Being On Tilt

I am terrible at chess.

No, hang on - that's not entirely true. I'm terrible at chess, except for the occasions on which I'm actually not so bad. There are even moments when I might say that I was pretty good: I get the occasional Brilliant move now and again, and Great moves show up in a decent fraction of my games. By the numbers, my current Rapid Chess rating here is 1800 and that's a number I'm proud of. I've improved over the past few years after returning to chess following a long hiatus and have become more serious about trying to study, review past mistakes carefully, and learn more about the game. My current goal is to try and turn that 1800 into a 1900 (or dare I say it, a 2000?), which I figure will be tough. What I want to do in these posts is chronicle my progress, both forwards and backwards, while trying to explore some features of the game that I find both maddening and fascinating.

So, what to talk about first? Dear reader, I want to start with one of the big bads of trying to improve at chess: Being On Tilt.

You probably know the term already, but in case you don't, being "On Tilt" or "Tilted" means that you're angry and/or frustrated enough with your play that you keep making bad decisions. I started hearing it years ago as Poker slang, usually in reference to a losing player who was just sort of lashing out through ridiculously aggressive moves rather than trying to make the best choices possible. Needless to say, this rarely helps turn anything around - instead, it tends to lead you further down into the depths. That fatal plunge is where the term originates: In pinball machines, physically tilting the machine too much eventually leads to gameplay being shut off so that all you can do is watch the silver ball slowly drop past silent bumpers and frozen flippers until it's gone.

Fair Use. Even digital pinball felt the need to recreate the experience of getting so mad at the game you could totally ruin your chances.

In chess, it's much the same: Being On Tilt means that things started to go poorly, so you started playing worse. Whether it means you made a mistake in a single game and couldn't right the ship, or that you started losing one 2+1 Bullet match after the other, Being On Tilt in chess feels terrible. Why can't I win?

That last sentence was ringing in my head for most of the last two weeks. After having a bit of a ratings surge across all time controls in early January (1400 Blitz! 1750 Rapid!) the slow regression to the mean began in earnest. First my Blitz games started tanking - I'd get good positions too slowly, or I'd fall for opening traps I hadn't seen yet. Then the Rapid games followed suit. I was making mistakes I hadn't made since I climbed through the 1500s and my board vision felt absolutely stunted. Don't even talk to me about Bullet play - at this point I think I only play Bullet to wallow in self-loathing for a while.

Why can't I win?

It started to feel like a mantra and I found myself opening games expecting to lose. How much worse would it get? Was I really a 1600-1700 player? Was 1800 even a reasonable ambition? Maybe the upward climb was the statistical fluke and this was cold, clear reality ushering me to my true rating. I re-worked the Woodpecker Method circuit I've been training on, read some more Reassess Your Chess, but it didn't help much. TILTED.

But then I started thinking about being On Tilt, and a question came to mind: Were things actually as bad as I thought? I'm both a cognitive scientist and a bit of a data geek, and it struck me that being On Tilt amounted to a quantitative assertion: When I lose, I will keep losing. Or, if we want to fancy about it: P(losing | previous loss) > P(winning | previous loss). If that last bit of notation isn't familiar, it's a statement about condition probabilities: the probability that I will lose my next game after a loss is higher than the probability that I will win my next game after a loss. Being On Tilt means (arguably) exactly this if we stick to the numbers and forget about the self-pity. But is it true?

This question is related to the idea of the "Hot Hand" in basketball, which is the notion that a player who is "on fire" and making shots will continue to make more shots. You may have your own intuitions about this phenomenon, but what I love about it is how much argument it's elicited from data scientists and cognitive psychologists over decades of research. In 1985, Amos Tversky and colleagues published an article in which they said that the Hot Hand was a cognitive bias - people would see a short sequence of successful baskets and decide that was enough to say that a player was having a streak, with evidence to the contrary being ignored. They did a lot of neat stuff in this paper to make their point, but that didn't stop researchers from Pitt taking another look in 2022. In their work, the Hot Hand seemed real! It wasn't huge, but players seemed to exhibit real evidence of a streak. I'll leave the argument there, but keep an eye on this space - there are bound to be more studies of this because it's too much fun to ignore.

But what about chess? More importantly for my own road to 1800, what about me? Am I really On Tilt? To be more specific, am I player who is "bursty" in terms of my losses, such that losing once probably means a big landslide is waiting for me? I decided to crunch my own numbers to find out.
I checked out my 212 Rapid games and entered the full sequence of Wins, Draws and Losses as a single vector. Next, the idea was to build a contingency table that would tell me about the relationships between each game and what tended to come next: How frequently did a Win follow a Loss, for example? What about all the other combinations of past and future events? A player who is prone to being On Tilt should see lots of Win/Win pairs and Loss/Loss pairs, rarely alternating from losing back to winning. On the other hand, maybe my stats would look more even, or more like what they'd be if there was nothing but statistical variation and my win/loss rate to determine my fate from one game to the next.

First, here's a look at that table of contingencies.

Each row/column entry shows you how often that outcome of last game/next game happened in my sequence of games: The '31' in the upper left means that there were 31 cases in which I lost a game and then lost the next one. By comparison the '5' in the bottom row means that there were 5 cases in which a Win was followed by a Draw.

What to make of this? Well, the most likely thing to happen after a Loss is...a Win? Wait a minute: I thought I was On Tilt? Part of the issue here is that my overall record favors Wins which means there just have to be more of those Ws in the sequence, some of which sort of have to be next to Ls. Can we be more precise? Am I On Tilt for my overall win/loss record?

To answer this slightly more nuanced question, I got a little fancier. I decided to look at what this contingency table tended to look like for randomized versions of my win/loss sequence. That is, if you take my full list of games and mix everything up, what do the new contingencies look like over time? Am I burstier than I should expect by chance? Is my actual tendency to lose after losing higher than it would be if there was no rhyme or reason governing the relative timing of my wins and losses? I shuffled the starting sequence 1000 times and calculated a new contingency table each time. Then, I averaged all of these together to see what the central tendency was. There are more accurate ways to do this I'm sure, but it lets me get at a coarse answer to the question: Is this pattern of contingencies more On Tilt than random chance predicts?

Here's a look at those contingencies.

They're nearly the same!

What I think this means is really that sometimes I lose, sometimes I win, and what's going to happen next doesn't have a great deal to do with the past. I neither have a Hot Hand, nor am I On Tilt - I just feel like it sometimes. In itself, that's an interesting cognitive question, but for now I'm going to try and take solace in the data and remind myself that every time a game starts, it's a new chance. A new chance to embarrass myself? Maybe. A new chance to be just a little Brilliant? Maybe that too. Either way, the road to 1900 is paved with one game at a time and you'll only get there if you keep playing.