Luck in Chess

A surprising amount of the time that I win a chess game online, my opponent says “lucky”.  In the seventeen or so years that I have been dealing with this, my reaction has generally been to mentally gloat, and at the same time get mildly irked for how rude people are on the internet. Once in a while, I’d take the bait and goad him on: “There’s luck in chess?”

A few years ago I noticed a twinge of double-think when I typed that.  I knew that there was some luck in chess: for example, if you play as black more than white in a tournament, that’s bad luck. If you are white against your biggest rival, that’s good luck.

However, not only were these types of luck insignificant, I knew my (possibly drunk) verbal assailant would probably not be able to name them.  So I would win the internet argument, which was always nice.

But it has become obvious to me now that there is luck in chess in a strong way. In fact, the luck in chess is very fundamental.  It is evident at every scale.

In terms of this particular game with my opponent, I have a certain chance to win, lose, or draw the game. For example, I might have an 80% chance to win, a 5% chance to draw, and a 15% chance to lose. So over time I would win my better share of games, by the law of large numbers. But it is even more variable: at that time on that day, perhaps those were my odds. Perhaps I play better in the morning and he players better in the evening. And there are considerations of internet connection, external distractions, how long we’ve been playing, etc.

My opponent and I in fact have a distribution of distributions of win, loss, and draw odds. Perhaps when all external factors favor my opponent, I win 50%, draw 10%, and lose 40%, whereas when all external factors favor me, I win 95%, draw 5%, and lose 0%. The expected value of the distribution of distributions might be 80%/5%/15% – if you average over our moods, sleep schedules, which color we get, and a host of other factors, perhaps those are the numbers you get. And the expected value of that final distribution, over the course of one single game, might be that I win.

If my opponent complains that I got lucky, he might be right. It might be luck that I was playing white. It might be luck that I was better rested than him. And even holding those effects constant, it might be luck that I won that game, rather than the 15% that I would lose, on average.

Of course he might be wrong. He might have lost because he was on the phone during the game – that would be his fault. But I should not dismiss the impact of luck out of hand. The only way to control for luck is to play a large number of games, in a variety of settings. This is why world championship matches used to be 24+ games, and often they would take place in more than one city.

I want to quickly address where the luck in chess originates. On every move of the game, we each have a certain small chance of making a big mistake, and a comparably larger chance of making a small mistake. When I was younger I would often be afraid of playing weaker, lower-rated players – what if they somehow came up with good moves, for just this one game? No matter how weak my opponent, they might just find five great moves in a row and beat me. And this is true. But the definition of being a weaker player is that the probability that they find five great moves in a row is much lower than mine, because on any given move they are more likely to make an error. The odds that a weaker player can find 40 good moves in a row is virtually zero.

And of course if we were playing poker, my opponent’s claim that I got lucky would hold more water. This is not because there is a fundamentally different decision structure. There is still a certain chance at each action that I or my opponent will make a small or large error. But this is compounded by an amount of randomness that is independent of the player. So even if you can’t blame the luck on your or your opponent’s decisions, it is easy to blame the luck on the deck.

It may not be possible to fully understand to what extent a game of chess was decided by luck or skill. And I suspect that when my opponent claims I got lucky, they might just mean that they would have won had they not made a huge mistake after and otherwise strong game. Regardless, thinking about outcomes in a probabilistic way has helped me overcome my misconception that there is no luck in chess.

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On Google Glass

I’m approaching my sixth month of having Google Glass, and it’s time to expose my views. My basic philosophy is that, because we humans operate on faulty and limited hardware, and because we are exposed to more and more information every year, it is our prerogative to vigilantly pursue technological means of enhancing our cognition. Google Glass, even it its prototypical form, is a major leap forward in cognition-enhancing technology. What are the major innovations behind Google Glass? In my opinion, there are many. First, there are the incremental improvements over mobile phone technology:

  1. Glass reduces querying time for information (Google searches, checking one’s calendar, looking at a map) from roughly 20 seconds to roughly 10 seconds.

    While this advance may seem inconsequential, I have found that saving ten seconds ten times a day adds up quickly. But mostly, I have found that there are many instances where the value of information I would query is near the cost of acquiring that information. So reducing the cost even marginally has dramatically increased the frequency with which I actually perform the query.

  2. Glass reduces the time it takes to record information, in the form of photos or videos, to nearly zero.

    Simply put, I’ve taken nearly a thousand photos and almost a hundred videos that I almost certainly would not have taken without glass. Glass captures pictures and video from the perspective of your eye, which makes recording concerts, parties, and even tennis games quite easy.

  3. Glass enables hands-free information querying and recording.

    This is mostly relevant for driving and biking. I now have many more total opportunities to query and record information. It used to be that, while driving or biking, I would idly wonder when an album I’m listening to was recorded, or where my next turn is, or I’d want to take a picture of a sunset, and I would have to decide whether it was worth the risk to get my phone out of my pocket.

