Kramnik and AlphaZero: How to Rethink Chess
chess.com
chess.com
https://en.wikipedia.org/wiki/Indian_chess
It will be interesting to compare how Alpha Zero learns with the Indian chess rules.
Does this add much variation to the game or does it slightly delay getting into the same positions we already know? Not castling is interesting though but would change the game quite dramatically, perhaps even making it slightly more predictable? I'm unsure. Interesting concepts.
I find chess very frustrating because I can analyze positions but almost always get thwarted because of misreading tempo. But honestly maybe I don't have a high enough IQ to play chess.
Perhaps just try counting the moves, and look for counters at each step? Most pro chess players think in patterns anyways, subset of moves that obtain a predefined position on the board. Then the game is more about rock, paper, scissors, where you try to guess the opponent’s pattern and employ a counter-pattern.
https://www.gwern.net/docs/iq/2019-vaci.pdf
> most “achievements” linked to IQ are measured in circular stuff s.a. bureaucratic or academic success, things for test takers and salary earners in structured jobs that resemble the tests
This is the point of the test. That people who do well on this test, do well at their job.
>Psychologists do not realize that the effect of IQ (if any, ignoring circularity) is smaller than the difference between IQ tests for the same individual.
This is actually evidence that IQ tests are measuring something that is even more predictive. Say I use an MRI and I'm able to predict schizophrenia far better than chance. The argument that the MRI I used was faulty and sometimes returned back false results is not evidence that my test is bogus, but evidence that it's even more powerful because it worked well despite the machine being wonky.
> if you want to detect how someone fares at a task, say loan sharking, tennis playing, or random matrix theory, make him/her do that task; we don’t need theoretical exams for a real world function by probability-challenged psychologists
This is referencing industrial psychology research. What he's referring to is a work-sample test, and IQ tests are equally predictive. With IQ tests outperforming when the jobs requirements are less defined, and work sample tests outperforming when the job is more defined.(think startup wear many hats lot of on the job learning vs enterprise DBA)
He also makes an argument that iq is less predictive of success at higher levels which isn't the case and is based on some bad research. (They measured childhood IQs instead of adult IQs)
Most of the article is a collection of strawmen, ad hominems, and just plain weird whatboutism. (just because the high IQ janitors score better than low IQ professors doesn't really tell us whether or not IQ is pseudo scientific)
Heh, I've been called crazy by chess players for saying that out loud. Glad I'm not the only one.
I also think basketball/handball tactics are a lot like checkers.
(I'm from Bangladesh)
It's not obvious that this is true at all. Once top-level players have played no-castling-chess as much as they've played ordinary chess, I don't see why they wouldn't have just as many patterns memorised.
This time around the adjustment period would no doubt be significantly shorter for a couple of reasons:
1) Computer-aided analysis will greatly accelerate the evaluation of new openings and positions
2) This change does not really affect end-game theory, so that part doesn't change
This is only true for the brief period until someone modifies an engine to train on the new ruleset.
This makes sense. It’s such a good idea to castle, players pretty much always do. That should indicate it is cutting off lots of uncontrolled variations.
Moving the king to a safe place is going to make threats have a narrower set of possibilities.
I see no reason, in principle, why such a rule change shouldn’t have a dramatic effect on the number of feasible strategies.
The evidence for the claim that no-castling would fix this is alpha go's performance against itself under no-castle rules.
In fact, it's so simple that it's sort of hard to believe. They've done tons of analysis with a retrained-from-the-ground-up AlphaZero and are convinced of it, so I definitely think it's worth a try, and look forward to see its effect.
If it does turn out to be true, it will be kind of amazing how one simple rule tweak affected the highest level of Chess play.
https://www.londonchessclassic.com/press/lcc19_pr5.htm
The current castling rule was an innovation of the Italians when the game was brought in from India. It, along with pawns moving two squares on their first move, ushered in the Italian School of Chess, known for its slashing attacks, sparkling sacrifices and all out aggression.
However, the Indian form of the game did have something like castling, the king could move from its start square to g2, where a fianchetto'ed bishop would normally sit.
Interestingly this goes against the entire point of the article, that castling results in defensive play which results in draws.
