Miscellany

Things I would blog about, if I weren’t on blogging vacation.

• A short piece I wrote for Seed about the arrow of time is now on the web. It’s basically a summary of the scenario that Jennie Chen and I are suggesting for spontaneous inflation. On a related note, Karmen at Chaotic Utopia has a series on complexity and time, starting here.
• Cocktail Party Physics advertises a call for proposals from Feminist Press.
  

  Girls and Science: Call for Proposals

  The Feminist Press, in collaboration with The National Science Foundation, is exploring new ways to get girls and young women interested in science. While there are many library resources featuring biographies of women scientists that are suitable for school reports, these are rarely the books that girls seek out themselves to read for pleasure. What would a book, or series of books, about science that girls really want to read look like? That is the question we want to answer.

  I don’t know; seems to me, if we start encouraging girls to become scientists, pretty soon they’ll be replacing equations with hugs and instead of performing experiments we’ll just talk about our feelings or some such thing. That can’t be right.

• Janna Levin, author of the uniquely compelling How the Universe Got Its Spots and the brand-new A Madman Dreams of Turing Machines, appeared on the Colbert Report! I can’t actually get the video to play, but maybe you can.
• Chris Mooney’s The Republican War on Science is now out in paperback. So all you poor liberals who couldn’t afford the hardcover edition now have no excuse.
• Speaking of books, Alex Vilenkin has come out with Many Worlds in One, about eternal inflation and the multiverse. Alex was the one who first realized that inflation could be eternal, and is a world-class cosmologist; whatever you may think of the issues, he’s worth listening to. (And don’t tell me that we cosmologists can’t have a little fun.)
• And Michael Bérubé also has a book out, What’s Liberal About the Liberal Arts?. So many books. Don’t these people know they’re wasting valuable time that could be spent blogging?
• George W. Bush has decided to close EPA regional libraries, to protect the public from information they don’t need.
  

  What has been termed, “positively Orwellian”, by PEER Executive Director Jeff Ruch, is indeed frightening. It seems that the self-appointed “Decider”, George W. Bush, has decided to “end public access to research materials” at EPA Regional libraries without Congressional consent. In an all out effort to impede research and public access, Bush has implemented a loosely covert operation to close down 26 technical libraries under the guise of a budgetary constraint move. Scientists are protesting, but at least 15 of the libraries will be closed by Sept. 30, 2006.

• On the other hand, John Kerry draws support from unseemly quarters, at least according to Yousuf al-Qaradawi.
  

  Kerry, who ran against Bush, was supported by homosexuals and nudists. But it was Bush who won [the elections], because he is Christian, right-wing, tenacious, and unyielding. In other words, the religious overcame the perverted. So we cannot blame all Americans and Westerners.

  So we really shouldn’t complain about the President.

• Weak lensing, uploaded to flickr by darkmatter. Amazing photos.

Sometimes the technological marvels that are the most useful are those you didn’t even know you needed. Here is a perfect example: from iFone, a version of Monopoly for your cell phone. That’s right, Parker Brothers’ classic board game, downloadable for a few bucks, so that you can match your wits against one or more computer players whenever you like. (One jarring feature of the iFone version: it’s a British company, so all the properties are named after places in London, rather than Atlantic City. Mayfair instead of Boardwalk, Trafalgar Square instead of Indiana Avenue, etc. Disconcerting.)

Monopoly, of course, is famous for being that game you used to play as a kid that never quite finished, since it took forever for someone to win. The cell-phone version is no different, but it’s trivial to stop and start again much later, and the patience of the little phone CPU brain is enormously better than that of your brothers and sisters. In fact the computer players are pretty good — they are capable of making trades and all that, and they’re smart enough to value a property very differently depending on whether it will complete a full set of one color or not. But there are a few things the computer doesn’t quite understand; for example, completing a monopoly is much more valuable for a player that has enough extra cash to start building properties than for one who is completely cash-poor. And building houses is the key to actually winning the game; the computer is also reluctant to mortgage a few properties in order to build on some other ones, a classic mistake.

So overall my cell phone provides a challenging opponent, but one I can usually beat. It does my sense of self-worth good to know that I am so much smarter than a piece of high-tech equipment. And the story of my stirring come-from-behind victory while waiting in the customs queue at Heathrow will be celebrated by epic poets for generations to come (or would be had there been better documentation of the event).

