New testing thread

[MartinBryant]

Forgot to mention...
I repeated the Fruit experiment with Spike and Colossus too.
Again no duplicates in 100 games.

When you say no duplicate you mean that no 2 games are the same or maybe you mean that the first game did not repeat.

Note that both options are different.

Uri

Yes I mean no duplicates at all, no 2 games are the same (well according to SCID anyway!).

[krazyken]

Forgot to mention...
I repeated the Fruit experiment with Spike and Colossus too.
Again no duplicates in 100 games.

I somehow missed this experiment, what were the conditions it was run under? Same starting position?

Yes.
The normal starting position for a game of chess.

Then 100 different games is not surprising to me. If you did the 100 games from one of the silver positions, I'd expect the number of duplicates to be greater.

Why? they are opening positions as well, and starting at the initial position, you may well encounter one of those along the way any and things should stabilize there if that is your belief. The variation occurs in any position that is either very balanced, or if it is not, where there are multiple nearly equal alternatives at some point (or multiple points) in the game as it progresses. Those are the positions where things will change. And this happens in the SIlver positions quite frequently, as remember those are the positions I have been using to produce all this volatile behavior.

It would seem to me that after going several moves down an opening line the number of equally viable alternatives would diminish the further you go. Also, Openings are frequently handled by special code and evaluations as compared to he rest of the game are they not? By starting further in to the game you are reducing the amount this code effects the outcome of the game. So the further you go into the game you should see less variability in repeated experiments.

Bob, could you provide a single Silver position at random and I will happily re-run the test for interest.

If you let me know the conditions you are testing under, I can also run a parallel test here.

what he had said previously was .5 seconds per move, from the opening position. Or in this case, from a position that is still in the opening part of the game, but not the starting position. Fruit vs Fruit. Or X vs X for that matter.

I might be stuck there, none of my GUI choices seem to allow a time per move mode for engine matches. Except Xboard which doesn't seem to have granularity below one second.

[hgm]

The programs are _hardly_ close together in strength, if you'd just look at the results. A relative rating difference of 300 top to bottom is quite a spread...

But there is no difference of 300, as the 4 full round-robins you did clearly show. Glaurung is about +75, Arasan about -50. That is only 125. With fewer games you have the larger statistical error quoted by BayesElo, which is again augmented by the fact that the 'World' plays only a single opponent in the Crafty vs World match. This causes the larger spread there. But it is pure coincidence, with another engine then Arasan as weakest one you might get the exact opposite.

Let me refresh your memory just a tad:

Code: Select all

760 game(s) loaded, 0 game(s) with unknown result ignored.
Rank Name                   Elo    +    - games score oppo. draws
   1 Glaurung 2-epsilon/5   115   44   42   153   69%   -31   17%
   2 Fruit 2.1               64   42   41   149   63%   -31   18%
   3 Glaurung 1.1 SMP        48   42   41   152   61%   -31   16%
   4 opponent-21.7           20   38   37   152   58%   -31   41%
   5 Crafty-22.2            -31   19   19   760   45%     6   22%
   6 Arasan 10.0           -216   43   45   154   26%   -31   16% 

There I see a range of +115 to -216. Last time I looked that was a range of over 300. Don't know what your problem is, but mine is neither math nor memory.

No, your problem is not reading what I write, or not understanding what you read: You are showing the result of the Crafty vs World games here. My remark you comment on, however, very explicitly stated that 'ratings' BayesElo coughs up for this test do not represent the playing strengths of the programs involved, but mainly statistical + systematical error, due to the use of too few games, and only single opponents. As the sum of all round-robins (with 3200 games and 5 opponents in stead of 160 games and 1 opponent clearly show).

Get it now? Or will we have go through it 5 more times before it seeps through your thick skull, so that you can take the opportunity to piggy-back a few more out-of-place smart-ass remarks on it? Let me spell it out for you then: You don't know what my problem is, because there was no problem other than that you apparenty did not understand what I wrote. While I would have thought that "4 round-robins" does leave very little ambiguity.

And goof's like that do contribute to the general stupidity level of this discussion infinitely more that the occasional smiley...

Never seen such a thing reported anywhere I read. I have seen programs excluded because they crash, or they play illegal moves, or they refuse to accept certain types of illegal moves like under-promotions, or... But not because they just lose an odd game here and there for no reason.

We are not talking about losing "an odd game here and there". That is normal statistical fluctuation. We are talking about things like a 6-sigma deviation, and usually that requires a lot more then "an odd game here and there". Unless, perhaps, you lose 5 games in a row against Chad's Chess, and then win the next 5 games against Fruit. I am pretty sure almost any tester would immediately throw out a program that pulled such a stunt, because such a program would completely corrupt their entire rating list. But if you have doubts about it, perhaps you should ask them.

In any case they are doing more than you think. OliThink was recently removed from the CCRL for no other reasons than that it did inexpliquable bad moves in the end-game, occasionally. No crashes, no illegal moves, no refusal of moves, no time forfeits, no sign of any trouble other than that the testers did not like the moves it played.

Please. "that cannot be the explanation" just won't cut it. You said you don't do partial iterations.

Hellowwwwwwwwwwwwwww... Fifth time: I do not do partial iterations in micro-Max. Joker does partial iterations if time is running out and it has a move not much lower in scre than the previous iteration.

I do. Clearly I can terminate the search after any number of nodes. You have discrete points where you can terminate the search.

Also not true (as said many times before...). Joker can abort a search at any stage (not just in the root) if it runs into the third, never-exceed time limit. A difference with Crafty might be that I set that limit is rather generous, so it does not happen too often. Which dos not really proof nything about the playing strength: usually time spent searching when there is trouble near the horizon is spent more usefully than it could be spent anywhere else.

If you terminate in mid-iteration then you will have this kind of non-uniform behavior, unless your search and evaluation are so basic that minor changes in the nodes is not enough to change the shape of the tree, or you are not carrying hash from move to move as most do, or something along those lines. It would be pretty easy to get rid of this effect. By first clearing the hash after each move. But I'm not willing to give up the performance that costs...

Plus it would create the problem that it would make accurate testing more difficult unless you would find another way to randomize the engne moves.

Actually I did have an idea, but no measurements made over the last 10 years. We were the first to do this approach in the old Blitz program, back when we wrote the original "using time wisely" paper in early in the ICCA journal series. And we did a lot of testing, even way back then, to compare old and new. We only had a few opponents we could automate test with, but we did it. Whether you believe it is better or worse is not an issue, believe what you want. But then wonder why almost everyone else _is_ doing it this way, and you might come to a startling conclusion...

Again, many words, but no number. Much talk, and no substance. As usual.

But, fortunately, I could calculate a theoretical estimate for this number, which came to ~7 Elo. Wow, big deal. No wonder that engines that do that are all at the very botom of the rating list...

I'm not impressed with numbers pulled out of that particular bodily orifice. You can't even _measure_ a change that small so there's no point in discussing such, unless we move this to computer chess fiction or something.