The better chess has already been invented and it's called go. And the top human player of that has called it a day in the face of machine learning advancements (wrongly I think). Also I think go is a much more obvious and flexible game to tweak, if you so wanted.
Very entertaining variant with a proud history. None of the usual defensive corner forms work.
They talk about that specifically. The claim is that at the moment, one grandmaster, unilaterally, can play in such a way as the result will be an inconclusive draw with a very high probability. I say "unilaterally" because even if the other grandmaster they're playing wants a higher-risk-higher-reward game, they can't force the game that way. Such games certainly require a lot of skill, but they're very boring to play and to watch.
"Better" in this case means more entertaining; and specifically, the claim is that with the king in the center, it's not possible to "bunker down" and play a very static, defensive version of chess.
It is not however, a completely new game. All the skills regarding pins, forced sacrifices, open files, and so on still hold. It's the same as if both players been forced early in the game to not be able to castle: the basic game is the same, but certain "boring" states are hard to get to.
I do agree that the whole thing about opening book seems a bit overblown to me: obviously getting rid of castling means you have to mostly throw out the current "book"; but surely a new one will be written.
I'd always thought another way to make tournaments more interesting would be to take a page from wrestling. In wrestling matches, each player takes a turn starting from a disadvantaged position, where it should be easier for the other person to pin them. They get points if they manage to break out of the position while avoiding the pin. Having some games start "in the middle" after an early "blunder" by one side would make things more interesting as well.
> I do agree that the whole thing about opening book seems a bit overblown to me: obviously getting rid of castling means you have to mostly throw out the current "book"; but surely a new one will be written.
This is my point. I wasn't denigrating the effort to make chess more entertaining. I'm arguing that they haven't made a more entertaining version, they're confusing novelty with entertainment.
I'm really not trying to troll you by suggesting that a more entertaining variant of chess is go. I mean, if we have to stick with the current set of pieces and how they move then I think that Fischer Random (Chess960) or something like it is the obvious improvement to go for. NoCastlingChess to me is a strange route to go down. Of course novelty makes an old form less jaded but that I'm not convinced it's intrinsically more entertaining – if it were shouldn't we ditch boring old chess?
Is your position that disallowing castling does not lead to less king safety and thus less draws, more mating attacks, piece sacs and complex tactical games? Or is it that you think these things do not contribute to more entertaining games?
My argument is that Kramnik is not recognising that most of the entertainment value comes from the fact that this is a new game (granted that it is an existing game tweaked), not that it forces more aggressive less draw-y games.
Which is why I suggested, either go for a lot more novelty and combinatorial complexity within the game (Fischer960) or drastically overhaul the game (but in my opinion that has been done, and the game is called go).
You can disagree with my opinion but it's not as if I'm not understanding what being said to me, it's just that I disagree with what's being said to me.
Well I'm afraid you're missing the main point of the change; but since I've said it twice now (and you've actually quoted me once), I'm not sure how to explain it any better. It's not primarily change for change sake; but rather, the entire class of possible games changes from "safe, boring, and almost always a draw" into "dangerous, dynamic, and someone almost always wins". At least, that's what I understood from the article.
EDIT: As an example, consider the shot clock in basketball [1]. From Wikipedia:
> The NBA had problems attracting fans (and positive media coverage) before the shot clock's inception. Teams in the lead were running out the clock, passing the ball incessantly. The trailing team could do nothing but commit fouls to recover possession following the free throw. Frequent low-scoring games with many fouls bored fans.
The introduction of the shot clock in basketball wasn't simply change for change sake; it forced teams to actually have a more active, interesting game.
Kramnik is claiming that the same thing has happened now to professional chess: the vast majority of games are boring draws. And he furthermore claims that when they trained AlphaZero from scratch without castling, the games were in fact much more dynamic and more interesting, not just different.
“What I'm arguing is that disallowing castling totally changes the opening book and that a lot of the supposed increased "entertainment" being felt by Kramnik is the delight in having an a plethora of opening lines to explore (opening lines having long being exhausted by humans and machines in trad. chess). The fact that it leads to games which are more exciting because the king is more exposed is a small bonus – notice most of the article talks about all the changes you have to make to opening theory owing to the fact that you can't castle.