But the interesting things, not having played Monopoly for years, are the moral and political implications that follow from the game. We think of Monopoly as the quintessential embodiment of laissez-faire capitalism: a competition within the unfettered free market, starting from a level playing field and allowing nature to take its course. Which is all true. But what the game really illustrates are the shortcomings of capitalism, as effectively as one could imagine; if I didn’t know better, I would think that Karl Marx himself had designed the game. Consider:

• The game perfectly demonstrates the instability of the free market (which it should, if someone is going to “win”). That is, the rich get richer, as they can leverage their wealth to increase their earnings. Makes for a better board game than a society.
• Talent does not win in the end. Sure, there is some judgment involved in when to make certain trades with other players, but the biggest single factor in winning or losing is a literal roll of the dice! How bleakly fatalistic can you get?
• The playing field is initially level, but only in a completely artificial way. It’s perfectly clear that, if the game worked like the real world in which some people were born into wealth and others were not, the aforementioned benefits of being rich would absolutely dominate. Not much room for social mobility. A devastatingly effective argument for preserving the estate tax!
• Most telling of all: your income does not come from working, it comes from collecting rents. Later in the game, when a few players have started to build houses, you quickly discover that you lose money during your own moves, and only make money during the other players’ moves.
• It follows that, later in the game, the best square to land on is Go To Jail! From the comfort of Jail, you don’t have to worry about paying rents to anyone else, but you are free to accumulate wealth from your own properties. It’s really just a vacation resort for white-collar criminals.
• The only mildly redistributive action that occurs in the game is the rare-but-devastating “building repairs” card that comes up occasionally in Chance and Community Chest, and which does impact the rich disproportionately. But, significantly, the money doesn’t go to other players, but to the Bank (which is the real source of evil in the whole game).
• On the other hand, the game does make you hate the Income Tax. So there’s some mixed messages there.

So I’m thinking that there is quite a subtle subversive message in the dynamics of Monopoly, now being spread to a new generation through their handheld gadgets. Of course, one must already be of a suspcious cast of mind to read the above features as cautionary tales; if cutthroat competition is more your style, you might just think they are cool.

Nevertheless, as we have been known to fearlessly suggest improvements in the world’s classic games, I have a couple of ways to make Monopoly even better — more equitable without having the income distribution settle into some happy socialist equilibrium where incentives are balanced against economic guarantees. (Where would be the fun in that?)

• To increase the role of skill in the game, change the dice-rolling procedure. Instead of simply rolling two dice and dealing with the consequences, players should be able to pick the number on one die, and then roll the other to calculate the number of spaces they are to move. Chance is obviously still involved, but a bit of calculation would be introduced, in weighing the relative merits of avoiding that property vs. being able to reach this other one. I certainly hope that the real world works like this at least a little bit.
• To prevent criminals from benefiting from their crimes, allow other players to spring for the $50 fine (or 50 quid, in the British version) needed for someone to leave jail — and allow them to do so whenever its their turn, regardless of the criminal’s actual wishes. Again, a bit of skill is introduced, as the other players will have to judge whether it’s worth their money to spring someone from the pen, or whether they should hope that someone else will do so.

Sadly, I can’t implement these genius suggestions on my cell phone. And nobody actually wants to play the game in person any more. Still, it’s important to fight for a just and equitable society, even in rather imaginary contexts.

There will be a conference in memory of Andrew Chamblin at Trinity College, Cambridge, on October 14. The registration deadline is September 1. Anyone who knew or worked with Andrew is encouraged to attend. Andrew, a theoretical physicist who several of us here at CV knew very well, passed away in February, and there was previously a conference in his honor in Louisville in March.

I know the tension has been building, so without further adieu, I present the answers to our poker quiz! And you should listen to what I say, as I am a recognized expert in the field.

Remember the set-up: you’re playing Texas Hold’Em, so you have two cards to yourself, and (eventually) five cards face-up in the middle, and your hand consists of the best five cards you can choose from your two and the five community cards. Which of the following has the best chance of winning against somebody else’s (unknown, obviously) cards at a showdown?

• Jack-10 suited
• Ace-7 unsuited
• Pair of 6’s.

Note that this is not really a poker-strategy question, it’s just a math question. There is a separate issue, which is “which is the best starting hand”, or for that matter “how should you play each hand?” — we’ll get to that later. But this is just a math problem — which is most likely to win if you choose to stay in the pot all the way to the showdown?