Ah, and there we hit the root cause of your problem. You seem to be completely incapable of embedding your empirical observations into a theoretical framework, dismissing mathematics as a valid scientific tool. Be it for a simple calculation of standard devations from a sampling procedure, or scaling laws of Elo vs time control. Thereby reducing what could have been useful science to the proverbial 'stamp collection'.

I don't have to measure differences that small, as it does not take a genius to see that if the strength of my engines varies to a high degree of accurracy by 70 Elo (a difference which I can measure very easily) for each factor 2 of thinking time, that it will increase by 1 Elo for every percent I increase that thinking time.

That such simple, elementary calculations do not impress anyone stands to reason. But that you dismiss them as crap says an awfull lot on your ability to do serious and fruitful science. "It is impossible to measure the distance to the Sun, because you could never go there with a ruler. Triangulation therefore is crap that doesn't impress me. Welcome to the Stone age."

Well, as I said, good for them. But not of any practical importance, as the randomization is trivial to program.

And of no beneficial value, since we want to play the _best_ move possible in every situation, unless you get into playing weaker players where the Crafty "skill command" can certainly introduce randomness. But not in any games I want to observe and analyze.

This is a very debatable statement, but perhaps a bit off-topic in the current thread. For one, apparently Crafty cannot tell what the _best_ move is with any degree of certainty, as it changes its opinion on this so fast that even a few milliseconds of time jitter make it regularly change its move. Not all these moves can be _best_ moves. In the second place, randomness in the evaluation can be used as a poor-man's mobility evaluation, which has been proven to strongly improve play of a random mover (that did not have any oher evaluation terms at all, not even material). So there are uncontested counter examples, where randomnes actually improves playing strength. Randomness, when implemented this way, can be used to mimic mobility evaluation, and as mobility evaluation is generally considered very benificial for playing strength. So it seems to me you are on rather thin ice here. But perhaps you can show us proof? Or are your statements concerning this matter pulled out of the same bodily orifice as you so much like to refer to?

[hgm]

I might be stuck there, none of my GUI choices seem to allow a time per move mode for engine matches. Except Xboard which doesn't seem to have granularity below one second.

You can achieve smaller granularity by specifying a time-odds factor for both engines, and playing with "-timeOddsMode 0", so that the times are not normalized to that of the slowest engine. So with

-st 1 -firstTimeOdds 100 -secondTimeOdds 100 -timeOddsMode 0

you would effcively have centi-second resolution.

[hgm]

Using the node count instead of time would mean you're not testing the time management code, right? I guess you'd then have to test that separately, which is really starting to make the testing complex.

This would not be true if you use the node-based time-control mode of WinBoard 4.3.14.

Then the time-control code would be fully active. It is just that the engine would be fed, (and uses internally) a virtual time, derived on its node count. But apart from the clock routine, the rest of the engine would never know that it is not dealing with real time.

How can that be? You tell me to search a specific number of nodes, then how can I go over that as I would if I fail low on a position? How can I go over that by variable amounts as I do now, depending on how much I appear to be "losing"???

If you tell me exactly how long, there is going to be node count jitter. If you tell me exactly how many nodes to search, there will be no timing jitter and I can't test my time allocation code at all.

Can't be both ways, at least in my program...

Of course it can. You get a given number of nodes for a given number of moves, and the engine will itself determine how it distributes those nodes over the individual moves. Just like it divides its time quota over the moves in a normal N moves / M minutes time control. What you had in mind is the direct equivalent to the 'st' command, that gives you a fixed, never-exceed time for a single move. But there is no reason to restrict node-based time controls to that mode.

So if you want to play 100,000 nodes (max) per move, you start WinBoard with arguments

-st 1 -nps 100000

If you want to play 4,000,000 nodes for 40 moves, you specfy

-mps 40 -tc 0:40 -nps 100000

That's all. Of course the engine has to implement the WinBoard nps command. So indeed you could not do it on Crafty.

OK, how does that make a fair test? Program A is fairly constant in NPS throughout the game. Program B varies by a factor of 3x from opening to endgame (Ferret was an example of this). So how many nodes do you tell Ferret to search in comparison to the other program?

So how is this going to give reasonable estimates of skill when it introduces a potential time bias toward one opponent or the other???

The purpose of node-based time controls is not to have a fair test of skill between programs, but to create a reproducible testing environment that is insensitive to CPU loading. I just point out that node-based time controls are not limited to 'st' type time controls, but come in all flavors: classical, incremental, sudden-death, or multi-session combintions of those.

Engines do not count nodes the same way, an have not the same nps rate anyway. So if a tester wants to use node-based time control to not have the chracter of a time-odds game, it is unavoidable that he adapts the nps parameter for each engine separately for equal time use.

To prevent the problem with highly variable nps that you point out, I would encourage any program that shows such behavior to ly about their node count accordingly in nps mode. E.g. counting each tablebase probe for 100 nodes, if that is necessary to make the nps rate in the end-game equal to that in the middle-game. Use any internal engine statistic to make the reportd node count reflect CPU-time use as accurately as possible.

[Uri Blass]

Forgot to mention...
I repeated the Fruit experiment with Spike and Colossus too.
Again no duplicates in 100 games.

When you say no duplicate you mean that no 2 games are the same or maybe you mean that the first game did not repeat.

Note that both options are different.

Uri

Yes I mean no duplicates at all, no 2 games are the same (well according to SCID anyway!).

Note that if you can get 1000 different games with probability of 1/1000
then you can expect more than one pair of identical games so the result that you report seems to be very surprising and I suspect that there may be some learning or some other bug(like bug in SCID.

I think that looking at the games may be productive to see if there is a problem and if SCID is reliable in detecting identical games.

I would like to know what is the probability of ply k to be different when we know that ply 1,2,...k-1 are identical.

Uri

[MartinBryant]

I might be stuck there, none of my GUI choices seem to allow a time per move mode for engine matches. Except Xboard which doesn't seem to have granularity below one second.

Try it at 1 second / move then.
The effect should still be there but perhaps less pronounced as the percentage wobble / move-time will be smaller.
It'll probably take 3-4 hours to complete at that speed.
I just chose 0.5 secs / move as I didn't want to tie up a PC for too long.

[MartinBryant]

OK I've re-run the test on Bob's randomly selected Silver position.

Firstly, I did as Uri (I think it was Uri? things just get buried here so fast!) suggested and ran a deterministic test just to ensure the setup is valid.
I played Fruit v Fruit from the opening position, no books, 7-ply fixed depth search for 10 games and got 10 identical games as expected. (I could've done 100 but that just seemed redundant...)
I used fixed depth as Fruit doesn't seem to work correctly with fixed nodes I'm afraid.

I then ran Fruit (2.1 by the way) v Fruit, 100 games, from Bob's Silver position, 0.5 secs/move.
(I actually made the book repeatedly select the line (12 ply) which leads to Bob's position rather than giving it the FEN as a starting position. It is just easier to do it that way with my GUI.)
In 100 games there was ONE duplicate game pair (out of 4,950 possible game pairings).
Games 9 and 27 played exactly the same moves (PGN below) but if you look carefully the scores do vary slightly throughout the game.

