This site uses cookies. When you browse the site you are consenting to its use. Know more.

The study of betting science

The study of betting science
We have prepared a special article that deals with the study of science on betting; stay tuned!
by Academia   |   comments 0
Tuesday, May 19 2020

To start this journey on the science of betting, we need to go back in time a little bit, more precisely to the last century. In the year 1927, the young Hungarian, John Von Neumann, was only 24 at the time when he gained the notoriety of being the youngest professor at the University of Berlin. However, in his life Neumann had a specific problem: being a bad poker player. When John decided to study the game deeply, he concluded that it was not just a mathematical category. We know that within Poker, there is one of the main tactics for pushing your game forward: the art of bluffing.

After this period, Neumann became fascinated by the theme and soon wrote his renowned article "Theory of Parlor Games". Here, John debuted Game Theory, where in the mathematical field, competition and cooperation strategies are studied. Neumann readily embraced the idea of "zero sum" - where there is only one winner and one loser.

In 1944, John Von Neumann applied his Game Theory directly to economy. Four years after that, in 1948 during the Cold War, Neumann received an invitation from the USA to help them with  a containment strategy against the Soviet Union. John's proposal to the United States was his application of Game Theory: Americans should send a nuclear bomb to the city of Moscow, without giving the Soviets opportunities to create their own. The "zero sum" should take place, as there is no possibility of cooperation: either the US won or lost, simple.

Fortunately or not, John's suggestion was not carried out. In 1949 the Soviet Union carried out its very first nuclear test. Now both powers had in hand the greatest nuclear weapon ever made at that time in human history. The game had changed, it no longer depended on "zero sum". The scenario became the "non-zero sum", which in that situation would be summed up in the annihilation of both States. Since then, the concept of Mutual Assured Destruction (MAD) has emerged, where there is no need to bet on anything, because in the end, both sides lose.

On February 8, 1957, at the age of 53, John von Neumann passed away in Washington, DC Science then lost one of the main names in the study of betting. The mathematician was unable to see the application of Mutually Assured Destruction in 1962, when there was the Missile Crisis in Cuba. However, Neumann's life story makes scientists study his works to this day. According to Adam Kucharski, author of the book "The Science of Luck", the mathematician says that "Bets are a production line of surprising ideas".

All questions of games and games of chance seek to scientifically study a vital point in the scenario, in this case: probability.

Let's see this in practice through dice games.



We know that a typical dice has six sides. If the player plays it, this can give him a chance out of six.

Ok, now if the player rolls two dice, as in the case of casinos, there will be a small margin of probability of winning, as there will be 36 possible pairs at the table, making a total of 21 different combinations.

An advance warning, never bet on the numbers 2 and 12. The player will have only one chance out of 36 to win at the table.

The most viable bet would be on number 7, because only six combinations have this sum. That is, a chance between 6 to drop 7.

Going back a little more in time, in the 16th century, more precisely in the lifetime of the polymath, Girolamo Cardano (1501 - 1576), who studied precisely all 36 combinations of dice. Cardano had noticed then that some combinations were more likely to come out than others.

Advancing now to the 18th century, the mathematician of Swiss origin, Daniel Bernoulli (1700 - 1782), realized that people choose to make low value bets, aiming at greater security and with a low profitable return than to risk in higher value plays. In other words, whoever has less money, prefers to guarantee their safety than to risk what they probably do not have. Bernoulli then created the Theory of
Expected Utility
, which serves as the basis for lotteries, insurance industry and health plans. This refers to periodic payments, in which case the person both wins and avoids a possible invoice. Both cases use the same logic. Everything originated from gambling: the probability and the behavior of the human being.



Now entering our present time, the 21st century, scientists are still studying the science behind the cards. Although we have the help of technology, computers, robots and so on, it is still extremely complicated for these devices to dominate Poker, because there is a lot of information during the game and, even worst of all, incomplete. During the game of poker, the player will never know the hands that his opponent has, so he needs to assume countless possibilities of winning or losing. Opening the doors for bluffing to enter the scene and the behavioral analysis of your opponent.

A specific case occurred in 2017, when four renowned poker players, Dong Kim, Jason Les, Daniel McAulay and Jimmy Chou played against the Liberatus program. More than 120,000 hands were played over 20 days at the Rivers Casino, located in Pittsburgh. The machine took $ 1.7 million. The program played in an unpredictable way and no one could predict its bluffs, since the program had three different algorithms in its script:
Effort learning:

Here the machine plays trillions of hands against itself for months, in order to make an error. Thus the program covers infinite plays.

Match Analysis:

Here the machine when facing an opponent, the algorithm activates and analyzes the entire game, predicting choices and scenarios during that situation.

Resetting Defaults:

Finally, after a long period of games, opponents end up noticing a certain frequency in which the machine emits its moves. Then comes the third algorithm that completely zeroes the behavior patterns of the machine.

Thus, an opponent impossible to win.