Then there are the non-incremental, potentially massively disruptive innovations:

  1. Glass can passively process audio.

    Imagine that any time you are engaged in conversation or idle musings, a virtual assistant is waiting patiently to chime in with a relevant Wikipedia page, Facebook profile, Youtube video, etc. in an attempt to answer an implied (or explicit) question. While the current model requires deliberate activation by saying “ok glass”, presumably future models will feature contextual and spontaneous querying. Already Google is trying to expand its search engine into an assistant.

  2. Glass can passively process video.

    Glass can see what you see and help you figure out what you’re looking at. If you see a species of plant or animal you don’t know, it can tell you. If you see someone and you have forgotten their name / the last time you saw them / where they work, it can tell you. If you see a famous landmark, building, or painting, it can provide context. If you witness a traffic accident or a robbery, it can save the video. If you are trying to learn a musical instrument or read a book in a foreign language, it can help. The possibilities are endless. The main technological hurdle now is that recording a constant stream of video, and analyzing it for features, is extremely computationally intense. But as we know, if the limiting factor is computational complexity, rather than algorithmic insight, Moore’s law should tell.

  3. Glass provides for passive learning.

    Recently the Niantic team at Google launched a glassware app called Fieldtrip. It has a list of roughly 200,000 significant locations across the world – buildings, monuments, museums, murals, etc. – and when you approach one of them, it pops up on glass with some information. Usually it shows pictures of the landmark from when it was built and from recently, along with a few cards with historical information. Here are a few tidbits that I’ve learned since the launch a few weeks ago: UC Berkeley has the oldest public college dorm in California, and it’s still boys only; the Stanford entrance on Palm Drive, while now small, used to be decorated with Roman columns; Shoreline Boulevard in Mountain View was once dotted with wineries until a pest called the phyllorexa devastated the region in the 1890’s.

    Generally speaking, while the internet has provided most people with the ability to learn about almost any topic, time and discipline are scarce resources. Imagine you are trying to learn French by taking online classes, and perhaps using software like DuoLingo or RosettaStone. Many people succeed with such methods, but it is common knowledge that the best way to learn French is to live in France. Why is this? I believe it’s because, while the energy and focus for active learning is limited, passive learning continues all day long. Reading road signs and menus in French, hearing snippets of conversation on the street or subway, and seeing movies and television in French provide a tremendous amount of reinforcement and practice.

    In the same way, Google Glass allows for passive learning in a variety of disciplines. If I want to become an expert botanist, am I more likely to succeed by taking an online class, or by having a virtual assistant point out the various flora I walk by in my daily life? If I want to become an expert in the history of San Francisco, am I more likely to succeed by reading a few books, or by having a virtual assistant point out of the history of famous locations as I bike by them? If I want to become an expert in body language, am I more likely to succeed by getting a masters degree in psychology, or by having a virtual assistant show me a feed of what I’m seeing, but layered with exaggerated microexpressions and highlighted changes in blood pressure?

Time will tell how much of glass’s potential will be realized. In the meantime, I’m quite enjoying the incremental innovations.

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Nassim Nicholas Taleb

Here’s Taleb’s self-biography:

Nassim N. Taleb spent 20 years as a derivatives trader and, after closing 650,000 option transactions and examining 200,000 risk reports, he changed careers in 2006 to become a scholar and philosophical essayist. Taleb is currently Distinguished Professor of Risk Engineering at New York University’s Polytechnic Institute, but he limits to a 1/4 position and self-funds his research and operates in the manner of independent scholars. He is the author of a 4 volume philosophical essay on uncertainty, Incerto (Antifragile (2012), The Black Swan (2007–2010), Fooled by Randomness (2001) and The Bed of Procrustes (2010)) as well as a mathematical parallel version, Silent Risk (freely available). His collected scientific papers are here.

Taleb’s works focuses on decision making under opacity, as well as mathematical and philosophical problems with probability, in other words on “what to do in a world we don’t understand” as well as on the properties of systems that can handle disorder.

I have read The Black Swan and am reading Antifragile. In my understanding, Taleb has performed a quadfecta of feats of rationality. He

(1) Insight – He identified a systematic error of reasoning.

He discovered, over the course of working as an options trader, that the tails of the distributions that the financial community used for a variety of underlying instruments were greatly underestimated.

(2) Understanding – He studied the underlying psychology behind the error.

According to Taleb, the tendency to be overconfident in the tendency for variables to tend to normally distributions (i.e. the assumption that they are independent and identically distributed) is based on errors such as Platonicity, over-reliance on theory / under-reliance on practice, and slow adoption of nonlinear dynamics and fractal geometry.

(3) Profit – Taleb made sure to gain personally from his insight.