[Event "test"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "9"]
[White "Fruit 2.1"]
[Black "Fruit 2.1"]
[Result "1/2-1/2"]
[ECO "C02"]
[Termination "Repetition"]
[TimeControl "0.5 secs/move"]
[Opening "French"]
[Variation "Advance, 5.Nf3 Qb6 6.a3 c4"]

1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.Nf3 Qb6 6.a3 c4 7.Be2 {-0.02/10} 7...Nge7 {-0.02/10} 8.O-O {-0.07/10} 8...Nf5 {+0.01/10} 9.Qc2 {-0.26/10} 9...Be7 {-0.18/10} 10.Bf4 {-0.24/10} 10...O-O {-0.03/10} 11.Nbd2 {-0.03/10} 11...h5 {+0.01/9} 12.Ng5 {-0.05/10} 12...Qd8 {+0.00/10} 13.h4 {+0.03/10} 13...g6 {+0.03/10} 14.Ndf3 {-0.09/9} 14...Bd7 {-0.06/9} 15.Rfe1 {-0.27/9} 15...Qb6 {-0.27/9} 16.g3 {-0.20/8} 16...a6 {-0.10/9} 17.Nd2 {-0.10/9} 17...Na5 {-0.16/8} 18.Bf3 {-0.21/9} 18...Rac8 {-0.20/9} 19.Rab1 {-0.14/8} 19...Nb3 {-0.28/9} 20.Nxb3 {-0.22/9} 20...Ba4 {-0.27/10} 21.Qe2 {-0.32/9} 21...Qxb3 {-0.27/10} 22.Bg2 {-0.27/10} 22...Qc2 {-0.33/10} 23.Qxc2 {-0.35/10} 23...Bxc2 {-0.35/11} 24.Ra1 {-0.35/11} 24...Rc6 {-0.28/11} 25.a4 {-0.33/11} 25...Rb6 {-0.29/11} 26.Ra2 {-0.32/10} 26...Rc8 {-0.32/10} 27.Nf3 {-0.24/10} 27...Kg7 {-0.17/10} 28.Bg5 {-0.15/11} 28...Bb3 {-0.17/11} 29.Raa1 {-0.12/12} 29...Bxg5 {-0.12/12} 30.Nxg5 {-0.11/12} 30...Bc2 {-0.08/12} 31.a5 {-0.05/12} 31...Rb3 {-0.07/12} 32.Re2 {-0.05/12} 32...Bd3 {+0.00/12} 33.Rd2 {-0.05/13} 33...Ne7 {-0.04/12} 34.Bf3 {+0.00/13} 34...Bf5 {+0.00/13} 35.Bd1 {+0.00/13} 35...Rb5 {+0.00/12} 36.Be2 {-0.17/12} 36...b6 {-0.17/12} 37.axb6 {-0.08/12} 37...Rxb6 {+0.06/11} 38.f3 {+0.03/11} 38...Nc6 {+0.09/11} 39.Bd1 {+0.00/11} 39...Rh8 {-0.03/11} 40.Kf2 {-0.01/11} 40...a5 {-0.03/11} 41.g4 {+0.22/11} 41...Bd3 {+0.20/11} 42.Kg3 {+0.21/11} 42...Rhb8 {+0.00/11} 43.Ba4 {+0.00/12} 43...Na7 {+0.00/12} 44.Bd7 {+0.00/11} 44...Rd8 {+0.00/12} 45.Ba4 {+0.00/14} 45...Rdb8 {+0.00/16} 46.Bd7 {+0.00/12} 46...Rd8 {+0.00/14} 47.Ba4 {+0.00/15} 47...Rdb8 {+0.00/16} 1/2-1/2

[Event "test"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "27"]
[White "Fruit 2.1"]
[Black "Fruit 2.1 - Duplicate"]
[Result "1/2-1/2"]
[ECO "C02"]
[Termination "Repetition"]
[TimeControl "0.5 secs/move"]
[Opening "French"]
[Variation "Advance, 5.Nf3 Qb6 6.a3 c4"]

1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.Nf3 Qb6 6.a3 c4 7.Be2 {-0.02/10} 7...Nge7 {-0.02/10} 8.O-O {-0.07/10} 8...Nf5 {-0.07/10} 9.Qc2 {-0.26/10} 9...Be7 {-0.18/10} 10.Bf4 {-0.24/10} 10...O-O {-0.03/10} 11.Nbd2 {-0.03/10} 11...h5 {+0.01/9} 12.Ng5 {-0.05/10} 12...Qd8 {+0.00/10} 13.h4 {+0.03/10} 13...g6 {+0.03/10} 14.Ndf3 {-0.09/9} 14...Bd7 {-0.09/9} 15.Rfe1 {-0.06/9} 15...Qb6 {-0.27/9} 16.g3 {-0.20/8} 16...a6 {-0.22/9} 17.Nd2 {-0.10/9} 17...Na5 {-0.16/8} 18.Bf3 {-0.20/9} 18...Rac8 {-0.21/9} 19.Rab1 {-0.19/9} 19...Nb3 {-0.28/9} 20.Nxb3 {-0.22/9} 20...Ba4 {-0.27/10} 21.Qe2 {-0.27/9} 21...Qxb3 {-0.27/10} 22.Bg2 {-0.28/9} 22...Qc2 {-0.33/10} 23.Qxc2 {-0.35/10} 23...Bxc2 {-0.35/11} 24.Ra1 {-0.35/11} 24...Rc6 {-0.28/11} 25.a4 {-0.33/10} 25...Rb6 {-0.29/11} 26.Ra2 {-0.29/10} 26...Rc8 {-0.31/10} 27.Nf3 {-0.24/10} 27...Kg7 {-0.17/10} 28.Bg5 {-0.15/11} 28...Bb3 {-0.17/11} 29.Raa1 {-0.12/12} 29...Bxg5 {-0.12/12} 30.Nxg5 {-0.08/12} 30...Bc2 {-0.08/12} 31.a5 {-0.22/12} 31...Rb3 {-0.06/12} 32.Re2 {-0.02/12} 32...Bd3 {+0.00/12} 33.Rd2 {-0.05/13} 33...Ne7 {-0.04/12} 34.Bf3 {+0.00/13} 34...Bf5 {+0.00/12} 35.Bd1 {+0.00/14} 35...Rb5 {+0.00/12} 36.Be2 {-0.17/12} 36...b6 {-0.17/12} 37.axb6 {-0.08/12} 37...Rxb6 {+0.06/11} 38.f3 {+0.03/11} 38...Nc6 {+0.41/11} 39.Bd1 {+0.00/11} 39...Rh8 {-0.03/11} 40.Kf2 {-0.01/11} 40...a5 {-0.03/11} 41.g4 {+0.22/11} 41...Bd3 {+0.20/11} 42.Kg3 {+0.03/11} 42...Rhb8 {+0.00/11} 43.Ba4 {+0.00/12} 43...Na7 {+0.00/12} 44.Bd7 {+0.00/11} 44...Rd8 {+0.00/12} 45.Ba4 {+0.00/14} 45...Rdb8 {+0.00/16} 46.Bd7 {+0.00/12} 46...Rd8 {+0.00/14} 47.Ba4 {+0.00/15} 47...Rdb8 {+0.00/16} 1/2-1/2


So there you have it.
Draw from that whatever conclusions you like.