My argument is that Kramnik is not recognising that most of the entertainment value comes from the fact that this is a new game (granted that it is an existing game tweaked), not that it forces more aggressive less draw-y games.
Which is why I suggested, either go for a lot more novelty and combinatorial complexity within the game (Fischer960) or drastically overhaul the game (but in my opinion that has been done, and the game is called go).
You can disagree with my opinion but it's not as if I'm not understanding what being said to me, it's just that I disagree with what's being said to me.”
F.T.A.
> The win/loss percentages for both White and Black are similar to classical chess
So just as many draws?
> suggesting that the no-castling variant should be quite playable without favoring a particular player. Preventing the king from retreating to a safe distance means that
Ok, so the game isn't broken
> all of the pieces have to engage in the melee, making the play more dynamic and entertaining, with a number of original patterns.
I'm saying that it is the original patterns where Kramnik is getting most of the dopamine boost from
---
Does that clear things up?
> So just as many draws?
Right, we interpret that differently. He said "win/loss" ratio, not "win/loss/draw" ratio. It's possible your interpretation is correct, but I think the full sentence favors my interpretation:
> suggesting that the no-castling variant should be quite playable without favoring a particular player.
The question he's trying to answer is, "Does a lack of castling make it harder for Black (or White) to win?" And the answer is, "No; Black and White still win about the same percentage of the time, so removing castling will not suddenly make it harder for Black (or white) to win." The draw ratio isn't important to answering the question, and isn't mentioned, so I assume he wasn't saying that the draw ratio was the same.
> I'm saying that it is the original patterns where Kramnik is getting most of the dopamine boost from
That's possible, but it doesn't necessarily follow, even if your interpretation about the draw percentage is true. A draw after a dynamic and unpredicatable battle down to a pair of kings is a lot more interesting than a draw after a "trench battle" of small moves.
But in any case, time will tell. :-)
I know it's bad form around here to complain about downvoting but god damn I'd like to know why I got downvoted so much for the opinions I expressed :(
Oh well, must try harder to be more articulate.
I don't have a huge amount of experience here, but people seem to value 1) politeness and 2) correct information.
I haven't talked to the people who downvoted you obviously (and in case you didn't know, you can't downvote a direct reply, so it wasn't me). But to me the first reply sort of came off as, "chess sux0rz, just play go". Go is of course a very nice game, but it's very different than chess; seeming to show disdain for all the people who like to play chess and watch chess played fails somewhat on the "politeness" front.
The second reply didn't really articulate well your position, so seemed to be just "repeating the mistake" from the first post, and so failed (it seemed) on the "correctness" front.
I think if your first reply had been more like the previous reply in this thread -- asking whether there actually were fewer draws, and whether the gameplay was actually more "dynamic" or was simply "different" -- or perhaps adding in your take on games played that way; say from the recent exhibition in London, or from analyses of AlphaZero games played under these rules (e.g. [1]) -- it would have been seen more as a contribution than a detraction.
That's my guess anyway. :-)
That's what I thought too.
Kramnik said "For example, the openings seem to be more complicated in the AlphaZero no-castling games,"
Assuming it is more complicated, I wonder what that means in terms of the number of openings someone will have to learn? I'm going to take a wild guess and say there will be more than standard chess.
If it takes off, I guess time will tell what effect it has on the game after everyone memorises the main lines and variations.
Chess feels kind of like a sniper duel. You have two high value pieces (the kings), and the rest form a kind of terrain for them to fight in (although the kings don't literally attack each other). It's all about careful maneuvering so you can take a clear shot at the enemy king. Victory depends on high pressure calculation, with no room for the slightest error. Knowing the terrain in advance (memorizing openings) gives you a big advantage.
Go feels more like a huge bar fight between two criminal gangs. It starts off with just posturing, but the participants move into position and prepare, and eventually the violence breaks out and you get multiple fights. Sometimes fights merge together into a big chaotic brawl. The winner is determined by calculating which side got the best of it after it's all over, and both preparation and fighting skills matter.
