Tournament Math: Antianxiety Medication?

Introduction
For those of you going to the World Open this week, let me try to ease your anxiety so you can relax and have some fun.

Objectively speaking, there is a range of possible tournament results from zero to nine (there are nine total games at the World Open), and a distribution of probabilities that you will get one of those results.

People tend to get anxious when they start to focus on the tail ends of the distribution ('What if I crash and burn and get 0/9', or 'Oh boy what if I get 9/9 and bring home the million dollar prize?'). Both of these extremes are unlikely (unless you are playing in the wrong section), and tend to evoke extreme emotions that may distract you from the game itself.

Getting practical with the mathtical
To inject reality into the situation, let's look at the math. The following graph shows the probability distributions of overall tournament scores, assuming for each game you have a fixed probability of winning (given in each panel), and that the games are independent. Basically this is the scenario of 'How many heads will you get when you throw nine biased coins?' Obviously these assumptions are simplistic, but the general point holds even if we were to make things more complicated.



The bottom distribution shows the probability of getting different overall tournament scores if the probability of a win in an individual game is 0.8 (this number means if you were to play 100 games, you'd win about 80 of them). If you are lucky enough to have this for each game, then you are either a sandbagger and should be playing in a higher section, or just at the top of your game. Either way, you can expect to score between six and nine points at the tournament, and fewer than six would be disappointing.

(Note while most chess players probably subjectively feel that the probability of winning is much higher than 0.5 in any given game, clearly if you are in the right section and the rating system works, this cannot be the case for most players).

The middle panel shows the more realistic case of a fair coin, when the probability of winning an individual game is 0.5. Note the distribution of tournament scores peaks where it should, around 4 or 5 games won. Technically, the mean number of wins is 4.5, so you should do something like win four and draw one. For those playing in the right section, this is probably what you should realistically expect. Don't worry too much about going 0/9, and don't put too much pressure on yourself to win nine games. Yes, it would be nice, but relax and have fun. If you were just destroying everyone you would be in the wrong section.

The top panel shows the distribution of overall results when the probability of winning an individual game is 0.2. In this case, you indeed have a very low chance of winning many games, and can expect to get between zero and four points at the tournament. This might be a scenario when you are playing up a section and really trying to learn, so buck up you have a lot to learn from the people you are playing!

From slices to pies
The above probability histograms are really just slices in a three-dimension space with probability of winning on the x-axis, tournament score on the y-axis, and overall probability on the z-axis. This more general plot is shown below.

Despite the fact that it is awesomely cool, the above plot is hard to interpret. Hence, let's represent the same information as a contour plot below. In the contour plot, the x- and y-axes are as above, but the z-axis is represented by "isoprobability" lines. That is, the parts of the probability mountain with the same height (probability) are traced together in one line of a single color--the bar on the right gives the mapping from line color to probability.


We can see that as the probability of winning an individual game goes up, the center of the distribution of overall tournament results shifts up as well. Interestingly, this relationship looks quite linear, and we can quantify the expected points as a function of individual win probability:

Expected Net Points=9xP(one win)

I drew this linear function as a dotted line in the diagram.

That equation makes sense: if P(one win)=0.5, then Net Points expected is exactly 4.5. If P(win)=0, then you will win zero games. Etc..

Take-home message
So, the take home message is: Chill Out! If you are playing in the right section, then there is a distribution of likely scenarios. Given an honest assessment of your skills within that section, you get a picture of what reasonable (as opposed to extremely optimistic or pessimistic) expectations are. Don't focus on the tail ends of the distribution. Just forget all that crap, go in and play chess. When you start to focus on the tails, and get anxious, focus on the whole distribution, bring yourself back in line with mathematical reality.

That said, of course go in there and take home some scalps, but most importantly have fun with the game.

Anonymous contributors

Chess content brought to my attention by two anonymous commenters:

Quiz yourself on square colors. Refresh your browser and it lists the squares in a new order. Very nice! Now that I've become a fan of board visualization (the ankle weights of chess training), I will probably use it.

Chess puzzles blog. There is no shortage of such things online, but it can't hurt to do more.

Chess Rage

ICC tonight, one of my two slow games a week, I got to a dominant position (a rook and two pawns up with a passed pawn). In other words, I had a clear win, not a subtly better position. I was feelin' good.