My 2 cents...
1) Ken may have a point that moving the position further into the game does increase the chance of more duplicates (although these two experiments by no means prove that at all). Looking at the games there were many that finished with similar locked pawn chains (which are an artefact of this particular opening position) perhaps thus reducing the reasonable choices.
2) There's still a mass (excuse the un-scientific term) of variation.

[MartinBryant]

OK Karl,
here's another experiment for you, not quite the one we were discussing but perhaps shedding some more light...

I thought it would be interesting to play a game between two engines at a fixed node count and then gradually increase that count to see how long it took until the game changed. I thought I would increase the node count by 1, 2, 4, 8, 16, etc nodes, doubling each time in case it took quite a while for a change to occur.

For this experiment I used Spike 1.2 (I'm afraid Fruit 2.1 doesn't actually work on fixed node count searches!).

Note that the experiment is deterministic so anybody should be able to confirm the results for themselves or investigate this phenomenom further in different ways.

The first game was played at 1,000,000 nodes / move and is given below.

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000000 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000000|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.55/11} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Ra6 {-0.25/11} 21.Re1 {-0.25/11} Rd6 {-0.05/12} 22.Rxa5
{-0.02/11} c6 {-0.02/11} 23.Rh5 {+0.08/12} f5 {+0.15/12} 24.Bxf5 {+0.28/13} Bxf5
{+0.35/13} 25.Rxf5 {+0.38/13} Rd2 {+0.45/12} 26.Rf4 {+0.46/13} Rxc2 {+0.45/12}
27.Rxc4 {+0.45/12} Re6 {+0.55/11} 28.a4 {+0.55/11} f5 {+0.41/11} 29.g3
{+0.56/11} Rh6 {+0.61/11} 30.h4 {+0.53/11} Re6 {+0.55/11} 31.a5 {<=+0.25/11} Ra2
{+0.13/13} 32.Rc5 {+0.23/13} Rg6 {+0.24/13} 33.Rxe3 {+0.12/13} f4 {+0.05/12}
34.Re8+ {+0.18/12} Kf7 {+0.15/13} 35.Re4 {+0.18/12} Rxg3+ {+0.18/11} 36.Kf1
{+0.22/12} Rxf3+ {+0.00/12} 37.Ke1 {+0.00/12} Kg7 {+0.00/12} 38.Rf5 {+0.03/10}
Kg6 {+0.00/11} 39.Rc5 {+0.00/12} Kg7 {+0.00/11} 40.c4 {+0.00/11} Rh3 {+0.00/11}
41.Rg5+ {+0.00/13} Kf6 {+0.00/14} 42.Rxf4+ {+0.00/13} Ke6 {+0.00/14} 43.Re4+
{+0.00/14} Kf6 {+0.00/12} 44.Rf4+ {+0.00/10} Ke6 {+0.00/10} 45.Re4+ {+0.00/10}
Kf6 {+0.00/12} 46.Rf4+ {+0.00/10} 1/2-1/2

The next game was at 1,000,001 nodes / move and is a repeat of the first game. So far so good!

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000001 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000001|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.55/11} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Ra6 {-0.25/11} 21.Re1 {-0.25/11} Rd6 {-0.05/12} 22.Rxa5
{-0.02/11} c6 {-0.02/11} 23.Rh5 {+0.08/12} f5 {+0.15/12} 24.Bxf5 {+0.28/13} Bxf5
{+0.35/13} 25.Rxf5 {+0.38/13} Rd2 {+0.45/12} 26.Rf4 {+0.46/13} Rxc2 {+0.45/12}
27.Rxc4 {+0.45/12} Re6 {+0.55/11} 28.a4 {+0.55/11} f5 {+0.41/11} 29.g3
{+0.56/11} Rh6 {+0.61/11} 30.h4 {+0.53/11} Re6 {+0.55/11} 31.a5 {<=+0.25/11} Ra2
{+0.13/13} 32.Rc5 {+0.23/13} Rg6 {+0.24/13} 33.Rxe3 {+0.12/13} f4 {+0.05/12}
34.Re8+ {+0.18/12} Kf7 {+0.15/13} 35.Re4 {+0.18/12} Rxg3+ {+0.18/11} 36.Kf1
{+0.22/12} Rxf3+ {+0.00/12} 37.Ke1 {+0.00/12} Kg7 {+0.00/12} 38.Rf5 {+0.03/10}
Kg6 {+0.00/11} 39.Rc5 {+0.00/12} Kg7 {+0.00/11} 40.c4 {+0.00/11} Rh3 {+0.00/11}
41.Rg5+ {+0.00/13} Kf6 {+0.00/14} 42.Rxf4+ {+0.00/13} Ke6 {+0.00/14} 43.Re4+
{+0.00/14} Kf6 {+0.00/12} 44.Rf4+ {+0.00/10} Ke6 {+0.00/10} 45.Re4+ {+0.00/10}
Kf6 {+0.00/12} 46.Rf4+ {+0.00/10} 1/2-1/2

The next game is at 1,000,002 nodes / move but already we get a different game as black varies at move 20. Just 2 nodes difference causes a change! I honestly wasn't expecting this so soon.

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000002 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000002|100|0

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.49/12} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Rab8 {-0.45/12} 21.Rxc7 {-0.57/11} Be6 {-0.62/12} 22.Bb7
{-0.48/11} Rbd8 {-0.33/11} 23.Bc6 {-0.12/13} Rc8 {+0.00/14} 24.Rxc8 {+0.00/16}
Rxc8 {+0.00/16} 25.Ba4 {+0.00/16} Rb8 {+0.00/16} 26.Re1 {+0.00/17} Rb2
{+0.00/17} 27.Bc6 {+0.00/16} Rb6 {+0.00/15} 28.Ba4 {+0.00/10} Rb2 {+0.00/10}
29.Bc6 {+0.00/18} Rb6 {+0.00/16} 30.Ba4 {+0.00/10} Rb2 {+0.00/10} 1/2-1/2

Now the next four games (i.e. +4, +8, +16, +32 nodes) are the same as the previous +2 game.

