controls which is not appropriate? In light of the advancement in hardware since 80s, isn't a 6sec per move not enough to match the long time control used at the time the +70 elo per doubling is reported ? Maybe the number of opponents with different style of play is not enough that made the results obtained similar to what could be found in a self test. I am just speculating but there must be a reason that can be pinned down..

I'm unsure of the conclusion. The tentative conclusion is that the maximum ELO is in the low to mid 4k range but ELO is a slippery dude and it will depend a lot on what assumptions you make.

If we can figure it out then it would be fun to run the test to a significantly deeper level.

Another, more practical question is: this is the maximum Elo at +Oo plies, so which depth would be necessary to be at, say, 50 Elo points from this theoretical maximum?

2nd question: if the computers' speed keeps doubling every 18 months, when will we reach this point of nearly perfect play?

It should be the case that as we get closer to perfect play it will be more or more difficult to make improvements. A projection I did indicated that at one move per day we may be withing 200 of PERFECT play. But adding an extra day of thinking would probably only give you a small improvement, wild guess just 5 or 10 ELO.

Another way to look at this is how likely it is that the move the computer wants to play is best. A top program searching for a few days is going to produce a playable move almost every time - but there will be one non-optimal move every few games where I don't know what "few" is.

[Daniel Shawul]

What is the conclusion of this discussion? Were the previous results of +160 elo or so per doubling down to the use of fast time controls which is not appropriate? In light of the advancement in hardware since 80s, isn't a 6sec per move not enough to match the long time control used at the time the +70 elo per doubling is reported ? Maybe the number of opponents with different style of play is not enough that made the results obtained similar to what could be found in a self test. I am just speculating but there must be a reason that can be pinned down..

I'm unsure of the conclusion. The tentative conclusion is that the maximum ELO is in the low to mid 4k range but ELO is a slippery dude and it will depend a lot on what assumptions you make.

If we can figure it out then it would be fun to run the test to a significantly deeper level.

I am not sure of what the significance of that number is. Obviously elo is not bounded if you use the elo model that relates elo difference with winning percentage 400 * log ( w / (1 - w) ). If you win 100% your elo is infinity. It seems that what you obtained is a fit for your data and an extrapolation for a certain degree of confidence. Clearly over-fitting and similar problems give you very different results (eg the first extrapolation of 10000 elo as max). Why not use the standard elo model as I gave above instead and calculate elo diffences for a give CI and add it to the elo base 1500 f.i.
Anyway I thought that was an aside discussion. I am more interested in what can be concluded (learned) about from the contrasting results.

[Adam Hair]

Here are my results for Elo per node doubling, where Level 0 = 512 nodes and Level 12 = 2097152 nodes:

Code: Select all

Level	Elo
0	1500 (at Level 0, Gaviota and Komodo are roughly equal)
1	1604
2	1790
3	1979
4	2127
5	2269
6	2406
7	2540
8	2668
9	2787
10	2891
11	3005
12	3099

Using Peter's model, I get the following equation:
1465.36 + 3703.38*(1-e^(-X/20.50))

The asymtote is 5168.74 Elo

The best fit to my data (restricted to 3 parameters) is the following Gompertz function:

4041.10*e^(-e^(0.0078-0.11*X)), which has an asymtote of 4041.10.

For completeness sake, here is my Bayeselo output (commands used were 'mm 0 1' and 'covariance'):

Code: Select all

Rank Name         Elo    +    - games score oppo. draws 
   1 Gaviota_12  3099   23   23  2400   93%  2297    9% 
   2 Gaviota_11  3005   21   21  2400   89%  2305   13% 
   3 Gaviota_10  2891   17   17  3412   85%  2271   13% 
   4 Gaviota_09  2787   16   16  3413   79%  2280   13% 
   5 Gaviota_08  2668   15   15  3413   71%  2291   13% 
   6 Gaviota_07  2540   15   15  3413   62%  2302   12% 
   7 Gaviota_06  2406   15   15  3414   53%  2314   11% 
   8 Gaviota_05  2269   15   15  3414   45%  2325   10% 
   9 Gaviota_04  2127   16   16  3413   36%  2338   10% 
  10 Gaviota_03  1979   17   17  3413   28%  2351    7% 
  11 Gaviota_02  1790   20   20  3413   18%  2368    6% 
  12 Gaviota_01  1604   23   23  3413    9%  2385    4% 
  13 Gaviota_00  1500   26   26  3413    6%  2394    3% 

I have not checked, but 3100 Elo for 2 million nodes per move for Gaviota may be high.

Finally, I just want to say that cutechess-cli rocks!