The point you make about chess about having "no room for the slightest error" is also why I never liked it as much as Go (as most westerners, i grew up with chess but then learned Go as adolescent): In Go you are baffled by genius strokes, in chess you are baffled by idiotic strokes (funnily, in both cases it doesn't really matter if it comes from your enemy or yourself). At least that's what my impression is. Opinions may differ :)
Having a game where one player always tries to win and the other player always tries to draw might not really be the effect you want though.
This always attracted me as a concept and seems well received, per link above.
It should increase the branching factor considerably, and complicate its evaluation - not saying good or bad, just is.
Gaining positional advantage at cost of anything other than pawn is probably not worth it. AFAIK in high level play gambits are not true gambits as you get the sacrifice back.
> Gaining positional advantage at cost of anything other than pawn is probably not worth it
This kind of post makes me want to give up on HN. I have actually played it (albeit a very long time ago) and you are wrong. Please try it.
But even if true, and only a pawn dies, it drastically changes the nature of the game as a white pawn is a barrier to white pieces. Make that barrier permeable and the entire game changes.
> Taking your own pieces would be sub-optimal choice in every-case other then avoiding mate
Or inflicting mate, if you're blocked from that by your own piece. Or opening an attack that otherwise blocked. Or freeing pieces otherwise useless (bishops seem to get this badly, though maybe it's just me - I was never a great player). Any major piece otherwise trapped can now escape by taking any lesser piece of its own that's fenced it in.
It totally changes the game. Position is just as important as pieces, and maybe more at different times.
And yet you have not brought up a single example.
It hard to imagine a self sacrifice that would be better than just taking a bad trade.
Is branching factor actually that relevant? Just from writing some naive AIs for fun I got the impression that the only thing that actually mattered is how well you can evaluate a position without branching further. Whether you have 40 or 100 (or 1000) moves available, you usually just want to only look at "the best" 10-15 (ideally even less if you can), and how reliable this determining of "the best" is seems like a way larger factor than just how many branches there are in theory.
I dunno. Granted evaluation is key but so is branching, surely, as that is what generates new positions, and their complexity in evaluation as there are more factors to consider.
How does one 'look at "the best" 10-15 [positions]' without culling all the others first, however cheaply? I thought evaluation really was just tree searching (hence branching factor is crucial) with various weights (obviously this is traditional chess evaluation, not fancy NN stuff). I honestly am clueless.
This is, from my understanding, also the reason why traditional AI approaches struggled so much with Go. Not because Go has so many possible moves, but because given a certain game state it is so difficult to evaluate which player is ahead.
I think this is where the slight issue is. The branching factor of your game is related to but not the same as the branching factor of your search.
> I thought evaluation really was just tree searching (hence branching factor is crucial)
The most basic way would be to play every possible game through to completion, fully exploring the tree. If you have no way of estimating the value of a position you have to try it out and see what happens, and your branching factor of the game is the same as for your search. A small increase in possible moves makes an enormous difference - 5 to 10 for a 10 move game is a 1000x jump.
However, imagine the complete opposite. You have a perfect way of estimating your chance of winning for any particular board move. In that case, you'd just check all the moves you can make right now and not look any deeper in the tree. Going from 5 to 10 is a doubling of positions to check, no matter how many moves in the game.
Because of the exponential here, the number of positions to evaluate per move that you don't explore further is almost negligible (similarly it's easier to just calculate the size of the lowest expanded bit of the tree as that dominates the total).
So, the better you get at evaluating your position without searching, the more deeply you can explore because you're not branching off so much,
I'm an amateur who's a fan of the Fisher Random chess variant, and feel it is a tremendous improvement over the enormous amounts of opening memorization that is required in traditional chess, and which is yet another thing that gives computers (who have a perfect memory) an edge over humans.
Note that despite the anti-computer design, classical computer chess techniques (with some clever hand-written heuristics) were enough for computers to exceed humans.