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000004 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000004|100|0

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.49/12} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Rab8 {-0.45/12} 21.Rxc7 {-0.57/11} Be6 {-0.62/12} 22.Bb7
{-0.48/11} Rbd8 {-0.33/11} 23.Bc6 {-0.12/13} Rc8 {+0.00/14} 24.Rxc8 {+0.00/16}
Rxc8 {+0.00/16} 25.Ba4 {+0.00/16} Rb8 {+0.00/16} 26.Re1 {+0.00/17} Rb2
{+0.00/17} 27.Bc6 {+0.00/16} Rb6 {+0.00/15} 28.Ba4 {+0.00/10} Rb2 {+0.00/10}
29.Bc6 {+0.00/17} Rb6 {+0.00/16} 30.Ba4 {+0.00/10} Rb2 {+0.00/10} 1/2-1/2

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000008 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000008|0|0

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.49/12} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Rab8 {-0.45/12} 21.Rxc7 {-0.57/11} Be6 {-0.62/12} 22.Bb7
{-0.48/11} Rbd8 {-0.33/11} 23.Bc6 {-0.12/13} Rc8 {+0.00/14} 24.Rxc8 {+0.00/16}
Rxc8 {+0.00/16} 25.Ba4 {+0.00/16} Rb8 {+0.00/16} 26.Re1 {+0.00/17} Rb2
{+0.00/17} 27.Bc6 {+0.00/16} Rb6 {+0.00/15} 28.Ba4 {+0.00/10} Rb2 {+0.00/10}
29.Bc6 {+0.00/17} Rb6 {+0.00/16} 30.Ba4 {+0.00/10} Rb2 {+0.00/10} 1/2-1/2

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000016 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000016|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.49/12} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Rab8 {-0.45/12} 21.Rxc7 {-0.57/11} Be6 {-0.62/12} 22.Bb7
{-0.48/11} Rbd8 {-0.33/11} 23.Bc6 {-0.12/13} Rc8 {+0.00/14} 24.Rxc8 {+0.00/15}
Rxc8 {+0.00/16} 25.Ba4 {+0.00/16} Rb8 {+0.00/16} 26.Re1 {+0.00/17} Rb2
{+0.00/17} 27.Bc6 {+0.00/16} Rb6 {+0.00/15} 28.Ba4 {+0.00/10} Rb2 {+0.00/10}
29.Bc6 {+0.00/17} Rb6 {+0.00/16} 30.Ba4 {+0.00/10} Rb2 {+0.00/10} 1/2-1/2

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000032 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000032|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/10} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.26/12} a5
{-0.49/12} 18.Rb5 {-0.55/11} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/11} Rab8 {-0.45/12} 21.Rxc7 {-0.57/11} Be6 {-0.62/12} 22.Bb7
{-0.48/11} Rbd8 {-0.33/11} 23.Bc6 {-0.12/13} Rc8 {+0.00/14} 24.Rxc8 {+0.00/16}
Rxc8 {+0.00/16} 25.Ba4 {+0.00/16} Rb8 {+0.00/16} 26.Re1 {+0.00/17} Rb2
{+0.00/17} 27.Bc6 {+0.00/16} Rb6 {+0.00/15} 28.Ba4 {+0.00/10} Rb2 {+0.00/10}
29.Bc6 {+0.00/17} Rb6 {+0.00/16} 30.Ba4 {+0.00/10} Rb2 {+0.00/10} 1/2-1/2

But now at +64 nodes we start to vary again with another unique game...

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000064 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000064|100|0

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.a3 {<=-0.24/8} Bxc3+ {-0.35/10} 8.bxc3 {-0.35/11}
d5 {-0.42/10} 9.Be2 {-0.62/10} Qe7 {-0.61/9} 10.O-O {-0.37/10} dxe4 {-0.43/10}
11.Bg5 {-0.45/10} e3 {-0.45/10} 12.Nxc6 {-0.34/11} bxc6 {-0.45/12} 13.Qd4
{-0.45/11} Re8 {-0.45/11} 14.Bd3 {-0.38/11} c5 {-0.38/11} 15.Bxf6 {-0.30/11}
Qxf6 {-0.19/11} 16.Qxf6 {-0.29/12} gxf6 {-0.26/12} 17.Rab1 {-0.25/12} a5
{-0.49/12} 18.Rb5 {-0.49/10} c4 {-0.38/13} 19.Be4 {-0.43/12} Bd7 {-0.39/12}
20.Rc5 {-0.34/12} Rab8 {-0.45/12} 21.Rxa5 {-0.45/11} f5 {-0.31/12} 22.Bxf5
{-0.23/13} Bxf5 {-0.25/13} 23.Rxf5 {-0.30/14} Ra8 {-0.34/13} 24.Rf4 {-0.25/13}
Rxa3 {+0.05/13} 25.Rxc4 {+0.05/13} Ra2 {+0.05/13} 26.Rxc7 {+0.03/13} Rxc2
{+0.00/13} 27.Re1 {+0.00/13} Rb8 {+0.00/12} 28.h3 {-0.04/12} Rbb2 {-0.22/14}
29.Rxe3 {-0.30/13} Rxg2+ {-0.27/14} 30.Kf1 {-0.27/14} Rh2 {-0.46/14} 31.Kg1
{-0.40/14} Rbg2+ {-0.47/14} 32.Kf1 {<=-0.40/5} Rc2 {-0.42/12} 33.Kg1 {-0.45/12}
Rhd2 {-0.48/13} 34.Re1 {-0.56/14} Rg2+ {-0.59/14} 35.Kh1 {-0.59/14} Rh2+
{-0.65/13} 36.Kg1 {<=-0.57/5} Rxh3 {-0.62/13} 37.Re3 {-0.63/12} h5 {-0.81/12}
38.Rc5 {-0.79/11} h4 {-0.73/10} 39.Rf5 {-0.77/11} Rg3+ {-0.79/11} 40.Kh1
{-0.86/12} Kf8 {-0.88/12} 41.Rd3 {-0.85/12} Rg6 {-0.94/12} 42.Rf4 {-0.93/11} h3
{-0.83/11} 43.Rg4 {-0.81/11} Rh6 {-0.79/11} 44.c4 {-0.71/11} Re6 {-0.72/10}
45.Rd8+ {-0.58/13} Ke7 {-0.58/13} 46.Rh8 {-0.53/12} Rc1+ {-0.54/12} 47.Rg1
{-0.47/13} Rxc4 {-0.45/12} 48.Rxh3 {-0.42/11} Rc3 {-0.39/11} 49.Kh2 {-0.36/11}
Rd3 {-0.38/10} 50.Rc1 {-0.36/9} Kd7 {-0.26/10} 51.Ra1 {-0.13/11} Red6 {-0.10/11}
52.Ra7+ {-0.07/12} Ke6 {-0.04/13} 53.Kg3 {-0.06/12} R6d5 {+0.01/11} 54.Rh4
{+0.02/11} R3d4 {+0.02/11} 55.Ra6+ {+0.00/12} Ke7 {+0.00/13} 56.Rxd4 {+0.00/12}
Rxd4 {+0.02/13} 57.Rc6 {+0.00/14} Rd6 {+0.00/13} 58.Rc4 {+0.00/13} Rg6+
{+0.00/14} 59.Kf2 {+0.00/15} Rd6 {+0.00/16} 60.Rc7+ {+0.00/15} Ke6 {+0.00/17}
61.Rc4 {+0.00/17} Ke7 {+0.00/19} 62.Rc7+ {+0.00/16} Ke6 {+0.00/14} 63.Rc4
{+0.00/10} Ke7 {+0.00/10} 1/2-1/2

And again at +128 nodes we get another unique game...