In addition to successfully taking advantage of systematic mispricings as an options trader, by his own admission, Taleb has multiplicatively increased his net worth approximately once a decade – first with the 1987 flash crash, then the 1999-2001 internet bubble, and recently with the 2008 Great Recession, which he predicted in detail in his 2006 book The Black Swan.

(4) Impact – He has made a subtantial impact in erasing the error on a global scale.

Taleb’s books have been extremely successful. The Black Swan is a household name for anyone in finance or statistics. He continues to lecture, debate, and write at a rapid pace. He is known for his extremely confrontational, anti-bullshit rhetorical style. He quite often synthesizes writings from past civilizations and broadens his technical points into philosophical ones. He is well respected in the statistical, financial, and philosophical communities.

I can understand how many people would be satisfied by accomplishing some, but not all, of the above. For example, a path from (1) Insight to (2) Understanding to (3) Profit is success in its own right – technologists come to mind. Likewise, (1) Insight to (2) Understanding to (4) Impact is a common trajectory – think academics. Also, the second step, understanding, may be optional (Did Jobs understand why his design intuition was popular? Did MLK understand the true sociological and evo-psych causes of racism? Maybe.)

But I maintain that the full trajectory, (1) through (4), is the best goal.

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Unpacking

I remember fondly when I was in 2nd grade, and one day at lunch it occurred to me that the meaning of life is happiness. I knew intuitively that I was correct about this, and I felt smug that my classmates weren’t mature enough to understand what I had discovered. When I got home from school that day, I remember telling my father what I had deduced, and his reaction was something along the lines of, “Yes absolutely.”

Of course, my answer to the Big Question will ring true for some more than others, mostly depending on what the question means to them.

Only around age 21 did I actually learn to unpack the content of a very overloaded question and break it down into parts that can be addressed without appeal to intuition.

Here is a very rough unpacking of the question, “What is the meaning of life?” The word ‘meaning’ in that sentence may refer to many things. I can think of the following meanings for the word ‘meaning’: ‘definition‘, ‘purpose‘, ‘value‘, ‘nature‘, and ‘reason‘.

Q: What is the definition of life?

A: Life is a state of matter with certain properties: it is self-replicating, it has persistent information, etc.

Q: What is the purpose of life?

A: Life has no purpose. One does not live life in order to achieve aims that are outside the scope of life.

Q: What is the value of life?

A: There are many valuable things in life, and from my perspective, the most valuable parts of life are happiness, exploration, and interconnectedness.

Q: What is the nature of life?

A: Some types of life, for example human life, have a subjective component that is very poorly understood in the scientific community. The experience of being alive is both very familiar and very mysterious.

Q: What is the reason for life?

A: Initially, life arose through random chemical reactions that eventually led to stable replication. Then life evolved through mutation and selection into the form we recognize today. All of this is partially, but not nearly completely, understood in the scientific community.

There are probably many other ways of interpreting the Big Question. But for my own satisfaction, after thinking about all of these different ways of unpacking the word ‘meaning’, I do not feel that there is an underlying special meaning of life left to be addressed. I do, however, expect to update my answers to these questions as I learn more.

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My Grandma Janet

I greatly regret that my grandmother passed away before I was at all satisfied with my understanding of identity, memory, value, and love.

As a result, in my many long moments dwelling on the subject of her death, both when it was imminent and when it was recent, I think more about the general case than the specific.

I think: “What is lost in death, and what lives on?”, when I wish that I would think: “What is lost in my Grandma’s death, and what part of her lives on?”

I ponder: “What is the sadness of losing a loved on?”, when I wish I would ponder: “What is my sadness for having lost my grandmother?”

I wonder: “How can we honor the dead, that we may all extend and enrich our legacies?”, when I wish I would wonder: “How can I honor Janet, such that her legacy is extended and enriched?”

But the truth is that I lack the maturity to fruitfully dwell on the latter questions.  I can’t make progress on them.

And still my emotions guide me, slowly but surely, towards an understanding.  My emotions are chaotic and unpredictable.  They are low-level and they are high-level.  They are consistent and they are inconsistent.  And, most of all, they come and go.

Perhaps the greatest insight from my limbic system and temporal lobes is just how great the magnitude of one’s effect on the world, society, and one’s family really is.  Or rather, just how great an effect Grandma had.  And the great mystery is that we can never really understand what that effect is on us, as individuals.  Or rather, the effect she had on me.

One thing I do know, at the very least, is that I owe a lot of my sense of humor to my Grandma Janet.

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A Simple Case of Updating

Suppose you’re starting to get to know Taylor, a friend you’ve recently met.  He or she has just turned 25.  To your surprise, discover that he/she has been married for a year.

In what way might it be appropriate to update your model of this person?

Before I suggest an answer, I must start with this: are you wary of the notion of making presumptions about someone just because you found out that he or she married younger than you would have guessed?

