Jotam Trejo

Last November saw the final of the World Chess Championship — a match between the reigning world champion (Magnus Carlsen of Norway) and his latest challenger (Sergey Karjakin of Russia) to determine the World Chess Champion. Carlsen ended up winning the tie, but he could only make the difference after the match had gone to overtime, having drawn as many as 10 out of 12 ‘normal’ (i.e. afternoon-long) games. This isn’t an usually high number, but it’s still quite high, and we do see an increase in the amount of games played out to a draw at the very highest level. What’s the reason behind this? Can we still reverse the underlying mechanism? And if not, what are the implications?

Welcome to the machine

Early variants of chess arose in India well over 1,500 years ago, but its current rules were only established a few decades ago, when the so-called fifty-move rule — the rule that states that either player can claim a draw after fifty moves without any captures or pawn moves — was established. However, if you really thought that the nature of the game would never change again after that, you couldn’t have been more mistaken. It wasn’t so much a rule change that invoked it in recent years, but rather the advent of computer engines and their ability to evaluate board positions objectively — in other words, without the flaws that inevitably make us human. They do this by essentially constructing a large tree of all legal moves, then using increasingly complicated algorithms to evaluate the board positions, and finally picking the best continuation — i.e. the one that gives them the greatest possible advantage in the foreseeable future. The strength of engines, then, depends on what the word ‘foreseeable’ means to them; just how far can they see ahead? The same applies to us, but there’s one big difference: engines continue to improve at exponential speeds following Moore’s Law, while we — mere mortals — take many decades to achieve even a small bit of improvement. Garry Kasparov already fell victim to an engine when he lost a game against IBM’s chess computer Deep Blue in 1996, and he lost a full match the year after. The seemingly impossible had come true.

Nowadays, playing engines is of little interest to us; we’ve long accepted that they’ve surpassed us. (Even Carlsen considers playing them to be “depressing”.) Instead, they’ve become an analysis tool, and an amazing one at that. Since engines simply plough through every legal move in a given position, their top move is usually considered to be the objective truth, especially in the latter stages of a game, when there are fewer pieces on the board — thus simplifying calculations. At this point in time, we have endgame tablebases of up to seven pieces (including both kings), which means that the outcome of every position of up to seven pieces is known (given perfect play from both sides). Now, if we could one day expand this to a 32-piece endgame tablebase, we would’ve solved chess, but Moore’s Law or not, it seems extremely unlikely that this’ll happen anytime soon — if ever. (Just consider the fact that the 7-piece one takes up as much as 130 TB, and you’ll understand why.)

Eye-opener

Even if engines won’t solve chess, they still have a huge effect on the way that chess is approached at the very highest level. Engines have opened our eyes to ideas that were previously invisible to us, and the depth of their analyses is simply mindblowing. While they might not have affected chess as a simple board game, there’s no doubt that they’ve changed chess immensely as a professional sport. This is because the insights that engines continue to provide us with create more of a level playing field among the best players in the world. They’re continuously expanding their opening repertoire, gradually ironing out mistakes. While you could argue that this improves the general level of play, the downside is that games become more monotonous. Nowadays, playing the first 10 moves of any game is basically just deciding on an opening, and if you make a mistake here, you’ve almost lost. Competitors are also no longer just nerds trying to outwit their opponent — their lifestyle is like that of any other sportsman, often engaging in physical activities and sometimes even following a strict diet. Endlessly staring at the board is no longer enough if you want to compete with the best!

Long-term trends

You get it — these players would totally smash us. However, how do they fare against each other? Do statistics reveal any interesting long-term trends? As it turns out, they do — or at least I think so.

1

Since the early 20th century, theoreticians have feared that the over-analysis of chess will lead to a ‘draw death’. In this scenario, experts become so skilled at chess that it’ll be impossible to decisively win a game anymore. The first graph illustrates their fears; only 1 in 10 games ended in a draw in 1850, whereas 1 in 3 games ended in a draw in 2013. The small drop in draws since 1980 looks promising, but it could very well just be noise — a coincidence that’ll be overwritten as time passes.

2

 

Logically, as draws are seen more and more frequently, checkmates are becoming a bit of a rarity. However, even if draws hadn’t become so common, we would still be seeing very few checkmates. The reason? Resignations. Players usually resign well before a checkmate is actually on the board, for the simple reason that they often see it coming long in advance. (It’s also a bit less humiliating.)

3

However, most games are still hard-fought battles that go all the way until the bitter end; chess resembles a war, after all! This trend is reflected in the third graph, which illustrates that games have been getting longer since the 1970s. This is probably no coincidence, because this is exactly when people started getting their first PCs. Since engines teach us how to play more perfectly, defensive techniques have been getting more resilient, and so games have been getting longer — more draws being the inevitable result. Why? Because drawn endgames aren’t easy to convert at all.

Having gotten that out of the way, we’re left with one obvious question: what’s the solution to this?

The show must go on

One solution could be to play more Fischer Random Chess in the future. In this variant, named after the great Bobby Fischer, the starting position is randomised by putting the pieces on the first and eighth rank on the board in random order — so long as the bishops still occupy opposite colours. By doing this, opening preparation is nullified, and games will once again be fresh — thus interesting. Former World Chess Champion José Raúl Capablanca proposed a more complex variant of chess to help prevent the draw death, but it never really seemed to catch on in tournaments. We’re now only left to see whether the computer-aided analysis of chess will push us ever-further into a sea of drawn games, but then again, we’ll undoubtedly always think of new ways to keep chess interesting.

 

Many thanks to Randal S. Olson for his useful graphs.