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Insufficient Material"]
[TimeControl "1000128 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000128|300|0

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.Bb5 {+0.09/9} a6 {-0.01/9} 8.Bxc6 {-0.18/10} dxc6
{-0.20/10} 9.Be3 {-0.11/10} c5 {-0.09/10} 10.Ne2 {+0.11/10} Qe7 {+0.07/10}
11.O-O {+0.00/11} Be6 {+0.21/10} 12.Qe1 {+0.16/10} Rad8 {+0.07/10} 13.a3
{+0.19/10} Ba5 {+0.18/10} 14.Qf2 {+0.09/10} b6 {+0.16/10} 15.Rfd1 {+0.16/10} c6
{+0.29/9} 16.Qg3 {+0.23/10} Kh8 {+0.39/9} 17.Bf4 {+0.47/10} Rxd1+ {+0.43/10}
18.Rxd1 {+0.38/12} Rd8 {+0.45/12} 19.Bd6 {+0.45/11} Qa7 {+0.48/11} 20.Qg5
{+0.60/10} c4 {+0.47/10} 21.Qe3 {+0.51/10} Qb7 {+0.43/11} 22.Nf4 {+0.42/10} b5
{+0.48/11} 23.Nxe6 {+0.50/10} fxe6 {+0.56/12} 24.Kh1 {+0.58/11} Bb6 {+0.50/10}
25.Qg5 {+0.53/11} Qf7 {+0.65/10} 26.e5 {<=+0.35/10} Nd5 {+0.34/12} 27.Bc5
{+0.00/12} h6 {+0.00/12} 28.Qh4 {+0.25/12} Bc7 {>=+0.30/11} 29.Ne2 {+0.49/11}
Qg6 {>=+0.57/10} 30.Qe4 {+0.56/11} Qh7 {+0.46/11} 31.c3 {+0.54/10} g5 {+0.66/11}
32.g3 {+0.64/11} Rd7 {+0.70/11} 33.Qxh7+ {+0.56/12} Kxh7 {+0.49/14} 34.Nd4
{+0.51/13} Bxe5 {+0.58/13} 35.Nxe6 {+0.56/12} Bd6 {+0.56/12} 36.Kg1 {+0.59/12}
Bxc5+ {+0.49/12} 37.Nxc5 {+0.52/14} Re7 {+0.53/14} 38.Kf2 {+0.53/13} a5
{+0.41/12} 39.Re1 {+0.44/12} Rxe1 {+0.44/11} 40.Kxe1 {+0.55/11} Ne7 {+0.51/11}
41.a4 {+0.54/11} Nd5 {>=+0.85/11} 42.Nb7 {+0.78/10} Nb6 {+0.78/11} 43.axb5
{+0.78/11} cxb5 {+1.01/12} 44.Nxa5 {+1.12/11} Na4 {+1.07/12} 45.Nb7 {+1.14/12}
Nxb2 {+1.22/12} 46.Nd6 {+1.18/11} Kg7 {+1.21/11} 47.Nxb5 {+1.21/11} Kf6
{+1.20/12} 48.Kd2 {+1.20/11} Na4 {+1.25/11} 49.Na3 {+1.32/11} Nb6 {+1.43/11}
50.Nc2 {+1.39/11} h5 {+1.46/11} 51.Ne3 {+1.37/11} Ke5 {+1.49/11} 52.Ke2
{+1.46/11} Ke6 {+1.35/11} 53.Ke1 {+1.39/11} Kd6 {+1.32/10} 54.Kd1 {+1.34/11} Nd5
{+1.36/11} 55.Nxc4+ {+1.42/11} Kc5 {+1.44/12} 56.Ne5 {+1.44/11} Nxc3+ {+1.49/11}
57.Ke1 {+1.56/12} Nd5 {+1.56/11} 58.Nf7 {+1.36/11} g4 {+1.46/12} 59.f4
{+1.40/11} Ne7 {+1.39/11} 60.Ke2 {+1.39/12} Nf5 {+1.36/12} 61.Kf2 {+1.38/12} Kd5
{+1.38/12} 62.Ng5 {+1.36/12} Nd6 {+1.35/12} 63.Ke3 {+1.39/12} Nc4+ {+1.34/12}
64.Ke2 {+1.36/13} Kd4 {+1.34/12} 65.Kf2 {+1.33/11} Kd5 {+1.33/12} 66.Ke1
{+1.33/12} Ne3 {+1.33/12} 67.Ke2 {+1.35/13} Nf5 {+1.34/12} 68.Kd3 {+1.25/12} h4
{+1.38/12} 69.Ne4 {+1.19/12} Ke6 {+1.08/11} 70.Kc4 {+1.25/11} Ne3+ {+1.35/11}
71.Kd4 {+1.18/12} Nc2+ {+1.32/11} 72.Kd3 {+1.25/11} Ne1+ {+1.37/11} 73.Ke3
{+1.34/11} Nc2+ {+1.41/11} 74.Kd2 {+1.36/11} hxg3 {+1.57/11} 75.hxg3 {+1.52/12}
Nd4 {+1.54/13} 76.Ke3 {+1.52/12} Nf5+ {+1.51/12} 77.Kf2 {+1.42/14} Ng7
{+1.42/13} 78.Nc3 {<=+1.12/13} Kf6 {+1.47/13} 79.Nb5 {+1.35/13} Ke6 {+1.34/13}
80.Na7 {+1.17/13} Kd5 {+1.10/13} 81.Nc8 {+0.71/13} Nh5 {+0.59/13} 82.Kg2
{+0.29/12} Ke4 {+0.00/13} 83.Nd6+ {+0.00/14} Kd5 {+0.00/15} 84.Nb5 {+0.00/14}
Ke4 {+0.00/13} 85.Nc3+ {+0.00/14} Kd3 {+0.00/15} 86.Na4 {+0.00/14} Ke3
{+0.00/14} 87.f5 {+0.00/15} Ke4 {+0.00/15} 88.Nc5+ {+0.00/15} Kxf5 {+0.00/12}
89.Nd3 {+0.00/12} Nxg3 {+0.00/10} 90.Kxg3 {+0.00/5} Kg6 {+0.00/5} 91.Kxg4
{+0.00/13} 1/2-1/2

And again at +256 nodes we get another unique game...