The answer, to nobody’s suprise, is: it depends! It does not depend on your position, or whether the betting is limit or no-limit — those might affect your strategy along the way, but at the end of the hand it’s just a matter of who has the best cards. What it does depend on is how many people you are playing against. The absolute probability that you will win obviously goes down if you are playing against more opponents with randomly-chosen cards, just because there are more ways they could beat you. But, much more interestingly, the ordering of which hand is best also changes.

Here are the answers, presented in convenient tabular form. We’re showing the percentage chance that your hand will win outright, both against one other random hand and against four other random hands. The percentages come from running 500,000 simulated hands each, using the Poker Academy software. (It’s a very nice program, incorporating artificial-intelligence routines developed by the University of Alberta Poker Research Group. [Yes, there is such a thing.]) “Jd” stands for jack of diamonds, “Td” for ten of diamonds, etc. For later convenience we’ve chosen the ace to be the same suit as the JT, with all other cards being different suits (it doesn’t matter for this table, but does for the next one).

So the miracle is that the relative strength of the three hands reverses when we go from one opponent to four. Against one other player, the sixes stand the best chance, followed by the A7, followed by the JTs (where “s” stands for “suited”). But against four, JTs is the most likely of the three to win, while the sixes are the least.

It’s not hard to figure out what’s going on. But before we do, let’s take a peek at something even more surprising. What happens if, instead of putting one of these three hands against some other random cards, we put them up against each other, two at a time? What is the relative ranking? Here is what happens:

The table shows the chance that the hand listed on top will beat the hand listed on the left side at a heads-up showdown (no other players). The entries don’t add up to 100% because there can be ties . So, another miracle: it’s not transitive! Sixes are likely to beat A7, and A7 is likely to beat JTs, but JTs is likely to beat a pair of sixes. It’s a kind of combinatorial rock-paper-scissors situation.

So what is going on? Note that if we consider just the two hole cards, without taking advantage of the community cards, the sixes are the best hand, followed by the A7, with JTs bringing up the rear. For one of the latter two to win, the community cards have to help it improve (by pairing one of the hole cards, or making a flush, or whatever). So the question becomes, how many ways are there to improve? The only likely way for the A7 to improve is for either an ace or a seven (or both, or several) to land on the board, although it’s also possible to find four board cards that help make a straight or flush. Adding up the probabilities, it’s almost a fifty percent chance, but not quite. Against the sixes, there are more ways for the JTs to improve. Both because the cards are “connectors,” allowing for cards that would give low straights (7-8-9) and high straights (Q-K-A) or various intermediate possibilities, and because the cards are suited, making it much easier to make a diamond flush. So JTs will usually beat a pair of sixes. But it won’t usually beat A7 if the ace is of the same suit. That’s because some of the ways that JTs will improve will also improve the A7 — in particular, if four diamonds come up, the JT will have a flush but the A7 will have a better one.

The same reasoning explains the first table. Against only one randomly-chosen pair of hole cards, there is a substantial chance that the sixes won’t need to improve, so they do the best; likewise the ace can often come out on top just by itself, so it’s second-best. But against four opponents, chances are excellent that someone will improve, and JTs has the best chance.

Which leads us to the other question: which is the best starting Hold’Em hand? It should be clear that there is no universally correct answer, and it will depend on game conditions — although, in ordinary circumstances, JTs is clearly the best, for a couple of reasons. One is that the thought experiment of playing your cards against another pair of randomly-chosen hole cards isn’t what really happens; in a real game you have a bunch of opponents, and the ones with weak hands simply fold, leaving only the stronger hands. So it’s almost as if you are playing against a larger number of opponents, even if a small number stay in for the showdown. The other reason (much more important) is that the criterion for success is not how many hands you win or lose, but how much money you win or lose. The A7 is not going to make you much money. If no ace comes up on the board, you’re likely beaten. If an ace does come up, either someone else has an ace with a better kicker (in which case you will lose a lot), or nobody has an ace and they will just fold (in which case you will win a little). Likewise for the sixes — if nobody can beat a pair of sixes, they’re not going to be putting much money into the pot. The only way to win big is if another six comes up, which is possible but unlikely, and you’d still have to worry that someone else made a straight or flush. This is why beginning players often over-value low pairs and aces with low kickers.

