Carlsen - Nepo Game 4

Another draw, so now the score is 2-2. Carlsen's chances continue to fall. When Carlsen draws with black, there is little change. White has a slight advantage, but Carlsen is the stronger player, so it roughly balances out. But when Carlsen is white, the model has higher expectations of him - he has the advantage of the first move and he is the better player, so a draw is a disappointment.

Carlsen - Nepo Game 3

 Another draw. Not much changes in the forecast:

Carlsen - Nepo Game 2

 Nepo held a draw with Black, so his chances improved a bit. The forecast with the new model:

Carlsen - Nepo Game 1

Carlsen drew with black, and the new model's forecast barely changes:

Carlsen wins: 81.45%

Nepo wins: 8.9375%

Match drawn: 9.6125%

Carlsen vs. Nepomniachtchi 2021 - and a new statistical model!

The match will be 14 games instead of 12. This is an improvement. In longer matches, there is a better chance that the stronger player wins (see my articles in ChessBase and Chess Life for more information). However, it is still too short. In "Reforming the Candidates Cycle," I ran simulations and recommended 24-game matches.

Carlsen's rating is 73 points higher. This gives him a big edge. The forecast from the traditional model:

Carlsen wins: 82.86%

Nepomniachtchi wins: 9.115%

Match Drawn: 8.025%

However, the traditional model is due for an update. Sometimes it assumes a draw rate that is too low. I had taken games from my database and plugged them into a statistical model (see the methodology section for more details). However, most of the games didn't come from elite tournaments. A battle between 2400s doesn't tell us much about what will happen in the world championship. The model did correct for the ratings and acknowledged that stronger players draw more often. However, the adjustment wasn't fully satisfactory. It expects the draw rate between Carlsen and Nepo to be just 50.1569%! We could get more decisive games in this championship than in the last three combined!

Now for the paragraph that most readers will want to skip. I built a new model using games where both players were 2700+. Rapid, blitz, and online games were dropped. An ordered logit estimated the probabilities of win, loss, or draw. The independent variables were a second degree polynomial of white's rating, black's rating, and year (higher order terms were insignificant). Then I compared the model's draw rate to the actual draw rate in a subsample: both players 2750+. In this group of about 4000 games, the model expected 57.4% of them to be drawn; the actual draw rate was 58.4%. Not bad. Earlier I tried a larger database with both players 2600+ or 2500+, but in those samples, the predicted draw rate for 2750+ was too low. I tried various ways to put more weight on games with stronger players, but the predicted draw rate barely budged. The other main difference is that the traditional model uses the expected score formula to generate the probabilities of a win or loss. The new model uses the ordered logit to obtain these probabilities.

At the end of the day, the new model's predictions are quite similar:

Carlsen wins: 81.34%

Nepomniachtchi wins: 9.395%

Match Drawn: 9.265%

I will be updating the new model's forecast after each game

2021 National Memory Championship: The Final

Those who qualified back in August were joined by two former champions, Nelson Dellis and John Graham. Four elimination events would whittle down the field from 11 finalists to one winner. I felt more pressure this time. Back in 2018 and 2019, I barely qualified, so I didn't expect much of myself in the final. But in this year's qualifier, I won the Memory League section and got 3rd place overall. I was supposed to do well. The date of the championship - October 23 - loomed over me for weeks. But somehow I was calm on the night before. I slept reasonably well without any medication.

The opening event was Pinball Recall, a game from Lumosity. The bumpers appeared on the screen for about a second and then vanished. We had to remember where they were in order to predict where the ball would go. It looks simple in the tutorial, but when there are 8 bumpers spread out over a 5x5 grid, it gets tough.

The finalist with the highest score got to choose their seat. Whoever finished #2 got the second choice, etc. For example, if you pick the 11th seat, you will get asked the 11th question when you are on stage. This could be advantageous; if the round ends in the middle, then those at the beginning had to answer an extra question. I barely trained for this. The other events were more important. I screwed up the very first one. I pulled myself together and made it up to level 12. But it wasn't enough. I was next to last and ended up in the second seat.

