Monday, May 5, 2008

Evolution, 21, the Gamblers Ruin, and Zero Sum Games

One of the favorite fallacious arguments of the evolution deniers is to claim that statistics somehow make it impossible for evolutionary mechanisms to work. Invariably however, their arguments contain fundamental flaws in their assumptions. The most common of these is the assumption that all evolutionary events are independent (Hoyle's 747 in a junkyard), when they are in fact extremely dependent. It can be very tiresome seeing these same lame arguments over and over again, so it is somewhat refreshing to see Sal Cordova make some brand new mistakes in his newest article called Gambler's Ruin is Darwin's Ruin. Unfortunately, it is a tiresomely long piece, containing several subtle errors, the most important being that evolution proceeds in an unwavering, unfailing, line of ascent, instead of one with many failures, and as a zero-sum game. Once one understands this, Cordova's argument collapses.

He attempts to draw an analogy between counting cards in blackjack, as depicted in the Movie "21" and the evolution of species. However, his knowledge of gambling is apparently quite limited, and prone to making ridiculous statements like this:

"The real story behind the movie began with an associate of Claude Shannon by the name of Dr. Edward O. Thorp of MIT. In the Early 60’s, Thorp published a landmark mathematical treatise on how to beat casinos. His research was so successful that Las Vegas casinos shut down many of their card tables for an entire year until they could devise counter measures to impede Thorp’s mathematics."

As a former card counter, I can say this is complete nonsense. Thorpe's system, while no doubt groundbreaking and ingenious, received considerable criticism from other mathematicians, and even at the hyped 5% edge, would still not allow just anyone to walk into a casino and leave a winner on a consistent basis. All the casinos did was move the "cut" in the "shoe" of cards used for play, further from the end of the deck, where the counter's advantage is maximized. They could also "shuffle up" on suspected counters (thus nullifying the count), and as a last resort, being private clubs, they could simply bar the counter from playing. Thorp did not cause Las Vegas card tables to come to a stop.

Cordova further illustrates his ignorance when attempting to explain what a statistical advantage in gambling means:

"If he has a 1% statistical advantage, that means he has a 50.5% chance of winning and a 49.5% chance of losing."

No, that isn't what it means. That would be the case only in a game that resembled coin flipping, with a win paying the amount of the wager. However, in most Vegas games, such as blackjack, there are several plays, such as splitting hands, doubling down, or getting a blackjack, which pay far more than the wager. The same can be said for craps, the other game Cordova mentions. A player in such games with a 1% edge can expect to win, on average, 1% of the amount of his wager, per play. He will most certainly NOT expect to win 50.5% of his plays as Cordova suggests.

So right away Cordova reveals that he doesn't understand the basics of the subject of his article. He also doesn't seem to understand the concept of Gambler's Ruin, which he also tries to tie to evolution. The Gambler's Ruin refers to when a gambler loses the last of his stake, goes broke, and can no longer gamble. This comes into play for professional gamblers because no matter what advantage you have, there is still a nonzero possibility that you will run into a long enough streak of bad luck or mistakes to exhaust your funds, or "bank". Thus, such gamblers use statistical analysis to determine the size of a bank they need to keep their probability of ruin sufficiently low given the edge they have and the wagers they will place. For example, a blackjack player with a 3% edge and wagering $5 a hand would need a bank of about $275 for a probability of ruin of 5%.

How does any of this apply to evolution you ask? Well, Cordova attempts to draw an analogy between the gambler's bankroll and the population of biological organisms with new genetic variation:

"The problem is that a selectively-advantaged traits are still subject to random events. The most basic random event is with whether a parent will even pass down a gene to a child in the first place! Added to that problem is the nature of random events in general. A genetically advantaged individual may die by accident, get consumed by a predator, etc.

And the problem gets worse. Even if selectively advantage traits get spread to a small percentage of the population, it still has a strong chance of being wiped out by the sum total of random events. The mathematics of gambler’s ruin helped clarify the effect of random “selection” on natural selection...Darwin was absolutely wrong to suggest that the emergence of a novel trait will be preserved in most cases."


But Darwin never suggested that, and modern evolutionary theory certainly does not say that. Cordova is criticizing the old, flawed, single unbroken line version of evolution, which no one supports today. In doing so, he is erroneously applying the ruin theories of gambling to a single evolutionary line, rather than the entirety of life. In his view, showing one line would die out disproves the entire theory. But in evolutionary terms, everything that is alive is part of the genetic "bank". Cordova's analogy is to a single session of a gambler's day, which could, of course, be a loser, not the entire bank.

