Article: Vegas comes to Ohlone, if only for a day - Mathematics Department in the News

Vegas comes to Ohlone, if only for a day

By Eric Dorman, Editor-in-chief.

Thursday, October 23, 2008—Reprinted from Monitor.

Jeff O'Connell demonstrating a card game. Math Instructor Jeff O’Connell gambles with students at Friday's Brown Bag Science Seminar. —Photo by Eric Dorman.

Don’t quit your day jobs, folks.

It may not have been the conclusion students were looking for at Friday’s Brown Bag Science Seminar, but it was the advice Math Instructor Jeff O’Connell gave to those hoping to “beat the system,” Las Vegas-style, through card counting.

“I’m not saying you shouldn’t count cards...[but] I don’t think it will work out as well as you think it will,” O’Connell told the packed house at the seminar, entitled “21—The Math Behind The Movie.” In the talk, O’Connell examined how likely it is for one to consistently make money at blackjack and other card games through card counting (answer: not very) and whether the claims of the card counting-based movie “21” were exaggerated (probably).

“21,” a film released in March, chronicles the story of how 6 MIT students made millions in casinos through card counting—the process of keeping track of the cards already played from a deck and modifying one’s bet based on the odds of a particular card appearing. “21” is based on a true story, but O’Connell suggested, through math and card-playing demonstrations, that the claims might have been exaggerated.

O’Connell began the talk with a simple premise: “If you want to try to beat the system, you have to understand the system.” Understanding the system, O’Connell explained, has to start with understanding “expected value”—the average loss or gain a player can expect to see in a given game. A game in which the odds are in your favor will have a positive expected value, while one in which the odds are against you will have a negative one.

But in general, there’s no need to calculate the expected value in a casino game. Why? “Every single game played in a casino has a negative expected value,” said O’Connell. “Negative expected value is the system.”

This isn’t to say it’s not possible to win money in a game at a casino, said O’Connell. In fact, a quick poll revealed that many of the audience had. If you only play a given game a small number of times, the probability of winning, while low, is still significant. However, if you play many games, the probability of coming out ahead decreases drastically—a rule known as the “law of large numbers.” Thus, while some bettors playing roulette, for example, may walk away from the table with more money than they started with, the vast majority will lose money. It is the law of large numbers that the casinos are betting on, and it’s because of this that they are able to pull in a steady cash flow (for example, a roulette player can expect to lose, on average, 5 cents per $1 bet).

So if the expected value is always negative, how can one consistently make money at a casino game? While it is statistically impossible to consistently make money at a game of chance like roulette, said O’Connell, games of strategy—like blackjack—are a different story. In roulette, every spin of the marble is independent (in other words, it is not influenced by prior spins), but in blackjack, cards already played do influence later hands (because the already-played cards are no longer in the deck).

This fact is vital for the success of card counting, O’Connell explained. In blackjack, higher cards tend to form better hands than low ones, so a common card-counting scheme (called the “high/low strategy”) calls for the bettor to assign each card played from the deck either a “+1” if the card is low or “-1” if it’s high. This way, a player who keeps track of the “count” of the deck can maintain a rough idea of the odds of a particular card coming up. For example, a deck with a low count still has many low cards in it, while a deck with a high count is stocked with valuable face cards (suggesting that it’s a good time to bet).

With a little more math, the player can obtain a more accurate assessment of the deck’s content by calculating the “true count”—the basic count divided by the number of decks left.

All this math pays dividends, said O’Connell, when the true count climbs above “+2”—at this point, the player has a one percent advantage over the house. It is with high counts like these that the characters in “21” made their millions, and it was with these kinds of counts that other educated gamblers could presumably make their fortunes, too.

To test how well this really worked, O’Connell staged an experiment with six students and six decks of cards, pre-loaded with high counts. Even with the favorable decks, the house (whose duties were performed by O’Connell) still came out ahead.

Even assuming card counting provided that one percent advantage, though, said O’Connell, the financial rewards were slim and somewhat risky. Betting $100 per hand, one could expect to make an average of about $50 per hour using the strategy, he said—but the margin of error for that figure was a whopping $2,800 per hour. So, on any given hour of playing, a card counter can expect to win anything from $2,750 to a loss of $2,750.

After examining the math behind card counting, O’Connell told the audience why he has never counted cards and has no intention of ever doing so: the tremendous amount of work that goes into it isn’t justified by the modest (and questionable) rewards. “I think the movie exaggerated things greatly,” said O’Connell. “I think it made [card counting] seem like the silver bullet.” In his own experiments, said O’Connell, the success of the method has not been clear.

The clincher, though, came with a segment from “21” O’Connell showed at the talk’s conclusion. The short clip showed one of the MIT gamblers facing the wrath of a casino hit man. In the clip, the hit man (played by Laurence Fishburne) accosts the student and teaches him a violent lesson about the consequences of attempting to outsmart a casino. “Think you can beat the system?” Fishburne intones to the cowering and bloody student. “This is the system—beating you back.”

“Stop counting.”

The next Brown Bag will be held Friday, Nov. 7 from 1 to 2 p.m. in Room 3201. The speaker will by Adjunct Anthropology Instructor Mark Dobbs, who will deliver a talk called “Forensic Anthropology.”