I don’t think you should be wary – I think we should be comfortable with the process of working on probable information.  And of course taking guesses about this person simply means taking guesses. If you think it’s a bit more likely that they are a kind person, that doesn’t mean you know for sure that they are kind.  You just think it’s more likely.  Don’t make assumptions, make educated guesses.

(I have other answers why I think you shouldn’t be wary.  Maybe they are apparent in other posts.)

But here I want to make a simple point that is easy to forget.  We don’t really know anything about anyone.  Not for sure, anyway.  All that evidence of what they’ve done: what they’ve said, their choice of habits, their facial expressions and tone of voice and posture, tough decisions they have made, is just that – evidence.  Everything that you learn about them informs your ability to understand what they are like [1].

As a quick but important corollary to this point: the more surprised you are to find out that Taylor is married, then the more you learn about Taylor, and the more your model of Taylor ought to change (Bayes theorem).  And just the same, the better you know Taylor upon learning this, the more you ought to be surprised: if you have a higher expectation that your model of Taylor is accurate, you’ll be more shocked to find that Taylor is not the bachelor you thought he was!

Another big disclaimer on the question at hand.  When trying to update your model of Taylor, don’t forget that it is both the things that getting married younger causes, and that with which getting married younger is correlated, that help our understanding of Taylor.  Take the trait of kindness for example.  Any combination of the following explanatory frameworks is fine:

  1. Getting married caused Taylor to become more kind.
  2. Taylor’s kindness, in part, helped him get married.
  3. Some other factor led in part to Taylor’s kindness and the fact of his marriage.

We’re just trying to guess if Taylor is in fact a kind person.  We aren’t asking the question of why Taylor is as kind as he is.

So with those concerns aside I want to take a stab at the question.  I suppose that, when I find out that Taylor is married, in roughly the order of highest to lowest amount of updating, I would update towards Taylor being:

  • more conscientious and agreeable, defined normally [2]
  • from a religious background
  • from a more socially conservative place
  • more orderly
  • happier
  • probably many other minor things

Now of course, this is what I might start to suspect only if I don’t know Taylor very well!  Perhaps I know other things about Taylor.  Perhaps I know that Taylor is a very accomplished competitive gamer, and highly intelligent for that matter.  How might it be reasonable to update my model of Taylor now?  I think I would consider updating to view Taylor as:

  • not a typical gamer (in ways other than being unmarried)
  • street-smart, aka talented at pragmatism and compromise
  • having multi-faced intelligence
  • the type of person I would love to learn more about

That’s it!  I was simply curious to lay out, in a slightly more formal manner, a simple case of understanding someone better by learning more about them.  I felt writing that out was illuminating.

I’m curious what you might guess about Taylor.

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[1] Or help you to guess “what it is like to be them”.  See Dennett for more on folk psychology and how reliable it is.  It’s important not to forget that we are often overconfident with our ability to guess what people are thinking and feeling, aka the nefarious Mind Projection Fallacy.

[2] http://en.wikipedia.org/wiki/Big_Five_personality_traits

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A Difficult Life Transition

I believe I am running up against all of the following interrelated problems right now.

1) Exploration vs. Exploitation – I am rapidly approaching (or have recently passed) some major pivot points in which it would be wise for me to cull exploration and massively exploit.  Primarily, it seems evident that I should un-diversify my habit portfolio: I should consolidate bodies of knowledge to study, such as programming, and cut out frivolous areas of inquiry, such as video game strategies.  I would maintain, though, that at a younger age studying video game strategies is an extremely effective use of time.

2) Levels of Action – I have naturally been attracted to higher levels of abstraction as opposed to Actually Doing Something.  For example, I have generally preferred math to physics to engineering, I have generally preferred life-planning to decade-planning to year-planning to week-planning, and I have generally preferred studying philosophy to rationality to habit-formation.  In a sentence, I’m studying theory of language instead of Django, which again makes a lot of sense earlier in life but is rapidly losing its effectiveness.

3) Habit Destruction vs Construction – I have always been proud of my excellent habit destruction techniques.  Some triumphs include the destruction of habits related to social awkwardness, poor nutrition, mind projection, fear of novelty, and cultural backwardness.  However I have not been nearly as successful in habit construction.  I am aware of excellent techniques for habit construction, and have a few successful cases (work habits, exercise habits, and empathy habits come to mind), but in general are in dire need of a whole slew of good habits.  I can easily decide on them, and fairly easily construct plans for hacking them into existence, but am not effective in executing on them.  When habit destruction was more important, I was excelling, and now that habit construction is more important, I’m struggling.

4) Freedom vs. Structure – This one is a simple result of having more freedom than I’ve ever had while needing more structure in my life than I’ve ever needed.

I think that in all these cases, I am realizing as I mature that balances are shifting and I am both slow to react and afraid to react.

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