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "0-1"]
[TimeControl "1000256 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000256|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.25/9} O-O {+0.06/9} 7.Bb5 {+0.09/9} a6 {-0.09/9} 8.Bxc6 {-0.18/10} dxc6
{-0.18/10} 9.Be3 {-0.11/10} c5 {-0.03/10} 10.Ne2 {+0.11/10} Qe7 {+0.06/10}
11.O-O {+0.00/11} Be6 {+0.15/11} 12.Qe1 {+0.16/10} Rfd8 {+0.17/10} 13.Qg3
{+0.10/10} b5 {+0.24/9} 14.Rfd1 {+0.22/9} c6 {+0.35/8} 15.Bh6 {+0.04/8} Ne8
{+0.14/9} 16.a3 {+0.43/10} Ba5 {+0.34/11} 17.Bg5 {+0.39/11} f6 {+0.26/11} 18.Be3
{+0.42/11} Rxd1+ {+0.15/11} 19.Rxd1 {-0.05/12} Rd8 {-0.05/11} 20.Rxd8 {+0.10/11}
Qxd8 {+0.18/12} 21.Qf2 {<=-0.11/11} b4 {-0.34/12} 22.Na4 {-0.33/12} bxa3
{-0.46/12} 23.bxa3 {-0.42/12} Qd1+ {-0.44/13} 24.Qf1 {-2.74/13} Qxc2 {-3.98/13}
25.Nxc5 {-4.00/13} Bc4 {-4.01/14} 26.Nd4 {-3.99/14} Qc3 {-4.09/15} 27.Qc1
{-4.05/14} Qxc1+ {-4.02/14} 28.Bxc1 {-4.11/16} Bb6 {-4.14/15} 29.Nxc6 {-4.14/15}
Bxc5+ {-4.26/15} 30.Kh1 {-4.09/14} Bb5 {-4.39/14} 31.Nd8 {-4.37/14} Bb6
{-4.47/15} 32.Ne6 {-4.43/15} Nd6 {-4.44/14} 33.h4 {-4.52/13} Kf7 {-4.67/13}
34.Nf4 {-4.63/14} Nc4 {-4.63/13} 35.Nd5 {-4.70/13} Bc5 {-4.94/13} 36.h5
{-4.99/13} a5 {-5.15/12} 37.Nc3 {-5.15/12} Bxa3 {-5.16/12} 38.Bxa3 {-5.20/12}
Nxa3 {-5.20/12} 39.Kh2 {-5.43/10} Bd7 {-5.66/11} 40.Kg3 {-5.66/11} Nc2
{-5.57/10} 41.Kf2 {-5.74/11} a4 {-5.74/10} 42.Ke2 {-5.71/11} a3 {-5.71/11}
43.Kd2 {-5.67/12} Nb4 {-5.70/11} 44.Kc1 {-5.70/11} Ke6 {-5.64/10} 45.Kb1
{-5.64/11} Kd6 {-5.58/11} 46.Nd5 {-5.64/11} Kc5 {-5.78/11} 47.Nf4 {<=-6.05/10}
Be8 {-7.01/10} 48.Ne2 {<=-7.47/11} a2+ {-7.79/11} 49.Kb2 {-7.88/12} Bxh5
{-7.87/11} 50.Nc3 {-8.16/13} Bf7 {-8.46/12} 51.Nxa2 {-8.69/12} Bxa2 {-9.11/12}
52.Kc1 {-9.32/12} Kd4 {-9.30/11} 53.Kd2 {-9.68/12} Bc4 {-9.70/11} 54.f4
{-10.21/12} h5 {-10.23/11} 55.e5 {-10.93/11} h4 {-11.88/11} 56.Kd1 {-11.88/10}
fxe5 {-15.26/10} 57.fxe5 {-13.89/11} Ke3 {>=-14.47/10} 58.Kc1 {-18.17/12} Nd3+
{-20.49/11} 59.Kc2 {-21.30/12} Nxe5 {-21.75/11} 60.Kc3 {#-13/12} Nd3 {#-13/12}
61.Kc2 {#-12/13} Be6 {#-8/12} 62.Kc3 {#-11/13} g5 {#-7/12} 63.Kc2 {#-6/12} g4
{#-6/11} 64.Kc3 {#-5/10} h3 {#-5/9} 65.gxh3 {#-4/8} gxh3 {#-4/7} 66.Kc2 {#-3/5}
h2 {#-3/5} 67.Kc3 {#-2/4} h1=Q {#-2/3} 68.Kc2 {#-1/2} Qc1# {#-1/1} 0-1

And again at +512 nodes we get another unique game...

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1000512 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Nf6"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1000512|800|800

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Nf6 {+0.34/10} 5.Nc3 {+0.34/10} Bb4 {+0.31/10}
6.f3 {+0.31/9} O-O {+0.06/9} 7.Bf4 {-0.02/9} d6 {-0.06/10} 8.Nxc6 {+0.09/11}
bxc6 {+0.09/11} 9.Qd2 {+0.09/11} Be6 {+0.00/11} 10.Ba6 {+0.00/11} Rb8 {+0.09/10}
11.a3 {+0.06/11} Bc5 {+0.02/11} 12.O-O-O {+0.19/11} Nd7 {+0.16/11} 13.Rhe1
{<=-0.27/10} h6 {+0.07/9} 14.Bg3 {+0.15/10} Qf6 {+0.15/10} 15.f4 {+0.22/11} Bg4
{+0.18/10} 16.Be2 {+0.26/11} Bxe2 {+0.21/11} 17.e5 {+0.18/11} dxe5 {+0.01/11}
18.Rxe2 {<=+0.10/11} Bd6 {+0.19/10} 19.fxe5 {+0.12/10} Nxe5 {+0.20/10} 20.Qd4
{+0.05/10} c5 {+0.08/10} 21.Qd5 {+0.27/10} Rfe8 {+0.45/10} 22.Ne4 {<=+0.03/9}
Qe6 {+0.15/10} 23.Nxd6 {-0.40/10} cxd6 {-0.40/11} 24.Bxe5 {-0.39/11} dxe5
{-0.49/11} 25.Re4 {-0.50/10} Qe7 {-0.64/11} 26.Rd2 {-0.69/11} Kh7 {-0.68/10}
27.Re3 {-0.71/10} Rbd8 {-0.60/10} 28.Qe4+ {-0.56/12} g6 {-0.64/12} 29.Rxd8
{-0.64/12} Qxd8 {-0.64/12} 30.Rc3 {-0.64/11} Qg5+ {-0.74/11} 31.Kb1 {-0.85/12}
Qe7 {-0.71/11} 32.Rd3 {-0.77/12} Qe6 {-0.76/11} 33.c4 {-0.62/10} f6 {-0.69/11}
34.Rd5 {-0.71/10} Rc8 {-0.67/12} 35.Qd3 {-0.63/11} e4 {-0.83/11} 36.Qe3
{-0.81/11} a5 {-0.80/11} 37.b3 {-0.78/11} Qe7 {-0.59/10} 38.g4 {-0.53/11} Qe6
{-0.46/10} 39.h3 {-0.38/11} Qe7 {-0.44/11} 40.Ka2 {-0.45/12} Kg7 {-0.34/11}
41.Kb2 {-0.43/11} Rc6 {-0.41/11} 42.h4 {-0.41/10} g5 {-0.44/11} 43.hxg5
{-0.44/10} hxg5 {-0.54/11} 44.a4 {-0.48/9} Kf8 {-0.48/11} 45.Qh3 {-0.45/10} Kg8
{-0.34/11} 46.Qe3 {-0.41/11} Rc8 {-0.33/11} 47.Kc1 {-0.39/12} Kf8 {-0.48/11}
48.Qh3 {-0.48/10} Kg7 {-0.43/12} 49.Qe3 {-0.47/11} Kg6 {-0.46/11} 50.Kb2
{-0.45/12} Rc6 {-0.47/10} 51.Kc1 {-0.37/12} Qe6 {-0.71/12} 52.Rf5 {-0.74/11} Rd6
{-1.20/11} 53.Qxc5 {-1.20/10} e3 {-1.08/10} 54.Rf1 {-1.26/11} e2 {-1.26/11}
55.Re1 {-1.30/12} Rd3 {-1.25/11} 56.Kc2 {-1.30/11} Re3 {-1.29/11} 57.Qxa5
{-1.22/11} Qe4+ {-1.23/10} 58.Kb2 {-1.30/10} Qxg4 {-1.30/10} 59.Qd2 {-1.44/9}
Qf3 {-1.35/9} 60.Ka2 {-1.44/8} Kh5 {-1.27/8} 61.c5 {-1.27/8} g4 {-1.35/9} 62.Qc2
{-1.31/9} g3 {-0.94/9} 63.c6 {-0.56/10} Qe4 {-0.09/9} 64.Qd2 {+0.00/10} Qe6
{+0.00/10} 65.Qc2 {+0.00/11} Qe4 {+0.00/12} 66.Qd2 {+0.00/11} Qe6 {+0.00/11}
67.Qc2 {+0.00/12} Qe4 {+0.00/13} 1/2-1/2

