Practice poker online for free

I enjoy playing poker. I'm not that good, but I do OK in small home games and I enjoy myself.

Recently I've been having a lot of fun playing online for free. How, you ask? Well go to http://www.fulltiltpoker.com/, sign up for free, get a free account, and start playing with play chips. Work your way up to the level you've got skills for, then have fun.

Now everyone's first reaction when I tell them this is that people play really stupidly when they are playing online for free. It isn't worth trying.

But this is not necessarily so! When you play on Full Tilt you can reload to 1000 play chips every 5 minutes. And at the bottom tables people play like complete donks because they can with impunity. However there are a lot of different buy-ins. As you move up, the skill level increases. So you get a gradation of skill from ridiculously soft at 1/2 up to a boss level of 50K/100K. At the latter level typical buy-ins are 4,000,000. The game I just looked at had 2 players, each with about 25,000,000 in front of them. You can't play that game unless you've managed to earn your way to that level. Anyone who does that has legitimately beaten a *lot* of other players, and put a lot of time in. Do you think those people play poorly?

If you've got basic skills (easily acquired), it isn't hard to beat the easy "donk" levels of free poker online. Then you can move up to more fun levels that require more skill. And once you can play poker well? Well, then you can buy in with some confidence about your skills (at least for low level play) and enjoy both the game and the money you're making at it.

Here is a data point. My sister read a couple of books, went online, got a free account, worked her bankroll up to a few hundred thousand and was playing at the 100/200 level. Then she began playing for money, entered the WPS, and look what happened.

So if you find poker fun, and want to practice, you can online for free. The only thing you'll lose is your time. Which isn't a cost if it is fun for you.

Piaget Water Level Test

Many years ago in a dentist's office I read an interesting article in a magazine. It talked about how there were questions that were specific to certain adult genders. In particular until puberty there was no measurable difference in performance on the question, but after puberty there was a large difference. As examples they offered a verbal question that women do well on, and a question where they drew two cups, one tilted, and asked people to fill in the water level if both were half full. (Artistry not required.) Men do well on this. Most women don't. And education doesn't matter, women who graduate college do worse than men who drop out of high-school.

I botched the verbal one due to something that looked silly to me, got the male one, and dismissed the article as garbage. Then a month later it came up in a conversation with my girlfriend, and she got the men's question wrong. I couldn't remember the one that women do well on. This made me curious, so I asked my mother the same question and she got it wrong. I can call my mother many things, but unintelligent is very much not among them. As an example, when she was at Stanford in the 50s they gave her a battery of ability tests. The only one she was not in the top 1% on was manual dexterity.

(Side note for married men. Do not rush to give your wife this test. I've started many marital fights that way, and I have never tracked down a question that women do better than men on. I know there is one, and I know that at 19 I couldn't do it, but I don't remember what it was and have never encountered another.)

Since then I've learned that this question is called the Piaget Water Level Test. The background on this is that Piaget found that children typically gain specific mental abilities at specific ages that are tied to specific growth spurts. And so he collected examples. For instance there is a specific age at which children learn that people who were not present would not have seen what they did, and another at which children learn that when you pour water into a tall thin glass you don't have more than you used to. And as he collected examples, he eventually offered the water level test. Which, oddly, men gain the ability to do during our last growth spurt, puberty, and most women never do.

I've seen various estimates for how well people do on it. One was that 90% of men can do the task, and only 30% of women. That seems to be a good fit with my experience.

An interesting side note. It is widely noted that there is a large gender imbalance within programming. But I've found through experience that programmers I know, whether male or female, have a 100% success rate on this question. I have no idea what to make of this tidbit, but I find it interesting.

Incidentally for those wondering what the answer to the question is, the water level is horizontal to the ground. The most common answer among women I've asked is to draw the water level parallel to the bottom of the cup. The second most common answer from women is to realize that there is a trick, and to draw the water level tilted twice as much as the cup. When the correct answer is pointed out, women recognize it as very obvious. I imagine that their feeling is much like how I felt after botching the verbal question that I blanked out of my memory.

BTW if anyone knows of any question with the reverse gender characteristics, I've been looking for it for over 20 years. It is frustrating - I know that at least one such question exists, but I've never found it.