Here are the steps:
1. Think of a new rule change;
2. Train AlphaZero for a period of time with the new rule;
3. Validate the viability of the new rule, based on two criteria: a) enough interesting lines discovered by AlphaZero; b) no obvious advantage for either black or white, based on the results of the AlphaZero training games;
4. Make the new rule officially accepted at FIDE for the next N years.
5. Repeat for the next cycle.
In fact, I have done a lot of research into chess engine theory and believe flaws in the stockfish algorithm directly contrubute to the "boring" chess we see today, since all pros use engines to train now. The old engines cant see lines that alphazero sees which involve long term positional sacrifices, and use a linear evaluation function which in principle can never capture the strong non linearities inherenit in chess. (alphazero uses a non linear evaluation function, which is its nueral net)
Considered as a mathematical space, the universe of possible chess strategies is an extremely large order of infinity. There are also many aspects of time management in relation to the computational complexity of the position which modern engines dont model at all.
I believe that modern engines are overly materialistic and that aggresive positional sacrficies in the style of Tal and alphazero are the future of chess strategy for humans
To avoid chess (real chess, with castling and all that) because AlphaZero exists is like avoiding singing because Taylor Swift exists. Or like avoiding painting because Chagall existed. Or like avoiding Starcraft because Serral exists. Yeah, with a 99.999999% chance, you're not going to exceed the performance of these individuals (or others I could name) in their respective fields. That doesn't take the joy out of learning and growing, at least not for me.
AlphaZero and similar add a few more nines to chess, in terms of the likelihood of being the best-performing entity at that game. But that should hardly make a difference except to maybe the two or three very best human players in the world.
Chess theory is "always getting better". This is because chess has the property that the skill curve is so extreme and the game so deep that it is seemingly always possible to continue to improve and find new ideas.
Chess engines play a fundamental role in modern human chess. There is a causal relationship between the state of the art in chess engines and the play styles of the top pro's. This is because better engines can find new idea's in positions previously thought to be completely explored. It happened recently with an alphazero game in a spectacular way iirc
There is a theorem which says that given any chess engine, it's impossible to decide if that chess engine is playing in an optimal way. So when you say "in terms of the likelihood of being the best-performing entity at that game", I think its important to be very precise about what we mean, even though in spirit I agree with that statement =)
I started working on a project to build a chess engine that is specifically designed to beat other chess engines by playing in a non-optimal way specifically tailored to find and exploit bugs in the opposing chess engine code/flaws in its algorithm.
I also once proved that any chess engine based on the principles of stockfish will necessarily contain positions where it can be exploited into making bad moves. If you fixed the algorithm to make it not exploitable in that specific position, the theorem says there would exist another position where it would be exploitable. This is what I call the theory of "exploitative chess engines" (in the sense of maximizing the possible gain), as opposed to ones which attempt to play in an "optimal" way (minimizing the maximum loss)
Careful with that formulation.
https://en.wikipedia.org/wiki/Rice%27s_theorem
https://en.wikipedia.org/wiki/Solved_game
Several major strategy games, notably checkers, have been formally solved. That does make it possible to prove that some engines for those games behave in an optimal way (although it would still be impossible to verify whether an arbitrary program is equivalent to an optimal engine, because the arbitrary program could do something else first whose outcome couldn't be foreseen by the optimal-engine detector).
Although chess has a higher branching factor and a greater depth in various ways than games that have been solved, nobody has found a theoretical barrier to solving it, which in turn means that we can't rule out the possibility of a proof that a particular engine is optimal.
From the formal computation theory standpoint, the situation is even more extreme: the game tree given the threefold repetition rule is finite, which means that we can immediately write down an explicit game tree brute force engine which is guaranteed to perform optimally in every position. This is probably just a handful of lines of code! While this engine can't actually make a single move in a human timescale, from an algorithmic point of view it plays perfectly and we can be sure of that.
The theorems on undecidability of program behavior don't include time constraints like this because they're established using models of computation like Turing machines, where physical limitations of real computing devices are no issue.
