## Mathematicians beat bookmakers thanks to modeling

The following plot often appears in culture: a brilliant mathematician, using his knowledge, beats casinos, bookmakers, becomes a poker champion and a winner in life. A special case of such a plot is Barry Levinson’s 1988 film «Rain Man», in which one brilliant brother helps another solve financial problems with the help of mathematics. Such cases occur in reality.

An international group of mathematicians tested a huge number of football matches and betting quotes. And after math, we won about a thousand dollars from bookmakers. However, the bookmakers saw through the scientists and made it difficult for them to bet.

Experts have known about the connection of rates with analytics for a long time. If we consider football, then the outcome of each regular match can be predicted based on a certain set of factors. First of all, we need to look at the current form of the team: and we are talking about the ratio of wins, losses and draws recently, and not about clothes. Then the physical condition of the players, their injuries and the indicators of previous games are considered. And other factors are added to all this: the weather, the importance of the tournament, the game away or at home. Comparing all this, you can deduce the key indicator for betting — the coefficient.

A betting coefficient is a number by which your amount will be multiplied if you win the bet. For example, you bet on Zenit winning the Russian Championship with a coefficient of 3.2. The bet amount is 1000 rubles. And if the blue-white-blue ones win, then you get 3,200 rubles.

The odds are set by the bookmakers themselves, based on the calculated probabilities of a particular event. At the same time, a higher coefficient is given for a more likely outcome in order to attract people to a less likely option.

However, bookmakers do not always set the coefficient in exact accordance with the calculated indicators. If they bet too much on a certain team, they can increase the coefficient on its opponent in order to pull over part of the bets and avoid too much losses. This trick was used by scientists.

Mathematicians have done a truly titanic job: in total, they analyzed the results and bets of 479440 matches from 2005 to 2015. As a result, they have a formula that allows you to accurately determine the probability based on the quotes offered by the bookmaker. From this, they deduced the strategy of correct bets and tested it on a set of real-life matches. For comparison, they launched a random player model in parallel, which bet on the same matches in any order. The amount of the bet was the same everywhere — $ 50.

The result turned out to be quite predictable: the mathematicians’ algorithm greatly outperformed the random player. While meaningful bets on the scheme brought about a hundred thousand, a random player went into the minus 90 thousand.

Of course, this result prompted scientists to «field tests». First, the experts tested their theory on virtual bets on real matches, and they managed to win 35 thousand, albeit fake dollars. And then the scientists decided to try to win against the bookmakers themselves. And they did it.

In five months, mathematicians won about a thousand dollars from bookmakers — the small amount is explained by the fact that bets had to be made manually and many opportunities left the hands of scientists. And when the bookmakers realized that there was a catch, they limited the maximum bet size and the experiment ended ahead of schedule.