Tuesday, November 21, 2023

Monday, October 2, 2023

US Chess Championship 2023 forecast

 Nakamura won't be playing, but the field is still very strong.

The 2023 National Memory Championship

The host asked all the finalists why they decided to compete.

"Not sure exactly - it's very difficult and stressful."

That was my response. Back in July, I had made it through the qualifier (results). I won the numbers event, memorizing 80 digits perfectly in 31.92 seconds. This compensated for my performance in the other events. Then in September, I joined the other finalists and reigning champion John Graham in Orlando, Florida.

The first event was a Lumosity game, Pinball Recall. 

After about a second, the bumpers disappear. We have to remember where they were. Then the pinball is launched from a random location and we have to predict where it will go.

It's very straightforward when there are only a couple of bumpers. But as you progress, the boards get larger and more bumpers are added. I didn't train a lot for this event. No one would be eliminated; it only set the seeding. Though it is advantageous to be the top seed, I didn't think that it mattered much. I mainly wanted to avoid embarrassing myself with a last place finish, like I did last year. Right before the competition, I set my 2nd highest score and went on to finish 7th. Not terrible. 

Next was Long Term Recall. A month earlier, we were given a massive spreadsheet with information on US Senators, the Grammy Awards, and WWI Medal of Honor recipients. This event is always a ton of work. You only have 15 seconds to respond to the question, so you have to know it very thoroughly. After many, many hours of work and late nights, I had mastered the Grammys and the senators. I was a little shaky on the Medal of Honor recipients. Sometimes I mixed up "Private First Class" with "Private." Two mistakes and you are out. But if I got the first question wrong, maybe that would derail me. I was already tense going into the event. Fortunately, we started with the senators and I got an easy question. Then we moved on to the Medal of Honor section. Luckily, I wasn't asked about "Private First Class" vs. "Private," or "First Sergeant" vs. "Sergeant." I just had to name an Army Major who had won the Medal of Honor. After a brief pause, I got it right. Two rounds done and I was still perfect, while many of the others were starting to struggle. I nailed the next question about the Grammys. Two finalists were eliminated, and I safely advanced to the next event.

We had 15 minutes to memorize a list of 200 words. But no one attempts all 200 - you only need to know more than the two finalists who would be eliminated. I went for 100. The finalist in the first seat would say the first word. Then the finalist in the second seat would say the second word, etc. But if the 3rd finalist made a mistake, then the 4th finalist would have to correct them, saying the 3rd word. Then the 5th finalist would say the 4th word, and so on. This means you can't skip around, e.g. memorizing only the 1st, 8th, 15th, and 22nd words. All seven of us made it through the first two rounds safely. Then I jumped ahead, saying the 21st word instead of the 19th. Two mistakes and you are out, so now I was on the cusp of elimination. I had trained for this event, but not seriously enough. Words was supposed to be after Pinball Recall, but a few days before the competition, that was changed. Now it came after Long Term Recall. The weakest competitors had already been knocked out, so now it would be tougher. Hardly anyone was making mistakes. It flashed across my mind that the memorizing 100 words might not be enough. We got to the 66th word. I had visualized a doctor, but I knew the word was slightly different. I said, "documentary." But it was "document"! That was my second mistake, so I was out. A painful end to my tournament. After about another 20 words, another finalist was eliminated and the round ended. So 100 words had been enough, but I needed to avoid those mistakes.

I had finished 4th last year, so my expectations were sky high. 7th is not what I had in mind. But I probably would not have made it much further. The next event was the Tea Party. The remaining finalists watched videos where 6 guests stated their name, occupation, hometown, and other information. This event had always been tremendously difficult for me; it had knocked me out in 2018, 2021, and 2022. But this time the other competitors did noticeably better. I probably would have been knocked out quickly. Reigning champ John Graham advanced to the next round along with Jason Smith and dark horse Cameron Russell. James Cumming, who won the qualifier, had been eliminated after making a few minor mistakes. 

In the last event, the finalists have 5 minutes to memorize 2 decks of cards. Cameron's amazing run ended midway through the first deck. Jason Smith didn't last much longer, so John Graham claimed his 3rd national championship. 

Saturday, May 6, 2023

Wednesday, May 3, 2023

Wednesday, April 5, 2023

World Chess Championship 2023

Nepo and Liren are only 7 points apart, so there is a decent chance that the 14-game match will end in a draw (100% - 45.685% - 38.685% = 15.63%)

Saturday, March 18, 2023

MinStrength Methodology

In a game between Players A and B, there is a normal distribution centered at A’s rating and another centered at B’s rating. The standard deviation is 200. In the Elo system, the expected score for Player A is the probability that a random number from A’s distribution is higher than a random number from B’s. This seems to ignore the possibility of draws – there is a 0% chance that both random numbers are equal – but that will be addressed later. The expected score can be approximated with the logistic function:

Next, I model a tournament as n games against your average opponent. This is an approximation (the expected score isn’t a linear function, so a game against an 1800 followed by a game against a 2000 is slightly different from playing two games against a 1900). With this assumption, your score follows a binomial distribution. The mean is np and the variance is np(1-p), where p is your expected score against the average opponent. The issue with this binomial distribution is that there is no accounting for draws. However, the binomial distribution converges to a normal distribution, so I use that as an approximation. The normal distribution is continuous, so scores such as 8.5 are possible. This means that we aren’t ignoring draws.


If you pull a random number from a normal distribution, there is a 95% chance that it will be within 1.96 standard deviations from the mean (np). The standard deviation is the square root of the variance, so that will be (np(1-p))1/2. Thus, the upper end of the 95% range is np + 1.96(np(1-p))1/2. Therefore, your MinStrength is the rating such that score = np + 1.96(np(1-p))1/2