26/06/2019

In Folha de S.Paulo, the secret to winning the game.

Foto: Casino Comparador

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

In one of their songs, the Irish rock band U2 asserts that "every gambler knows that you bet to lose." This statement has a mathematical basis: in the vast majority of games of chance, the player has a greater chance of losing than winning.

For example, in traditional French roulette there are 37 numbered slots. Players can bet on any slot except number 0: when the ball lands there, the money goes to the casino.

Therefore, the expected value of roulette is negative, around -2.7%. It may not seem like much, but it's things like this that make casinos one of the most profitable businesses—just look at places like Las Vegas or Macau to see the extraordinary power of gambling to generate profit for those who control it.

There is another great advantage the house has over the bettor. Each time the roulette wheel spins, the outcome is unpredictable. But, according to the Law of Large Numbers, discovered by the Swiss mathematician Jacob Bernoulli (1654–1705), after a large number N of spins, it is guaranteed that the ball will have landed approximately N/37 times in each slot, including the number 0. The casino's profit is predictable.

Another Irishman, George Bernard Shaw (1856–1950), Nobel laureate in literature in 1925, expressed the idea very well: “He who makes a million bets [the casino], while the individual can only make one or two, runs no financial risk, for what happens in a million bets is guaranteed, even though no one can predict what will happen in each one of them.” Controversially, Shaw concluded that the existence of gambling is “the most perverse crime against society.”

Why would someone gamble under unfavorable conditions? In some cases, it's for fun, for the adrenaline rush. My mother, Dona Isaura, played the Christmas lottery for years, just for fun, knowing she wouldn't win (of course, she always had a glimmer of hope, but she never won).

Other times it's due to a lack of knowledge, a failure to understand how adverse the odds are. In fact, it's well known today that many human decisions are not rational, they are not based on mathematics: advances in this area earned Richard Thaler the 2017 Nobel Prize in Economics, for example.

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