The first event was "Words to Remember." We had 15 minutes to memorize up to 300 words. Two mistakes and you are out. The round would continue until 2 finalists were eliminated. I had been training on Memory League, where you have just 1 minute. About a week before the event, I realized that my results over there might not translate into a strong performance at the championship. Having 15 minutes to memorize is very different from having 1 minute. In training, I tried slowing down a lot and emphasizing accuracy. I figured that it wouldn't be too hard to outlast the 2 weakest competitors, but I didn't want to get complacent. What if I fly all the way to Orlando and get knocked out in the very first round? I was a bit jittery while memorizing and aimed for about 110 words. In the past, 100 had always been enough. Exception: 2019, where I got eliminated since I only knew the first 100. Everything started smoothly enough. A high schooler was eliminated quickly. Then we got to the 49th word. I thought it was "insult" and was shocked to get it wrong. The next finalist had to correct my mistake, but he also stumbled. He said "insulate." Makenna Good (last year's champion) also thought it was "insulate" and was eliminated since it was her 2nd mistake. The event ended and the 9 remaining finalists advanced. It turned out that the word was "insulted." It sounds like a minor mistake, but missing that is inexcusable for me. I went really slowly and reviewed multiple times. I have a system for common prefixes and suffixes; if a word ends in "-ed," I should add a graduation cap to the image in my memory palace. I had gotten sloppy about that. I was off to a shaky start, but I was still in contention.

The next event was long term recall. A month earlier, we were given a list of Pulitzer prize winners, US Winter Olympic gold medalists, and the periodic table of elements. About 2500 bits of information in all. Memorizing it was a tremendous amount of work. I finished about a week before the championship, but I still had to review it at least once a day. Each review took more than an hour. It exhausted my supply of memory palaces, so I also spent hours finding new ones and learning them. I hate this event. But all the work paid off, and I sailed through comfortably. This was the first time that I had ever made it past round 2. James Cumming, who had won the qualifier in August, was eliminated. Rishabh Kasarla (a pre-med student) and Kaitlyn Wei (high schooler and daughter of a former competitor) were also knocked out.

Round 3 was the Tea Party. We would watch videos where 4 "tea party guests" would introduce themselves. We would have to memorize their names, birthdays, phone numbers, occupations, and much more. In training, I was doing well, but by now the weakest finalists had been eliminated. I wasn't sure if I could outlast the best. Three strikes and you are out. The first video started playing, but the audio was very hard to understand. I only caught a few pieces of information. In the next videos, the quality didn't improve. This was going to be a disaster. About midway through, I had a realization. The other competitors were probably struggling just as much as I was. So as long as I get just 1 or 2 questions right, I might prevail. I focused on the first pieces of information: name, birthday, home town, and education. By now I was in the first seat - I had started 2nd, but the finalist ahead of me had been eliminated. So I knew that I would get the first question, and the first question was going to be, "what is this person's name?" In the last 5 minutes, we got to study the information on a sheet of paper, and I gave extra emphasis to the names. The five minutes raced by. The host pulled up the picture of the fourth guest and asked me what his name was. I was ready. But they accidentally revealed the name. So they moved on to the next question, "what is his birthday?" This derailed me. I had memorized the birthdays, but I thought for sure I was going to be asked about names. I had to answer in 15 seconds, and I couldn't adjust that quickly. Strike one. The rest of the field was also struggling. I failed to recover and was swiftly eliminated. Former champ John Graham was also knocked out, along with Michael Friedman. It was so tough that if I had only gotten 1 question right, I almost surely would have advanced. And I should have nailed the first question, but the name was accidentally shown. A painful way to go down.

Four time champion Nelson Dellis advanced to the final. He was joined by Kyle Matschke and Grace Smith; both of them were former finalists. The last event was memorizing 2 decks of cards in 5 minutes. Nelson was the big favorite and he went on to win his 5th title. Congrats Nelson!

2021 US Chess Championship

The field is very strong, even without Nakamura. We have five members from the 2700 club: