Almost three years since DeepMind’s
AlphaZero shocked the chess world
by taking just four hours to go from zero
to the best chess-playing entity anywhere, the team is back with another party
trick. This time AlphaZero used its self-learning ability to learn variants of
chess, so we can see how such changes as banning castling, making stalemate a
win or letting pawns move sideways or backwards would change the game after
decades, or even centuries, of top-level play. 14th World Chess Champion
Vladimir Kramnik was on hand to assess the results.

DeepMind today published the 98-page academic paper
Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in
Chess
, authored by Deep Mind’s Nenad Tomašev, Ulrich Paquet, Demis Hassabis and
14th World Chess Champion Vladimir Kramnik. You can download it below:

The paper features some mathematical formulas that the average
reader will skim over, but the analysis, based on a large number of sample
games, is much more accessible and packed with interesting detail. For
instance, the piece values for regular chess (the authors caution this should
not be taken as “a gold standard”) are Knight = 3.05 pawns, Bishop = 3.33
pawns, Rook = 5.63 pawns and Queen = 9.5 pawns.

The highlight for most chess fans, however, will be the over
70-page appendix with sample games, positions and commentary from Russia’s Vladimir
Kramnik. It’s a treasure trove of fun positions and curiosities, but let’s
first take a look at the chess motivation for the study.

Kramnik and the problem with classical chess

3rd World Chess Champion José Raúl Capablanca feared the
“draw death” of chess a century ago and came up with Capablanca Chess, played
on a 10×8 board with two new pieces. It didn’t catch on, but 11th World Chess
Champion Bobby Fischer’s Fischer Random Chess, or Chess960, has fared better.
The variant he announced in 1996 sees the pieces on the back rank shuffled
randomly before a game into one of 960 possible combinations – all but
eliminating opening theory, since no-one is capable of analysing or memorising
so many different positions in any depth (though come to think of it – it
sounds like a job for AlphaZero!).

Rebranded as Chess9LX
we’re going to see that game in action this weekend, as 13th World Champion
Garry Kasparov will take part and face 9 players who include the 16th and
current World Champion Magnus Carlsen – their first competitive meeting at the
board in 16 years!

Both those solutions are radical, however, while 14th World
Champion Vladimir Kramnik was drawn to something subtler. The scene is Kazan,
Russia in 2011, where the Candidates Matches are taking place to decide Vishy
Anand’s next challenger. Magnus Carlsen, already clearly the world no. 1, is
missing after deciding not to participate for reasons that left his colleagues
puzzled, but his replacement Alexander Grischuk is in top
form
at the press conferences:

I think, in general, we’re witnessing the burial of
classical chess. Two decisive games in 21; that’s about the same as in checkers!
On the one hand, that’s a great disappointment – to keep playing such boring
games, but on the other hand – maybe we’re doing a good thing.

Grischuk, who welcomed the end of classical chess, was
speaking after a third draw in his 4-game semi-final against Kramnik. He went
on to draw again, win the tiebreak and, by the time of the 6th and final
classical game in the final match, we’d seen 2 decisive classical games in 29, while
Grischuk had drawn 13 in a row. It was unlucky 14, however, as Boris Gelfand won
to make it 3 decisive games in 30 and earn a match against Anand.

It really was a low point for long, classical games, and
after the first game of the Kramnik-Grischuk match, Vladimir also shared
his thoughts on the situation
:

It’s obvious that the outcome of almost any opening is going
to be equality. The stronger computers get, the more lines are neutralised, the
more drawing resources are found for Black, unfortunately. Therefore, I don’t
know… by the way, yesterday we discussed that at dinner. My seconds and I
discussed the idea that instead of, for example, Chess960, maybe we could
change the form of chess by making some tiny changes to the rules which leave
it almost untouched. For instance, I had the idea of banning castling before
the tenth move. That’s an example. Essentially it doesn’t change the game at
all, but it gets rid of all the theory i.e. you have to create new theory, but
while that theory’s being created we can still play for another 50 years or so.

You can think up a lot of such little ideas. I’d be glad,
overall. It strikes me that maybe it’ll come to that. Despite the
inexhaustibility of chess it’s becoming harder and harder, and as the years go
by the tendency’s becoming more and more pronounced, particularly at the top
level where everyone’s well prepared. So perhaps it’d make sense to make such
minor changes. That was just one thought… we had some other ideas, like only
allowing pawns to advance one square at a time. But then it’d be hard for White
to get an edge. It’d be completely even. Or stopping capturing en-passant. A
minor detail, in principle. It doesn’t change much, but a lot of theoretical
positions would be altered. We were a fountain of new ideas over dinner. (smiles)

9 years later, and now retired from classical chess, it
turns out those thoughts never left Kramnik! But whereas before a statement
such as, “it’d be completely even,” would be hard to prove or disprove without
organising multiple tournaments and giving top players time to prepare and
devise new strategies, we can now do it “in
silico
”, as the paper puts it. For AlphaZero it’s no harder to become a
3000+ rated player of normal chess than to do the same for a variant, and when
it plays its only rival, itself, we get a glimpse of the balance of power and
richness of each new game.