Analysis vs Algebra predicts eating corn?

I like learning about odd connections between disparate things. This probably is the oddest example that I know.

Broadly speaking, mathematicians can be divided into those who like analysis, and those who like algebra. The distinction between the two types runs throughout math. Even those who work in areas that are far from analysis or algebra are very aware of the difference between them, and usually are very clear on which their preference is. I'll delve into this in more depth soon, but for now let's just take it for granted that this is a well-known distinction, and it has meaning for mathematicians.

Back when I was in grad school there was a department lunch with corn on the cob. Partway through the meal one of the analysts looked around the room and remarked, "That's odd, all of the analysts are eating corn one way and the algebraists are eating corn another!" Everyone looked around. In fact everyone was eating the corn in one of two ways. One way was to munch over the length of the corn in a straight line, back up, turn slightly, and do another row across. Kind of like how an old typewriter goes. The other way was to go around in a spiral. All of the analysts were eating in spirals, and the algebraists in rows.

There were a number of mathematicians present whose fields of study didn't make it clear whether they were on the analysis or algebra side of things. We went around and asked, and in every case the way they ate corn matched their preference. Since then I've made a point of amusing myself by asking mathematicians I meet whether they prefer algebra or analysis, and then predicting which way they will eat corn. I'm probably up to 40 or so by now, and in every case but one I've been able to correctly predict how they eat corn. The one exception was a logician who claimed to be exactly on the fence between the two. When I explained the corn thing to him he looked surprised, and said that he had an unusual way of eating corn. He went in loose spirals! In other words he truly was a perfect combination of algebra and analysis!

If you have even a passing familiarity of probability, it is clear that despite how unbelievable it initially is that the type of mathematics you prefer is connected to how you eat corn, it is pretty much certain that there actually is a very strong connection. If you believe, as I do, that this difference is connected to how we think about other things, then there must be some odd connection between how we like to understand the world and how we eat corn. Why is another matter.

How do I explain the distinction between algebra and analysis? Well the best way to understand it is to ask you to study advanced mathematics. You will have to take many courses with the word "algebra" in the name, and others with "analysis" in the name. By the time you're done you'll have experienced the difference, and you'll be clear on which you prefer. Odds are you won't do that, but that is the most reliable way to come to understand it.

If I have to wave my hands and explain it, I would explain it like this. In algebra there are sequences of operations which have proven to be important and effective in one circumstance. Algebraists try to reuse these operations in different contexts in the hopes that what proved effective in one situation will be effective again. By contrast an analyst is likely to form an idiosyncratic mental model of specific problems. Based on that mental model you have intuitions that let you carry out long chains of calculations that are, in principle, obviously going to lead to the right thing. Typically your intuition is correct to within a constant factor, and you're only interested in some sort of limiting behavior so that is fine.

If you don't know any advanced math, the odds are about equal that my explanation is going to mislead you as to give you an idea what I am talking about. You'd be better off figuring out your preference by looking at how you eat corn. That said, the distinction carries through into other subjects that I've learned about. But not in a clear and obvious way.

For instance I've noticed the difference cropping up in programming. The distinction is often hard to explain. There are a wide variety of programming techniques, and most programmers have only really learned a few. Some of those techniques appeal to analysts, and others to algebraists. But if you've only been exposed to techniques that are a good fit for one, then how do you know which you'd prefer? Worse yet, when two programmers talk and have different experience bases, how can they tell whether their natural intellectual tastes are similar or different?

Let me give some examples. Upon my first encounter it was clear to me that object oriented programming is something that appeals to algebraists. So if you're a programmer and found Design Patterns: Elements of Reusable Object-Oriented Software to be a revelation, it is highly likely that you lean towards algebra and eat your corn in neat rows. Going the other way, if the techniques described in On Lisp appeal, then you might be on the analytic side of the fence and eat your corn in spirals. This is particularly true if you found yourself agreeing with Paul Graham's thoughts in Why Arc Isn't Especially Object-Oriented. There was a period that I thought that the programming division might be as simple as functional versus object oriented. Then I encountered monads, and I learned that there were functional programmers who clearly were algebraists. (I know someone who got his PhD studying Haskell's type system. My prediction that he ate corn in rows was correct.) Going the other way I wouldn't be surprised that people who love what they can do with template metaprogramming in C++ lean towards analysis and eating corn in spirals. (I haven't tested the last guess at all, so take it with a grain of salt.)