Then my connection dies for one second. Automatic forfeit. Loss. I wanted to throw my computer out the window. It was especially painful because the dude was constantly badgering me to 'Hurry up' as I was thinking during the game (I eventually entered 'set quietplay 2' so as to block out his whining). So, not only did I lose, but I made an asshole happy by losing and giving him an undeserved rating boost.

Sure, I can set it so 'noescape' is off, so people can disconnect safely. Then I have to suffer through the dorks that disconnect when they start losing, or get tired, or just don't feel like playing anymore. Since I play only two slow games a week, each game is important to me, and I don't like dealing with that crap as it throws off my rhythm.

It's the old noescape Catch 22...And of course it isn't new, but was documented brilliantly by chessloser last year.

Alas, I've made my bed. I made the decision long ago that I'd rather lose some rating points in those rare instances when my computer disconnects, than deal with the much more common inconvenience of those that disconnect at their earliest convenience. So, yes, I've made my bed, and tonight I must sleep on one of the lumps and stop complaining.

Sham chess

Often when I win or draw against players much higher rated than me, in the postmortems it is striking how much more deeply they thought things through, the moves and lines they saw that I didn't even consider. This is a little depressing, makes me feel like a sham. For instance, in the game against Loomis it was clear he had a much better command of the game, and in particular, of some of the potential tactics I had against him which I didn't even think about (note I lost that game, but the general point still holds).

In the final game of the Blue Devil Open, I was lucky enough to draw a much higher-rated player (rated 700 points higher than me) because of this. In the postmortem it was clear that he was taking lots of time to think about potential responses from me that weren't even on my radar. Because of that, he got into time trouble and had to offer a draw from a winning position. Frankly I felt very guilty about this, like the draw was undeserved. I'm not going to post it because I'm lazy, but I played the Slav.

On the positive side, I haven't flat-out dropped a piece in six tournament games in a row. I don't want to jinx it. Knock on wood, burn a goat to the gods, supplicate myself to Caissa, and all that. That has become my new measure of success in tournament play: If I didn't give away a piece for free, or miss that my opponent was offering me a piece for free, then it was a good game.

Hence, while I may not see everything these chess ninjas see, I have started to see safety a lot better for some reason. I am not sure why, but perhaps one reason is all of the games were G75 or longer so I have time to savor the position.

My next goal is to not give away pawns for free (I have given away a couple in those six games), and to go a game without overlooking checks (either me checking, or me moving and not noticing that it allows him to put me in check allowing him to take the initiative).

These are coarse goals, but I'm a coarse player.

Weekend chess blog roundup

If I didn't mention your blog, feel free to put it in the comments. These are threads where I welcome shameless plugs from fellow bloggers.

J'adoube gives us his annual San Francisco chess update.

Where is Loomis?

Congrats to Polly who won the Westchester Club Championship.

Wang is still plugging away at his chess study. The Knights Errant are dead, so it is good to have someone to follow in their systematic program of chess study.

Blunderprone has another great historical survey. Check out Kotov's game with the queen sac. It is just gorgeous.

Mark Weeks has some cool art and some useful information about the Polgar lawsuit.

Chessmaster or Bust has started what must be his fifteenth chess blog. What is it they say about openings? Pick one and stick with it.

From long ago, a wonderful poem that Atomic Patzer posted. It is a good reminder to enjoy the game, not focus on prizes. Those going to the World Open should memorize this poem.

The Need to Win
When an archer is shooting for nothing
He has all his skill.
If he shoots for a brass buckle
He is already nervous.
If he shoots for a prize of gold
He goes blind
Or sees two targets–
He is out of his mind!
His skill has not changed. But the prize
Divides him. He cares.
He thinks more of winning
Than of shooting–
And the need to win
Drains him of power.
Chuang Tzu

We interrupt our regular broadcast

If you will get annoyed by non-chess content, don't read this post. This may be the first political post on this site, and I hope it is the last.

People in Iran are protesting by getting on their rooftops three times a night to shout 'Allaho Akbar' ('God is Great'). In this poignant video record, the woman speaking says, "They can take our phones, our internet, all our communications away, but we are showing that by saying "Allaho Akbar" we can still find each other. Tonight they are crying out to God for help."