According to Jonathan Schaeffer, his view on the mechanism applied to Poker “It is a perfect microcosm of many situations we encounter in the real world”, says the artificial intelligence researcher at the University of Alberta, located in Canada. Scholars conclude that all negotiations are based on incomplete information. This is where technology comes in, which can handle it in infinite ways, even in cyber security, financial areas and medicine on a large scale.


Now let's talk about roulette, we need to go back in 1947, when physicist Albert Hibbs together with Roy Walford, abandoned everything for a period of time, including the University of Chicago. With only their motorbikes, the boys who were only 23 at the time left for the Reno casinos in Nevada. With the simple amount of $ 300, these young men wanted to get rich by applying the laws of physics to gambling. The end of this journey culminated in them raising $ 114,000, after realizing that there were four tampered roulettes in the Palace and Harold's casinos. Everything revolved around the probability of the ball falling into any of the 38 channels, which would be normal in practice, however there were four tampered roulette wheels, so they readily understood how the probability would work on them, thus favoring them.

Later, in 1961, the mathematician Edward Thorp, decided to use physics to circumvent roulettes that were not tampered. However, by carefully observing how the roulette wheel worked, Thorp realized that it would not be possible to predict the result accurately. The ball could fall into any chute, randomly. But it could create an estimate on which part of the roulette wheel the ball would stop, using its base in location and variants, such as speed and acceleration of the object. This would be impossible without the aid of a machine to calculate this information in real time. Soon his colleague Claude Shannon came on the scene.

Shannon was one of the big names in digital technology, being the creator of the first wearable computer - an example of a wearable computer: the SmartWatch. The device measured the same size as a wallet, buttons were installed on shoes and headphones. On the other side there was a watchman who would mark the time of the ball and press the buttons with his feet, then the computer would process the information and emit musical tones to the headphones, warning the player in which of the roulette regions the ball would fall. Several tests were carried out until Thorp and Shannon traveled to Las Vegas to really practice hardcore. Everything went well, but unfortunately the device connections were too sensitive and he always needed to solder them again. As soon as it arrived, the device was quickly discarded. It is currently on display at the MIT museum.


But Edward Thorp's story did not end here, the man was brooding and went on to another game. After learning about the article published by four American soldiers in the 50's, saying that the high cards in Blackjack were favorable to the players, while the lower ones to the dealers. This only made Thorp interested in the area, so he went back to his studies. In 1962 Edward published his new discovery in the book "Beat The Dealer", which uses the card counting technique, which even today professional players rely on.

Here we have the following operation:

While the dealer deals all 52 cards, the number of high and low cards changes in the deck pile. If for some reason a larger amount of low cards is dealt, it means that there are more high cards in the deck pile, so the next cards will be the high cards and the probability only has to favor the player.

But the search for more earnings did not stop there, Thorp dropped everything and started his journey on the stock exchange. He formed an investment fund and got rich in 1969. Fortunately, his studies and teachings have left a legacy and are stored at MIT.


Now turning to the lottery part, James Harvey was a mere math student at MIT when in 2005 he decided to choose this topic for his CBT. Henry noted that no one could match the six numbers for the Massachusetts Lottery, WinFall. This factor caused the game to lose its luster, and that was when the lottery adapted a new way for WinFall to work: when the prize accumulated $ 2 million, the money would be divided to those who had hit three, four or five numbers in the grid . Soon, people went back to buying tickets and playing.

With all this, James wasted no time and started doing his math. There was a way to always win, according to his conclusions.

Henry's perception was based on:

By accumulating the prize the system relieved. Therefore, it was enough to buy a reasonable amount of tickets that would give the winner the biggest most of the prize pool. Because of this, the student asked his colleagues to buy tickets as well, thus gathering around 500 tickets. When they finally got the tickets, they managed to triple the amount invested in the lottery and since then James has taken this as his profession.

The culmination of his feat came in 2010, when Henry noted that the lottery would only reach $ 2 million when the jackpot was $ 1.6 million. So when the figure was close to $ 1.59 million, James acted with the help of MIT mathematicians. They bought tickets and more tickets and finally made a profit of US$ 700,000, after which they reinvested most of the money in betting to continue generating earnings.

Things got tight in 2011, when the scheme was discovered by the Boston Globe. However, it was too late. James Henry and his groups had already spent $ 40 million on tickets, and profitability of US$ 8 million. With this blow, the lottery rules ended up being drastically modified. On the other hand, James abandoned his career and migrated to the Software field in Silicon Valley.

But to end this time travel about betting, let's recap what our pioneers observed and that can still be applied to games.

In a whole there will be 36 combinations;

The most viable bet is the number 7, as there are six combinations for this number to fall.

Never bet on numbers 2 and 12. The player will only have one chance out of 36 of these numbers to fall.

Cards (Blackjack):

The purpose of BlackJack is to approach the number 21;

Thorpe's statistic says that high cards favor players, while low cards only favor the dealer.

The time to bet high will only be when there are the highest number of high cards in the deck pile, as they will come out in future moves.

Thorpe's trick for memorizing the cards that are still in the deck pile is as follows:

During the cards:

- 2, 3, 4, 5, 6: Add a point

- 7, 8, 9: Do nothing

- 10, J, Q, K: Decrease one point