And finally at +1024 nodes we get another unique game...

[Event "FNT"]
[Site "DELL8"]
[Date "2008.08.11"]
[Round "1"]
[White "Spike 1.2 Turin"]
[Black "Spike 1.2 Turin - Duplicate"]
[Result "1/2-1/2"]
[Termination "Repetition"]
[TimeControl "1001024 nodes/move"]
[Opening "Scotch"]
[Variation "4.Nxd4 Bc5 5.Be3 Qf6 6.c3"]
[ECO "C45"]
%CGM 3,0,0,0,0,300000,0,0,5000,250,5,1001024|0|100

1.e4 {+0.29/11} e5 {+0.52/10} 2.Nf3 {+0.52/11} Nc6 {+0.39/11} 3.d4 {<=+0.32/10}
exd4 {+0.52/10} 4.Nxd4 {+0.40/11} Bc5 {+0.54/10} 5.Be3 {+0.55/10} Qf6 {+0.55/10}
6.c3 {+0.55/10} d6 {+0.46/10} 7.Be2 {+0.39/9} Nge7 {+0.45/10} 8.O-O {+0.46/10}
Bd7 {+0.30/9} 9.Na3 {+0.25/9} O-O-O {+0.38/9} 10.Nab5 {+0.30/9} Qg6 {+0.35/10}
11.b4 {+0.27/9} Bxd4 {+0.49/10} 12.Bh5 {<=+0.00/10} Qxe4 {-0.12/10} 13.Bxd4
{-0.41/9} Nxd4 {>=-0.29/10} 14.Re1 {-0.38/11} Qxe1+ {-1.19/12} 15.Qxe1 {+0.21/5}
Nc2 {-1.33/13} 16.Qxe7 {-1.13/12} Rhe8 {-1.40/12} 17.Qg5 {-1.46/11} Nxa1
{-1.55/11} 18.h3 {-1.46/11} Re1+ {-1.24/12} 19.Kh2 {>=-0.96/5} f6 {-1.34/13}
20.Nxa7+ {-1.25/13} Kb8 {-2.05/5} 21.Qd2 {-1.16/13} Re5 {-1.16/12} 22.Bf3
{-1.19/12} Bf5 {-1.26/12} 23.c4 {-1.14/12} Kxa7 {-1.34/12} 24.Qd4+ {-1.21/12} b6
{-1.14/13} 25.Qxa1 {-1.07/12} Be4 {>=-0.86/11} 26.Bxe4 {-0.96/12} Rxe4
{-0.96/12} 27.Qc3 {-0.76/11} h6 {-0.78/11} 28.Qa3+ {-0.92/10} Kb7 {-0.88/13}
29.Qd3 {-0.98/13} Rde8 {-0.80/12} 30.c5 {-0.80/12} dxc5 {-0.83/12} 31.bxc5
{-0.78/12} bxc5 {-0.79/12} 32.Qb5+ {-0.75/12} Kc8 {-0.63/13} 33.Qxc5 {-0.71/12}
R4e5 {-0.52/11} 34.Qc6 {-0.59/11} R8e7 {-0.52/11} 35.a4 {-0.41/12} Ra5
{-0.43/12} 36.f4 {-0.48/11} Rd7 {-0.48/12} 37.f5 {-0.44/11} Rd6 {-0.45/11}
38.Qc4 {-0.62/11} Rad5 {-0.54/12} 39.Qg4 {-0.65/11} Rd7 {-0.60/13} 40.Qe4
{-0.59/12} c6 {-0.63/12} 41.g4 {-0.63/12} Kc7 {-0.63/11} 42.Qc4 {-0.43/11} h5
{-0.56/11} 43.Qf4+ {-0.49/10} Kc8 {-0.43/11} 44.Qc4 {-0.35/11} Rd2+ {-0.16/10}
45.Kg3 {-0.24/11} Kc7 {-0.19/10} 46.Qc5 {-0.19/11} hxg4 {-0.25/10} 47.hxg4
{-0.25/10} Rb2 {+0.00/10} 48.Kh4 {+0.00/11} Rd3 {+0.00/11} 49.Qe7+ {+0.00/12}
Rd7 {+0.00/13} 50.Qc5 {+0.00/10} Rd5 {+0.00/12} 51.Qe7+ {+0.00/12} Rd7
{+0.00/10} 52.Qc5 {+0.00/10} 1/2-1/2

I stopped there as I have to manually setup each game to run so it is rather labour intensive.


So in 12 games we have 7 unique games where the maximum percentage change was 0.1024%
Also most changes (all much smaller than our previously discussed 1000) produce a game change.
Now I guess this data doesn't help much with your desired correlation test but to a layman it does seem to add even more fuel to the 'boy isn't it erratic!' side of the argument.

I can't actually play your desired Crafty v Fruit match because my GUI only does UCI engines (which Crafty is not) and Fruit we now know doesn't support fixed node count searches anyway.

So is there another experiment you could propose using Spike v Spike or Spike v A.N.Other (I presume I can find another UCI engine that supports fixed node counts) which would help you?
I can run experiments of a few hundred games no problem but would be reluctant to try to run anything with many thousands of games.
I will have to mod my GUI to automate the changing of the node count but that shouldn't be too difficult.

Perhaps Spike v 'X', at 100 x +/-1024 node intervals around the 1,000,000 node game giving us 201 games, then re-run with the node counts shifted by 512 nodes.
I could then give you the 2 x 201 WDL sequences for you to aplly your magic formulae to?

Let me know what you think.

[jdart]

I'm annoyed too at programs that don't follow PGN standards (Aquarium is the lastest offender). But I assume when you refer to Arasan's output you are looking at the move command the engine sends to Winboard (or equivalent). That may indeed be putting out o-o, and I'ill fix it. I probably never noticed because neither Winboard nor other compatible UIs like Arena ever complained.

Arasan also inputs and outputs PGN for games, via its UI and that's alway been very standard compliant.

--Jon