I post the video (well, the audio really as the video shows only darkness) as a tribute to humanity's will for liberty. The people of Iran are speaking. I hope everyone out there is listening.

Chess overtraining

Overtraining frequently occurs in chess players who are training for tournaments, and train beyond the brain's ability to adapt. They often train longer and harder so they can improve. But without adequate rest and recovery, these training regimens can backfire, and actually decrease performance.



Do you overtrain?
Chess improvement requires a balance between chess time and recovery time. Too much time with chess and/or too little recovery time may result in some or all of the following symptoms of overtraining.

* Feeling tired, drained, lack of energy
* Sudden drop in performance
* Insomnia
* Headaches
* Decrease in training capacity / intensity
* Moodiness and irritability
* Depression
* Loss of enthusiasm for chess
* Decreased appetite
* A compulsive need to train/play chess

While there are many proposed ways to objectively test for overtraining, the most accurate and sensitive measurements are psychological signs and symptoms, especially changes in a player's mental state. Decreased positive feelings for chess and increased negative feelings, such as depression, anger, fatigue, and irritability often appear after a few days of intensive overtraining.

What to do
Although there is a tendency, particularly in new club players, to feel that “more is better” in terms of training volume, this approach will quickly lead to overtraining. Scheduled rest days should be incorporated into all training programs to allow for adequate recovery.

To avoid burnout, chess students should have a balanced programme of study. Studying tactical problems two hours a day for ten months is more likely to lead to burnout than a more balanced study of the game that includes playing games, studying strategy, endgame, and the opening.

Ignoring personal physical health also leads to chess burnout. Be sure to eat a healthy, balanced diet, and exercise at least three times a week. Of course sleep is essential to proper brain function and recovery. It is during periods of sleep that we experience the most recovery from tough chess study, so make sure you get enough sleep each night while training (for most people this means eight hours).

Disclaimer
Note this is partly tongue-in-cheek, but not totally, and most of it was taken from exercise sites discussion overtraining for athletes.

Computers in chess

The computer is both useless and indispensable for postmortems.

My game with Loomis

With superficial annotations, and some Fritz discoveries. I am frankly happy with my play overall, though obviously I made some big mistakes, and missed some of Loomis' mistakes (his mistakes were harder to spot, especially OTB).

(show chess board)(hide chess board)

BDO 1 result: loss

Last night was the first round of the Blue Devil Open 1 tournament at Duke. It was a fun game despite the loss, partly because I got to play fellow blogger Loomis!

The game actually reached an endgame, which was in Loomis' favor. He dominated my Knight with his Bishop, got the opposition, and proceeded to pass a pawn. We played for almost four hours, so my brain was spinning. The 120 minute time control makes a big difference, as I think it helped me avoid making egregious blunders. Even with the long time controls, I did end up with a bit of a time crunch so I stopped writing my moves at some point. Time management seems qualitatively different with these marathon games.

Frankly, it was nice to have a loss where I wasn't thinking, "Why do I bother" right after. Loomis was probably pissed. All that time and he'll probably gain one rating point from the win (he is rated about 600 points higher than me).

I played 1 d4 for the first time in a tournament. I was off book within move two, which is fine as I'm not focusing much on openings now. Because the game was long, I was able to take time and work some stuff out over the board which was a really nice luxury.

Blue Devil Open, Round One coming up!

An enterprising graduate student at Duke has started a chess tournament and baptized it the Blue Devil Open. One game a week on Sunday evenings, and the first round is this coming Sunday. I have to hand it to him for finding the greatest possible name for a tournament. I think I should get two-point byes just because of my alias here at the blog.

The tournament consists of 3 rounds (one round starting at 6:30 PM on 6/7, 6/14, and 6/21), Swiss pairing system. Registration will open at 6 PM in Meeting Room A of the Bryan Center, and the first round should get started around 6:30 PM.

Time control: G/120
Entry Fee: $10
Prizes will be determined on the first night, once the TD knows the number and distribution of players.

USCF rated/USCF membership required.

Click here for a map of Duke with the Bryan Center highlighted.

J'adoube is not allowed. Everyone else, whether from Duke or not, is welcome to come and have a fun game of chess.

Caveat

Your pin can easily turn into his discovered attack.