As Sports Betting Moves Online, Re-Examining Games of Chance

statistics offer a different view of gambling than many games advertise

By Jonny Lupsha, Wondrium Staff Writer

Legal sports betting is shifting increasingly onto the internet, The Westerly Sun reported. Eighty percent of sports bets in New Jersey in 2018 were made via computers or smartphones. Before grabbing your credit card, consider another look at the odds and risks of gambling.

Man using online sports betting apps on phone and laptop at cafe
The statistics involved in gambling show that the house usually wins, in the end. Photo by Kaspars Grinvalds / Shutterstock

According to the Westerly Sun article, legal complications regarding how to regulate online gambling at a state level have kept many states from embracing it. However, betting on football is now legal in 13 states, compared to just five last year. In addition, twice as many states have considered legislation on legal gambling in the first half of this year than in all of 2018—35, up from last year’s 18. However, before you jump in with both feet, take one more glance at a couple popular games of chance to give you an idea of what you can gain—or lose—and maybe even how to improve your chances a bit.

The Mathematics of Roulette

One of the most visually clear-cut examples of how to play the odds comes from the game of roulette. For purposes of discussion, the American version of roulette features two green numbers instead of one.

“A roulette wheel has 38 numbers: 18 of those numbers are red, 18 of those numbers are black, and two of the numbers—0 and 00—are green,” Dr. Arthur T. Benjamin, Professor of Mathematics at Harvey Mudd College, said. “The simplest bet in roulette is to bet on one of the main colors, let’s say red. Since there are 38 numbers, each of which has the same chance of occurring, and 18 of these numbers are red, then the probability that you win is 18 out of 38, which is a little less than 50 percent.”

Since the odds of winning by betting one main color are 18 in 38, the odds of losing are 20 in 38. Dr. Benjamin said the odds equal out to an average of losing 5.3 cents per every dollar you bet.

Alternatively, if you bet on a single number, the average casino pays out 35-to-one odds. “Thus, when you make this bet [for one dollar], then you either win $35 with the probability 1/38—just one winning number out of all 38—or you lose $1 with the probability of 37/38,” Dr. Benjamin said. Amazingly enough, due to the high winnings, it works out to the same loss/win odds mentioned above. “When you play roulette, practically every bet has the exact same expected value of -5.3 cents per dollar bet.”

The Martingale Strategy

One deceptively unprofitable strategy in gambling is called the Martingale Strategy or the “Double Your Bet” strategy. The way Dr. Benjamin describes it is that you bet $5 on red in roulette, and if you lose, you bet $10 instead. “If you win, then your overall profit—you just lost $5 but you just won $10—is a profit of $5,” he said. “If you lose [the second time], well, now you’re down $15, right? So you bet $20, and if you win, you go home with a profit of $5. Otherwise you’re down $35 and you bet $40.”

This sounds like a sound strategy to some, but casinos place limits on bets. Dr. Benjamin offers the following figures, each resulting in a loss. You bet $5, $10, $20, $40, $80, $160, and $320. Now, after seven bets, you’ve lost $635. So let’s assume the roulette table offers a maximum bet of $500. “You will not be able to place a $640 bet, and the odds are good that you will never recover that loss,” he said. Despite the low odds of losing seven bets in a row, the house still wins if we look at 100 people sticking to that rule.

“The chance of losing seven bets in a row is about 1.1 percent,” Dr. Benjamin said. “So if 100 people played this strategy, you could expect 99 of those people to win their $5, and that will cost the casino 99 x $5, $495, but one of those people will be down $635, which makes up for the $495. So as usual, the casino makes a profit.”

Roulette offers a good analogy for sports betting. It’s not that there are no winners, nor that people don’t get lucky, but the odds of coming out ahead may be different than they first appear. If the upswing of proposed state legislation and involvement in online sports betting is any indication, a far larger amount of people may learn that lesson in the next two to three years.

Dr. Arthur T. Benjamin

Dr. Arthur T. Benjamin contributed to this article. Dr. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989.