Going out on a limb, I wouldn't be surprised to find out that where people fall in the emacs/vi debate is correlated with how they eat corn. I wouldn't predict a very strong correlation, but I'd expect that emacs is likely to appeal to people who would like algebra, and vi to people who like analysis.

And now to wrap up, why would how we eat corn say something how we think? Here is what I think.

When you pick up a piece of corn on the cob, you have two cues for how to eat it. The first is that the corn is laid out in very nice rows. How can you not follow the lines that are laid out for you? The other is that as you eat, your teeth scrape down the corn. If you twist your wrist, you'll eat more efficiently. Why would someone want to eat inefficiently?

My best guess is that the cue you notice and follow reflects a natural tendency about how you tend to think in general. And this tendency is tied to such things as what kind of math you prefer or what programming techniques would prove interesting for you.

How did pterosaurs get so big?

The pterosaurs got going something like 230 million years ago. They died out with the dinosaurs 65 million years ago. Over their history they came in all sizes, from Rhamphorhynchus who was the size of a sparrow to Quetzalcoatlus with a wingspan of variously estimated as being 30-40 feet. Spread out it was a similar size to a t-rex, and on the ground its estimated height was close to a giraffe's. The largest bird ever, Argentavis was much, much smaller than that.

However the birds arose about 150 million years ago. Feathers were a big advantage in flight, and over time the birds took over a lot of what the pterosaurs were doing. But the pterosaurs did not go away. Instead they wound up being in niches for very big flying animals. This is competition through specialization, which I talked about some time ago when I discussed the Neanderthals.

This coexistence provides evidence that birds were generally better fliers, but there was a niche for very big fliers that the pterosaurs were better at. The question I'm curious about is why the pterosaurs were better at being big fliers than birds were.

I have a theory. But before I can explain it I need to provide some background.

Wings have evolved in vertebrates three times in pterosaurs, birds, and bats. All three started with the basic vertebrate limb structure and found different ways of constructing a wing out of it. In both bats and birds the arm bones form part of the wing. Now an important fact about vertebrate bones is that different bones grow at different rates as you grow. In particular arm bones start off shorter and catch up later. The result is that in birds and bats, babies have the wrong proportions for their wings to be useful. Therefore baby birds and bats can't learn to fly until they have achieved a significant fraction of their full size.

Pterosaurs were different. Their wings were entirely constructed from wrist and hand bones. (Fully half the wing was supported by an elongated 4th finger.) Hand bones stay in proportion your whole life. Comparisons of fossils of pterosaurs at different ages in the same species verifies that their wings always had good proportions for flight. Furthermore we have fossils from baby pterosaurs that died miles out at sea, which is direct evidence that they flew young.

What does this have to do with the eventual size of the animals? Well birds cannot learn to fly until they are near full growth. Which means that they need intensive care from their parents until they reach that growth. This care is a significant fact of life for bird species, and is why most types of birds have both parents providing care. Unlike most mammals where the mother is generally capable of taking care of young on her own. The larger the bird is, the harder this care is to provide.

By contrast pterosaurs were probably able to take care of themselves at a much younger age, and smaller size. Which means that they were free to grow for a lot longer, to a lot larger size, without unduly taxing their parents. (In truth we don't have any data indicating how much or little parental care baby pterosaurs got. But I suspect it was less than birds get.) And, I believe, that is why they were able to get so much larger than birds.

Random trivia I came across in preparing this post. The reason bats can't fly during the day is that their wings are vulnerable to sunburn. There is evidence that pterosaurs had a protective layer so they didn't have this issue. Also birds have stiffer wings than bats do, which provides better lift and less maneuverability. Pterosaurs had more joints in their wings than birds do, but didn't have finger bones inside of the structure of their wings like bats, which suggests to me that their wings would have been somewhere between.

