A wildcard in this list.>

I also think since computers made that list Anand learned with each year, like anyone else, to play as close as to what computers suggest!

Kasparov
Fischer
Karpov
Botvinnik
Capablanca
Morphy
Alekhine
Smyslov
Steinitz
Tal

I relate these players in terms of their innovation, longevity, creativity, fighting spirit, how much I like them, and what I had for breakfast.

<Looking at an analysis of Kasparov's combinations made with Crafty at 12 ply is like following a game at Chessbomb and seeing all the comments about mistakes when the 5 second analysis claims that a move isn't the best (often a move that Rybka recommends after much deeper analysis).>

As far as I'm concerned such shallow ply analysis doesn't produce data worth using when dealing with FMs, let alone GMs or Kasparov, except for the most obvious blunder checks.

When I mapped and analyzed the 1910 and 2008 world championship matches, I used continuous 16 ply two-way (forward and reverse) sliding analysis from the first move to the last of each game, bolstered with lengthy deep ply variation analyses, and hoped that produced usable data. If it doesn't and proves in hindsight to still be insufficient, I can console myself with the thought that it is more reliable than other methods in producing worthwhile information. The 21 games of the 1910 and 2008 took 13 months continuous machine time using this method.

The basic result of my research indicates Lasker, Schlechter and Kramnik were basically equivalent accuracy (and therefore strength), in respect of the matches that were analyzed, while Anand was the clear winner.

And what about ideas that are optically difficult but easy to calculate once they're pointed out to you? For some players their entire genius is in finding such ideas over the board. Are the Rybka using analysts taking opening innovations into consideration? How do you evaluate people like Reti and Nimzowitch who revolutionized the game?

Thank you for your kind words.

I'll just reiterate that there is no short cut for these sorts of projects...enormous processing power is useful (I'll settle for the Pentagon computer next time it has some spare processing time...) but whatever is used needs human guidance.

I recommend people try my method on at least one game to see what's involved, as this would inform the debate. The important thing is to deep ply analyze each move and to ensure that engine evaluations are fully consistent with proximate valuations, especially after opening theory is passed.

This takes a huge amount of machine time, but doesn't need to take as much human time because leaving a machine to compute while you're sleeping, having a picnic or going to work simply means a useful build up of hash files that assist analysis and verification of evaluations of other moves. Be prepared to take days or a week or more to finish the game...but don't switch the machine off during the game, as you lose those useful hash files that blaze a path for subsequent engine analysis and evaluation.

Take into account engine weaknesses, have a chessboard nearby and be prepared to use common sense and all your chess knowledge to ensure the engine isn't going off the rails. While engines are useful in a general sense, this sort of engine analysis is only really useful if the outcome of each and every move is clearly consistent. Such internal consistency gives you some confidence that the evaluations are actually accurate.

<Bridge> On one game I did it once (took me 6 hours of analysis - and I did it <only> forwards, running 16 ply "stadard" and longer if the evaluation was "borderline". Since my own chess level is quite low (1600), I couldn't contribute with much human analysis, but I think I would recognize a "draw mistaken by the engine for a win" in those endgames (the game I chose ended in a middlegame though, so no problems there).

I'd be interested to know which game you analyzed and what your results were!

<BTW how comes that if the player makes the same move as the engine suggested, the evaluation remains the same in your analysis? I mean, if players did ten "perfect" (in these terms) moves in a row, the eval must change, as you end up not on the same ply as at the origin of the sequence of perfect moves (be it forward or backward).>

If a player makes the engine’s preferred move immediately after a 16 ply analysis, the evaluation of that move will usually remain the same because playing the best move maintains the engine evaluation. But this is not always the case, as using a 16 ply evaluation on the next move is effectively turning it into a 17 ply evaluation of the original move.

The further you move along the game, the more likely the engine's evaluation of the "best move" will change as you are expand the engine’s “horizon” by bringing into “view” variations that were previously over the calculation horizon. Quite often, when a large additional amount of information from later analysis is brought back to the original move, not only will an evaluation change, but the engine might change it's mind about its preferred move.

That’s why I end up reversing the sliding process from the last move, so that each subsequent move can take advantage of the information that’s built up in previous evaluations both on the initial forward slide, and from the further information built up on the reverse slide.

The reverse slide will change just about all the initial evaluations from the initial forward slide.

Magnus World Champ by 2015.

Norge triumferende.

I mentioned in my last post that <[t]he further you move along the game, the more likely the engine's evaluation of the "best move" will change as you are expand the engine’s “horizon” by bringing into “view” variations that were previously over the calculation horizon.>

A simple well known example of this is that an engine may give you a favorable analysis of a move but it stops just short of a lethal knight fork at the top of a variation tree just over the move "horizon", regardless of whether it's a 16 ply or 25 ply evaluation - no matter how deep the ply, there is always a horizon with who knows what dwelling just beyond.

As you slide the engine along the game's moves, that fork (and other previously unexamined moves) will be eventually factored in and will change the existing evaluation. It can only change the earlier evaluations once you slide the engine back to re-analyze and re-evaluate the earlier moves.

The value of the sliding process is that you're constantly updating the engine's calculations with more information on a cumulative move-by-move basis. The value of the reverse slide is that it has all the information from the initial slide and uses the information gathered all the way from the end of the game to update its original evaluations, and sometimes its preferred moves.

The reverse slide also provides information additional to that acquired on the initial forward slide because the engine's heuristics are constantly gathering fresh information additional to that which has already been acquired.