Evolution is a giant bush with many branches and twigs that did in fact hit their ruin, just as population genetics predicts. Cordova's representations of the views of Darwin, as well as Thorp and Fisher, are simply inaccurate. None of them believed that 100% of creatures born with beneficial mutations would survive.

From there Cordova runs completely off the rails and shows once again that his understanding of evolution is little better than his understanding of gambling:

"A further constraint on selective advantage of a given trait is the problem of selection interference and dilution of selective advantage if numerous traits are involved. If one has a population of 1000 individuals and each has a unique, novel, selectively-advantaged trait that emerged via mutation, one can see this leads to an impasse – selection can’t possibly work in such a situation since all the individuals effectively cancel out each other’s selective advantage."

This contains so many errors it is difficult to know where to start. Most basically, a trait cannot be called "selectively advantaged" in a situation where "selection can't possibly work". This is just basic logic. It is either selectively advantaged or it isn't. Secondly, the selection on these individuals is done by many features of nature, not just each other. Sure, if every individual evolves to be a bit faster, that doesn't do much to change who gets to sleep where in the cave. But it sure does effect who outruns the wolves to the cave in the first place. If you and I both evolve traits that make us outrun the wolves where we couldn't before, there is no "cancelling out". We both win.

Third, and most damningly, his analysis has an implicit assumption of stasis with regard to the environment and the new niches the individuals might fill. This is a common mistake creationists make. If I may go all X-men for a moment, some of these 1,000 individuals evolve the ability to fly, others the ability to exist on less food by processing sunlight, and others develop the ability to breath underwater, there will be no "cancelling out". They will simple go live in places, and under conditions where they couldn't before. Everyone wins.

Extending Cordova's argument to gambling shows the zero-sum flaw inherent in it. It is as if he is saying "If all of you at the poker table improve your skills, it all cancels out, and no one will win any more than they did before." And yes, that is true, but only if they remain at that table, or never go play a different game. The players might take their improved skills and move to play Omaha, or craps, or blackjack.

Evolution is not a zero-sum game, and on that faulty premise lie all of Cordova's shoddy arguments. As usual, we see that the evolution-deniers do not understand the subjects they raise, and are too lazy to research them.

3 comments:

ollie said...

On a related note, there is an excellent article that talks about how probability theory is misused by creationists in the New Republic magazine (reproduced by Dawkins.net)

Roughly speaking it goes something like this: suppose 20 distinct mutations must occur within the genome to effect some biological "improvement". Say the chance of each mutation in a given time period (taken independently, which of course, is debatable) is .01.

The creationists tell you that the chances are then (.01)^20, which is very low.

But in fact, what must happen is that each individual mutation must take place and then get fixed by natural selection (or genetic drift), and so one is really measuring the time for 20 individual mutations to take place.

The relevant probability distribution is the negative binomial; that gives one a much, much, much greater probability.

Eeen said...

it's gratifying to see so many blogs popping up that are literate and mathematically and biologically cluey. I think even a decade ago there were too many evolution defenders who just couldn't convey the point. This entry is my idea of an excellent dismissal of the sort of creationist bunkum that takes up, and inspires, way too much web space. Neat neat neat.

In your arguments against Cordova's ridiculous "selection impasse" argument (I'm fighting to hold down my lunch here), I would add that the very next generation will see these advantages distributed unevenly. The magical symmetry invented to support this intuition-pumping argument disappears, and evolution proceeds as usual, even if there is only one environment and only competition within species.

ScienceAvenger said...

Sal claims on that thread that I misrepresented him, but he has no facts back him up.

The fact remains that his original statement is wrong, and demonstrates a basic lack of understanding of the issue. A 1% advantage in blackjack does NOT mean the player has a 50.5% probability of winning, because some of the plays (like a blackjack) pay better than 1:1, meaning the player can have a 1% edge while having a slightly less than 50.5% probability of winning a hand.

That Sal thinks it matters whether he was speaking of a specific set of rules or a specific counting system only reveals even more that he doesn't understand the basics here. But he sure is good at cutting and pasting a lot of impressive-looking irrelevancies to try to cover up that he has no idea what he is talking about.