And my whole train of thought was started by watching National Geographic - Sky Monsters. If you're interested in pterosaurs, it is a worthwhile video.

Dozenal glyphs - a modest proposal

A proposal that shows up every so often is to use dozenal arithmetic. The idea is simple, in base 12 more fractions work out very conveniently. You can easily divide things 3 and 4 ways. This is frequently convenient, and is why we often sell things in dozens. It is also why the much maligned Imperial system sneaks factors of 3 (3 tsp in a tbsp) and 12 (inches in a foot) in various places. And there are numerous minor benefits, such as the fact that the multiplication table becomes significantly simpler and therefore easier to learn.

When the French created the metric system, they based it on factors of 10 everywhere. They even went so far as to try to measure angles in gradians (a quarter circle had 100), and to use decimal time. The world as a whole rejected decimal angles and times, but has adopted decimal metric everywhere else. Which is very convenient for scientists, but is hard to divide into thirds and somewhat inconvenient for quarters. Furthermore the persistence of both systems results in occasional annoyances like the fact that in daily life we usually prefer to measure speed in km/h, but for energy and power calculations the units only work out properly if you measure in m/s. Resulting in an annoying factor of 3.6 that shows up converting between them.

The other day I read An Argument for Dozenalism that made many of these arguments. Nothing new. However it made the interesting point that ideally a dozenal arithmetic would have its own set of glyphs. It suggested that 0 and 1 could be kept, but everything else should be changed. In my opinion that argument is correct, it is very confusing if 21 sometimes is 5*5 and sometimes 3*7, which makes a mixed dozenal and decimal world harder than it needs to be. But this raises the interesting question of what a logical dozenal set of glyphs might look like.

I've amused myself with thinking about this, and I have a proposal for a set of glyphs that are (mostly) unused, easy to learn, quick to draw, and are much more logical than existing ones. All have a vertical line in the middle. At the top there is a choice of a hook starting on the left, a straight end, or a hook starting on the right. At the bottom there is a choice of a hook ending on the left, straight down, on the right, or bending right to cut across the vertical line. This gives 12 possibilities. By incrementing the bottom first, and the top when you get a carry, you get a sort of a 3,4 base. Which means that a glance at the glyph tells you immediately its sign mod 4. A glance at the top tells you whether it falls in the range 0-3, 4-7 or 8-11.

So instead of the current system of 10 random symbols to memorize, you get two simple rules. While at first it seems bizarre, it grows on you quickly. And it gives you a very quick way to tell whether a given number is written in decimal or dozenal. To get a sense what it looks like, take a look at the 12 times table (my apologies for the handwriting - my none too good penmanship gets worse when I'm using a mouse pad to draw with):



Note in particular how regular the patterns are for 2, 3, 4, and 6. Doesn't this look easier to memorize than the decimal times table? As an exercise try writing out your favorite sequences. Whether you're writing out squares, powers of 2, or primes you'll see that more patterns leap out at you in dozenal, making them easier to learn.

So there is my humble contribution to a dozenal future.

(In other news, I now have a patent to my name, though in fact it is owned by a previous employer. By the standards of the patent system, it is not a particularly bad patent. But if I had my druthers, it would have never been filed. Ah well.)

The stock market thinks Microsoft has just under 4 years left

(I posted this basic analysis at http://news.ycombinator.com/item?id=1417156, which was a discussion of this Newsweek article, and then decided that it was interesting enough to call out for additional attention.)

Those of us who pay attention to finance know that the market tends to be more accurate than any individual person. So sometimes it is worth analyzing what the market is saying about different companies.

If you look at the stock market, it clearly saying that Microsoft's future doesn't look as bright as Google's or Apple's. That's why Microsoft is worth a P/E of about 13, while Google is worth one of 22 and Apple is worth one of 21.

The market projection gets substantially more stark when you subtract current book value to find how much the market values future revenue. (Book value is what all of the company assets would be worth if it was broken up and sold today. For Microsoft this is largely made up of their cash reserve.) Microsoft's market cap is 221 B, their book value is 46 B, and therefore 175 B of their market cap is projected future earnings. Their current profit is 46.28 B/year, and that works out to the market valuing them at their current earnings stream projected over a bit under 4 years.