The variants investigated by AlphaZero all retain the normal
board and pieces in their standard starting positions, with the authors explaining:

The idea was to try to preserve the symmetry and the
aesthetic appeal of the original game, while hoping to uncover dynamic variants
with new opening, middlegame or endgame patterns and a novel body of opening
theory.

Let’s take a look at the variants and, just for fun, try to
rank them in terms of their appeal. What follows is, of course, subjective, and
you may well disagree! (please let us know in the comments section)

A Top 10 of Chess Variants

10. No castling before move 10

This was the first option Vladimir came up with 9 years ago
in that post-game press conference, but it feels like an artificial trick to
confuse professional chess players rather than an interesting new avenue for
chess. You have to keep count in your head or on paper, and Vladimir notes
something that could logically have been guessed at:

AlphaZero usually aims at playing slower lines where
castling does indeed take place after the first 10 moves.

The variant led to far fewer decisive games not just
compared to “no castling chess” but to normal chess, and is unlikely to catch
on.

9. Stalemate = win

The dream of English Grandmaster Nigel Short, who brought it
up, for instance, during the 2018 World Championship match:

Treating stalemate as a win was unlikely to affect early
play in games, but Kramnik also thought it would make chess less drawish. That
didn’t turn out to be the case, to any significant degree, at least when
AlphaZero was given more time to think.

I was at first somewhat surprised that the decisive game
percentage in this variation was roughly equal to that of classical chess, with
similar levels of performance for White and Black. I was personally expecting
the change to lead to more decisive games and a higher winning percentage for
White.

He reasons that many of the endings that can be defended by
stalemate can be defended by other methods if stalemate isn’t available. Also,
while stalemate (=mate) rather than mate did account for an impressive 37.2% of
AlphaZero’s wins, the authors explain this was largely based on the computer
preferring stalemate to checkmate when both were options. All in all, not a
convincing case to alter what many consider a beautiful motif of chess endings.

8. Semi-torpedo

A torpedo pawn move is advancing two squares, which in these
variants can be done not only on a pawn’s first move. “Semi-torpedo”, however, only allows
the extra option of such a move from the 3rd rank, so as Kramnik points out if
you want to advance your pawn to h5 you could first play h3, keeping the
position solid, and only then h5. A fianchetto with g3 or b3 can also suddenly
become an attacking lunge with g5 or b5. Vladimir explains the variant as
follows:

It is an interesting variation, to be potentially considered
by those who like the general middlegame flavor of Torpedo chess, but are
unwilling to abandon existing endgame theory.

Still, who wants to play “semi”-torpedo?

7. Pawn one square

When Kramnik mentioned this option back in 2011 he noted, “But
then it’d be hard for White to get an edge – it’d be completely even”. It turns
out that’s not quite true, since White gets an edge in every variant tested,
but here it is less than in classical chess and draws are more likely. The authors
point out that the slower play gives players more plausible options – they
looked at this while trying to assess the “richness” of the games quantitatively – but this
feels more like an attempt to dodge existing opening theory than an exciting
game to watch.

6. Pawn back

If there’s one thing we’re drilled about when it comes to
pawns it’s that they can’t move backwards, but in this variant they can! Any
pawn can move backwards one square, but not further back than the starting
rank.

Vladimir Kramnik points out this has some curious opening
implications:

It was interesting to see AlphaZero’s strong preference for
playing the French defence under these rules, the point being that the
light-squared bishop is no longer bad, as it can be developed via c8-b7 followed by a timely d5-d6 back-move.

Other openings change as well. After the standard 1. e4 e5
2. Nf3 Nc6
, there comes a surprise: 3. c4!

It is followed by 3…Bc5 4. e3 (a back-move!) 4…Bb6 5.
d4 d6

Who would have guessed that we are on move 5, after the game
having started with e4 e5?

Another amusing finding is that this is the opening in which
the Dutch Defence is soundest. As Artur Yusupov is reported to have said:

The problem with the Dutch is that Black very often in the
middlegame finds that his best available move is f5-f7.

Here you’d have to play f7-f6 and only then f6-f5, but even
that might be worth it! Overall, however, it’s unlikely pawn-back chess is the
solution to the game’s perceived problems, since at least in AlphaZero’s games
it helped the defending side and reduced the number of decisive games.

5. Pawn sideways

This is where things get wild, as in this variant pawns can
do all they usually do, but also move one square sideways. 

Such moves occurred in 99.6% of AlphaZero’s games and
accounted for 11.4% of all moves. The ability to move sideways transforms the
power of pawns, making the other pieces much less valuable in comparison:

“This is the most perplexing and “alien” of all variants of
chess that we have considered,” said Kramnik, who pointed out how it changes
endgames:

In classical chess, White would be completely lost. Here,
White can play b7-a7 or b7-c7, changing files. The rook can follow, but the
pawn can always step aside. In this particular position, after b7-c7, Rc3,
c7-d7 – Black has no way of stopping the pawn from queening, and instead of
losing – White actually wins!

Perhaps, however, it’s just too complicated and different to
become a popular alternative to normal chess?