The moral of the story is that you don’t win in Hold’Em by knowing the percentage chance that your pocket cards can beat some other random two cards — you need to know what kind of hand your opponents are likely to have. Part of that is just probabilities, but much of it is gleaning clues from the way they have played the hand up to that point (did they raise, or call? how many bets? from what position?). In other words, you need a model of your opponents. Poker players have invented a simple two-dimensional parameter space of ways to play that serves as a simple model. One axis ranges from loose to tight — how often someone plays vs. folding. The other goes from passive to aggressive — how often someone simply checks or calls vs. raising. At the crudest level of analysis, you can locate an entire table of players at some point of the tight/loose and passive/aggressive plane; with a bit more data, you can describe individual players this way, and at a very sophisticated level you can get as specific as you like in an extremely high-dimensional parameter space (“they like to raise 80% of the time with pocket nines or better in fifth position with one bet and one caller before them when their stack is less than half of its starting value,” stuff like that).

That’s why it’s much harder to program a computer to be a championship-level Hold’Em player than a championship-level chess player. There is no perfect strategy in Hold’Em — no decision tree you could unambiguously follow to guarantee the best possible outcome. (Indeed, if you had an opponent that used such a decision tree, you could in principle always beat them.) Unlike in chess, the computer can’t win by brute force; it needs to be clever enough to learn from the previous moves of its opponents to figure out how they are playing. Teaching computers to play poker is an active area of research in artificial intelligence. And teaching humans is an active area of research in Vegas (although the “tuition” can get a little steep).

… to Sabine and Stefan!

I don’t think I recall any previous instances of physicist-marriage-blogging. Another first!

“Fusion” is an important concept in nearly all artistic fields — music, cooking, painting, what have you. Each endeavor tends to feature multiple strongly-identified styles — Mexican food, Japanese food, Ethiopian food…; Jazz, Classical, Rock…; Impressionism, Abstract Expressionism, Pop… — and it is fun to mix and match to obtain exciting new combinations. Here in Chicago, you can visit SushiSamba for Latin/Japanese cuisine, then head over to the Empty Bottle to listen to some jazz/rock hybrid.

Despite the excitement, however, genres do not just blend together to form one homogeneous goop. While styles evolve, they are typically held together by distinct aspects setting them apart from other approaches. (Latin/Japanese fusion will never grow in popularity to displace the authentic cuisines of either region.) This can be informally understood through the concept of a fitness landscape, a function of the underlying variables that describes how successful a certain approach ultimately is. A typical fitness landscape has peaks and valleys, indicating that particular combinations work well together, much better than a random mish-mash. Imagine setting aside our delicate sensibilities for a moment to contemplate a giant “food machine” (or “music machine” or whatever) that can create any dish we want, simply by adjusting the position of a large set of dials. (A thought experiment, okay?) There’s a dial for the amount of jalapeno peppers, another dial for how long the food should be cooked, and so forth. There is a region of dial settings that corresponds roughly to “Japanese food” and another that corresponds to “Latin food.” If we simply adjust the dial setting to be a linear combination of the Japanese and Latin settings, the likely outcome is — some sort of horrifying mush. We would find ourselves in a valley of the fitness landscape where nobody would want to live. In other words, different approaches to cuisine (or other artistic endeavors) tend to cohere into sensible and distinct groupings, and random mixtures between them are unlikely to be an improvement; successful fusion is a delicate art.

Interestingly, however, there is a well-known counterexample to the peaks-and-valleys structure of aesthetic fitness landscapes: human faces. It’s been known for a while now that if you take a selection of randomly-chosen people, and construct a picture by averaging their features together, the result is typically a more attractive person. The phenomenon is extremely easy to notice in examples. Alex Tabarrok at Marginal Revolution writes about an experiment that tested this conclusion. He extracted this figure from Judith Rich Harris’s book No Two Alike. From top to bottom, it shows some actual faces, then the average of two faces, four faces, and so on up to 32 faces.

For an even more striking demonstration, see The Face of Tomorrow, a photography project that takes portraits of random people in certain cities around the world and blends them together (city by city), with the idea that these composite portraits will resemble future citizens in an increasingly interconnected world. (Alas, real heredity doesn’t work that way — stupid discretized genetic code.) Go to The Faces and click on a city to see the composites decomposed into the individual people. The future, I have to say, looks pretty hot.