For Google the equivalent exercise says a market cap of 154 B, and book value of 38 B so 116 B of market cap is projected future earnings. Their current profit is 14.81 B/year, which translates into the market valuing them at their current earnings stream projected over a bit over a decade. (10.4 years.)

For Apple the equivalent exercise says a market cap of 225 B, a book value of 39.4 B for 185.6 B of market cap due to projected future earnings. Their current profit is 17.22 B/year, which translates into their current earnings stream projected over a decade. (10.8 years.)

So the projection that Microsoft is walking over a cliff in a few years while both Google and Apple have a decent future. The market is perfectly aware that a lot changes in 10 years, and so they heavily discount any projections out that far. But the market is more likely to be correct for near events.

Now admittedly I've never liked Microsoft. But this isn't just claimed by some random haters on the Internet. This is the consensus of the stock market, which is based on a lot of informed people putting their money where their mouths are. This is worth thinking about.

(I took all figures for this from http://finance.yahoo.com/q/ks?s=msft, http://finance.yahoo.com/q/ks?s=goog and http://finance.yahoo.com/q/ks?s=aapl. I got book value by multiplying book value / share times shares outstanding.)

Le Châtelier's principle: not just for chemists

I seem to be updating my blog once a month or so. I don't intend to do that, I'm just busy. This particular entry is one I've been meaning to write for months, but just haven't gotten around to.

But before I get to it, a brief digression. My sister would like to get into a poker tournament that she needs to be voted in to. If you could take a moment and vote for Jennifer Tilly, it would be most appreciated. Thank you.

Now on to the main subject. One of my favorite principles of chemistry is Le Châtelier's principle. It has several forms, but the most general (though admittedly not perfectly accurate) is Any change in status quo prompts an opposing reaction in the responding system.

What does this mean? Well let's take a simple example. Suppose we have air in a chamber, and apply pressure to compress the chamber. From Le Châtelier's principle we expect it to push back harder. In fact it does. From the ideal gas law, applied in a simplistic way, once the volume is cut in half the pressure will double, and it will indeed be pushing back harder.

However this understates the true effect. It turns out that the act of compressing the chamber heats up the gas, increasing the temperature, and this causes it to push back even harder than it would have otherwise. This rise in temperature when you compress is called adiabatic heating. The corresponding decrease in temperature when you decompress a gas is used inside of your refrigerator or AC system to move heat from a cool place to a warmer one. Similarly when warm air rises the pressure drops, which causes it to cool down. This is why air on mountain tops is colder than air at sea level. (The drop is about 10C per km of height.)

Anyways, the fine details notwithstanding, what we find is that when you push harder on this simple system, it winds up pushing back harder. And you eventually find yourself at another equilibrium. Furthermore what works for simple systems, works for many more complicated systems.

The big question that I had as a kid in chemistry class was why. Why does this always work out? I never got a good answer from my teacher, and my dissatisfaction with "it works because it always works" answers was one of the reasons why I chose to go on in math instead.

Interestingly, many years later in an advanced math course I learned the trivially simple answer. Which requires essentially no math to understand!

Here is that answer.

A system is at equilibrium when all forces on it are balanced, and it can rest in that state indefinitely. For instance take a pencil and lay it flat on a table. It is at equilibrium there. There is also another equilibrium where it is balanced on its tip, but it is very hard to put it in that equilibrium.

Now not all equilibria are created equal. A stable equilibrium is one where any perturbation of the system will cause it to head back towards that equilibrium. An unstable equilibrium is one in which some perturbation exists that causes it to head away from that equilibrium. In the example of the pencil, laying flat on its side is a stable equilibrium, while balancing on its tip is unstable. The key fact to remember about unstable equilibria is that they have a tendency to not stick around. No real system is perfectly balanced, and the imperfection will grow over time until equilibrium disappears on its own. This is is why we run into lots of pencils lying on their sides, and none balanced on their tips.