4. No castling

This variant has many virtues. It eliminates the only move
in chess where two pieces are moved at the same time, and would therefore ease
the task for beginners or spectators (and perhaps even for grandmasters when it
comes to Chess960 – Vassily Ivanchuk recently noted in our Q&A session that
castling there feels “unnatural” to him). It’s also a change that can be
implemented anywhere simply by players agreeing not to castle and has already
been trialled “in the wild”, during the London Chess Classic and a tournament
in Chennai, India.

The complete ban on castling means kings are stranded in the
centre of the board and, as might be expected, are more susceptible to attacks,
leading to an increased number of decisive games. For Kramnik, however, the
main factor is simply to skip existing opening theory, where castling early is
key to most openings:

One of the main advantages of no-castling chess is that it
eliminates the nowadays overwhelming importance of the opening preparation in
professional chess, for years to come, and makes players think creatively from
the very beginning of each game. This would inevitably lead to a considerably
higher amount of decisive games in chess tournaments until the new theory
develops, and more creativity would be required in order to win. These factors
could also increase the following of professional chess tournaments among chess
enthusiasts.

There’s an element of self-sacrifice here, since AlphaZero’s
love affair with Kramnik’s Berlin Defence, which it considers by far the best defence against 1.e4, ends when castling is ruled out.

3. Torpedo

No half-measures! Full torpedo means that pawns can move one
or two squares at any time, and not just on their first move or from the 2nd
and 3rd ranks. That means that the dictum that Vladimir Kramnik’s passed pawns
always queen is more likely to be true than ever, with 28.7% of the AlphaZero
games featuring pawn promotion.

27.Qc2!! was AlphaZero’s amazing move here, attacking the a4-rook and h7-bishop. If 27…Bxc2 then 28.h8=Q+! and there’s a new queen on the board.

The 14th World Chess Champion comments:

All of the attacking opportunities increase and this strongly
favours the side with the initiative, which makes taking initiative a crucial
part of the game. Pawns are very fast, so less of a strategical asset and much
more tactical instead. The game becomes more tactical and calculative compared
to standard chess.   

In fact Kramnik points out that the players are forced to
play prophylactically to try and keep the pawns tied down, but nevertheless
this is the variant with the most decisive games and biggest advantage for
White, even if a draw still remains the most likely outcome. This would be a
dramatically different form of chess despite the rule change arguably making
the game more logical – no special case for the first move of a pawn.

2. Self-capture

This is the variant that gets the most glowing recommendation
from Vladimir himself:

I like this variation a lot, I would even go as far as to
say that to me this is simply an improved version of regular chess… To
conclude, I would highly recommend this variation for chess lovers who value
beauty in the game on top of everything else.

The idea really is powerful but elegant, since it’s even
easier to explain to a beginner than the current rules – instead of only being
able to capture your opponent’s pieces you can capture your own as well.

That unleashes numerous new options, with Kramnik pointing
out this position in the Ruy Lopez:

Here the black queen can play Qxh7!, suddenly threatening
mate after capturing on h2. The bigger changes occur in the middlegame and
endgame, however, with many fortresses easily dismantled. For instance:

In normal chess the white pawn can never queen, but here
simply Bc8 and bxc8=Q wins the game.

At the same time, the balance of power seems to remain
very close to that of regular chess. Which brings us to…

1. Regular chess

If it ain’t broke, don’t fix it, and it’s far from obvious
that even at the very highest level chess is any more broke now than Capablanca
imagined it was back in the 1920s. The 10% of decisive results in 2011 didn’t
prove to be the herald of things to come, and in fact computers such as
AlphaZero or its accessible counterpart Leela Zero have been showing that all
kinds of chess openings that were considered dubious are perfectly playable –
think Daniil Dubov turning the Philidor Defence into a fearsome weapon.

We continue to see exciting games in super-tournaments and,
for instance, the 2018 Candidates Tournament featured 36% decisive games,
although admittedly Kramnik was involved in 7 of those 20 games! The best
argument for classical chess being in trouble was perhaps the 12 draws in the 2018 World
Championship match, but in normal circumstances Magnus would have converted his
winning position in Game 1 and what followed might have looked very different.
In any case, many of the draws, especially when Magnus played the Sveshnikov,
were thrillers.

It’s unclear if current professionals would relish these variants, since rather than making preparation
unfeasible, as Chess960 does, they simply mean you’d have to work harder
than ever to develop a whole new theory – of course aided by computers. Even if
the players were up for that challenge, does it make sense to force chess fans
to learn new variants and the new tactics and strategy involved? If chess has a problem compared to
other sports it’s that a certain amount of knowledge is all but essential to
enjoy the action. Raising that barrier any higher is unlikely to be the best way forward.

Nevertheless, being able to answer such “what if?” questions
about different chess variants is another fantastic application of DeepMind’s
AI, and one that is no doubt more generally applicable. One suggestion appears
in the paper.

We believe that a similar approach could be used for
auto-balancing game mechanics in other types of games, including computer
games, in cases when a sufficiently performant reinforcement learning system is
available.

Computer games, especially new ones, aren’t tied
to a long tradition that it makes sense to uphold. You suspect, however, that AlphaZero can do more than help out in software design. 

See also:


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