Without being allowed to compare a given engine to a theoretically optimal one which is based on brute forcing the full game tree, and being careful about the problem statement, I suspect it would be possible to prove something along these lines
I would argue something like: "Gods evaluation function" takes as input a chess position and returns whether the position is a forced win, lose, or draw. The rules of chess are so complicated that to go from a continuous evaluation function to a discrete one like that would require an infinite number of steps (this last statement is the one that needs to fleshed out)
I will stop calling it a theorem until I remember why I started calling it that. This situation exists in many non-linear optimization problems, a subject I find really interesting, and in many cases in practice there is no way to decide if a given solution is optimal. For some reason I thought there was a theorem in non-linear optimization theory that was directly relevant here
What are other similar games that have a higher level of variation? Go comes to mind. How about we increase the size of the chess board to 9x9, while keeping the same 8x8 setup? That sounds like a number of variations more than no castling, while still keeping the same feel.
The post reads more as an submarine advertisement for DeepMind (0) than a serious article for chess players.
> Fischer Random is an interesting format, but it has its drawbacks. In particular, the nontraditional starting positions make it difficult for many amateurs to enjoy the game until more familiar positions are achieved. The same is true for world-class players, as many have confessed to me privately. Finally, it also seems to lack an aesthetic quality found in traditional chess, which makes it less appealing for both players and viewers, even if it does occasionally result in an exciting game.
(I have no idea if his view would be persuasive to you.)
> In particular, the nontraditional starting positions make it difficult for many amateurs to enjoy the game until more familiar positions are achieved.
Actually the nontraditional start is part of what makes it fun. It's fresh and forces you to start using your brain from move one. I don't buy the claim that the main enjoyment of chess is due to familiar positions.
> The same is true for world-class players, as many have confessed to me privately.
I can't speak to Kramnik's private conversations, but as a serious player what I can say is that my competitive advantage over an amateur diminishes considerably in Chess960. Perhaps what Kramnik's friends are complaining about is the fact that it's harder for them to win at Chess960 than standard.
> Finally, it also seems to lack an aesthetic quality found in traditional chess, which makes it less appealing for both players and viewers, even if it does occasionally result in an exciting game.
Yeah, there's a difference in aesthetics for sure. But who is to say that it is "worse"? Some piece configurations do feel a bit "ugly" but to me this is more than balanced out by the beauty of new patterns emerging where they weren't expected.
But he's selling it as a way to save late-stage classical chess from the era of boring draws and endless opening theory. We already have a better solution for that in Chess960.
The only way to be sure is to have a random chess variant with at least a billion different possible opening starting positions: the conceptually simplest way seems to be to place all pieces completely randomly in the first three ranks (in the same way for each color), while rejecting any position that allows white to make a capture, check or threaten to capture a non-pawn piece on the first move.
Seeing how there is no consensus on "best opening" for the normal game of chess, introducing 960 more variations is not going to be a simple case of memorising the "best opening". I would go as far to say that simply introducing 10 new standard opening positions would introduce more than enough complexity to shake up high level play. There's only so much a human can remember once the computer is turned off and you are over the board.
Even if not the "best" in an absolute sense, the moves those engines find are going to better than the move that an human comes up on the spot.
This means that memorization will still be necessary in Chess960 to be competitive at the highest levels and in fact it's probably going to be worse because memorizing those 960 starting moves sounds far more tedious than memorizing classic opening theory.
Scrabble players can memorize 10K+ word dictionaries in languages they don't know, and since (starting position, move number, chess move) triples can be encoded as words, it should be possible to memorize the main variation found by chess engines for each Chess960 position.
I personally can't imagine any of the current top chess players memorising hundreds of opening lines for all 960 starting positions and then being able to remember them over the board. Only a few players have a mastery of current known chess theory that's just one starting position. I am happy to be proven wrong though when some new chess savant presents themselves.
It doesn't have to be chess engines (although that seems the best approach), it can also be 100 people each spending 10 days analyzing one position per day, or it can be win-rate stats from high-level tournaments once Chess960 is widely played and there is enough data.
There’s no single “best” opening because you can always employ a defence for a specific opening. For example, there’s a trap against the London which is to play 1. d4 d5 2. Bf4 h5. 3. e3...
Ok. You've got your first "best" move, and then what?
You still have pretty much a random position after that, and it'll be up to you to think on your feet to win.
Solving this issue also naturally solves the game variety issue.
As for variety, there is still the risk that chess engines might be able to produce a single long consensus main variation for each 960 position, and so that even if people can only memorize one variation, everyone could memorize and play the same line.