Now what does this have to do with Le Châtelier's principle? Well if we run across a system that has settled down to the point that it has a status quo we can notice, that system is extremely likely to be at some sort of equilibrium. Based on the point I made above, we can be pretty sure that it is a stable equilibrium. But Le Châtelier's principle is just a description of what it means to be at a stable equilibrium, so Le Châtelier's principle must be true of our system!

Now I should note that there is a world of difference between a local equilibrium and a global one. The pencil that is flat on the table, would be at an equal equilibrium on a different side, as a small push demonstrates. And at a better equilibrium flat on the floor, as a strong enough push will demonstrate. A mixture of hydrogen and oxygen that is heated at little bit will heat up, which increases the pressure, which causes the container it is in to expand, which cools it down, in accord with Le Châtelier's principle. But heat the same mixture enough and a chemical reaction will begin that results in it becoming hotter still, rather than cooler. (These examples are why the overly general formulation I quoted at the top is not perfectly accurate.)

It is clear that this is a very general argument, and makes it clear that the principle has nothing really to do with chemistry per se. In fact it applies to any sort of equilibrium. In chemistry or not. On the whole I find the examples outside of chemistry to be more interesting.

A case in point appears in the classic economics paper Cars, Cholera, and Cows: The Management of Risk and Uncertainty. One of the key themes is that our risk-taking behavior as a society winds up in an equilibrium. If it is at an equilibrium, then we should expect that any change which reduces risk will cause a some sort of compensatory increase in risk. Which will undo some of the positive benefits of the change. An example from that paper is that seat belt laws increase seat belt usage. But people using seat belts feel safer, and therefore drive more aggressively, resulting in more accidents. The net result? It appears that drivers are safer, pedestrians are less safe, and benefits to society are less clear than a naive analysis would predict.

Over time I've learned that equilibria are extremely common, and therefore the "unexpected consequence" is more often something to try to anticipate than something to be surprised at. For instance when a faster variation of cheetahs is bred by evolution, it creates pressure for antelope to become some combination of faster, better at spotting predators, and willing to bolt when predators are farther away. The net result is that the more effective predators wind up about equal versus their prey. (Look up the Red Queen Hypothesis for more on this.)

But how do you anticipate the unexpected? Well there are several ways.

1. If you know that it is common to find some sort of push-back, you know to be on the lookout for it, which will make it easier to spot. For instance suppose that you start injecting a stable compound in at a constant rate. Eventually it has to break down at the same rate, the only question is where. It was not until Sherry Rowland and Mario Molina applied this line of reasoning to CFCs that it was realized that one of the most innocuous and inert chemicals discovered by man was destroying the ozone layer.


2. There will be a set of related push-back phenomena associated with any stable equilibrium that you can find. However equilibria are very common. So look for potential equilibria, then actively ask how they are maintained. If you find them, you frequently learn something useful. For instance suppose there is an equilibrium level of major disasters in given area of human endeavor. By what means is this level maintained? I submit that it is maintained by memories of previous disaster, and desire to not experience that again. Which means that once memory fails and people become less careful, corners will be cut until disaster happens again. However memory fails on a time scale set by human lives, which tells me that an equilibrium rate for major disasters of any particular kind is never going to be more than a small number of human generations, no matter what the engineers promise us. For example it took just over 60 years to lose the regulations that were put in place to prevent another credit crisis like the one that started the Great Depression (and about 10 more years after that to experience a credit crisis - note that before the Depression credit crises arrived on average about once every 10 years), nuclear options are now getting a boost from the fact that memories of Three Mile Island are now fading, and I am willing to bet serious money that the surprisingly good record of safety devices for offshore drilling helped result in dangerous shortcuts that were key to causing the recent BP disaster.


3. Certain equilibria and their corresponding compensation mechanisms come up very frequently to explain otherwise puzzling events. My favorite example is that people like to maintain a positive self-impression. The result is that anything that challenges our good opinion of ourselves causes serious cognitive dissonance. People do the most amazing things to avoid this cognitive dissonance. For some of the negative results on people's ability to learn, see What you refuse to see, is your worst trap.

So, even if you're not a chemist, if you squint at the world in the right way you can see Le Châtelier's principle popping up in the most unexpected and interesting places.