Kelly Criterion in Formula One Betting

Friday, February 17, 2012

In the recent years, the creations of online sports betting websites have been booming. It is evident that there is increase of gambling activities in our society, whether it is just an one off instance, or regular commitments.

However, the society in general has negative impressions on gambling. People believe gambling is a path that leads to ruin. But yet the gaming industry is expanding at a rapid pace, especially throughout the internet.

The negative impression on gambling is that the adrenaline rush from it can become an addiction. The casino and the bookmakers generate profit base on probability. And because the odds are always on the dealer’s side, players are more likely to lose money.

But imagine if there is a proven mathematic formula that ensures players to make money.

Kelly Criterion is a scientific formula developed by a mathematician – John Kelly in the 1950s. The formula determines the optimal wager for betting, and it is proven that by following this strategy on a long term basis, it is almost certain to profit from gambling.

Kelly Criterion is as shown below. The formula takes account of the odds offered by the bookmaker, and the probabilities of winning and losing the bets. The result of the formula is the fraction of the player’s entire bank roll (player’s defined budget) – which then determines the optimal wager for the bet.

f* stands for the fraction of bank roll to wager

b stands for the decimal odds offered by the bookmaker in decimals minus 1

p is the probability of winning in decimals

q is the probability of losing, which is the opposite of p. Hence q = 1- p

The odds b are always given by the bookmaker. The variable factor in the formula is p – the probability of winning.

P can be variable depending on the individual’s personal opinion, For example, a loyal supporter of Lewis Hamilton is more likely to have a biased opinion towards Lewis Hamilton or Team McLare winning the race. Hence the value of p would be different to a Sebastian Vettel supporter.

By substituting all the factors into the formula, the fraction of bankroll to wager can be determined.

At the start of each bet, the bankroll has to be adjusted according to the result of the previous bet.

For example, if the initial bankroll is $100, the calculated fraction of bankroll from Kelly Criterion is 0.6, and the odds for the bet is $1.50.

Then the wager for the bet is $100 x 0.6 = $60

If it turns out to be a winning bet, then the player’s bankroll after the first bet will be $40 + $60 x 1.50 = $130.

If the second bet has the same odds, then the wager for the second bet is $130 x 0.6 = $78.

And the process continues.

Vice versa, if the first bet turns out to be a loss, then the remaining bankroll after the first bet would be $40. Then the wager for the second bet is $40 x 0.6 = $24.

In order to improve the chance of winning bets, the player must make judgments of the event from a neutral perspective, and have as much information about the about as possible, ie. Track condition, weather and tyre compounds. These factors all improve the player’s judgement on p – the probability of winning. Hence it affects the accuracy to the calculation.

It is said by following this formula on a long term basis, the player can make profit from gambling. Given every single bet is placed the same way.

If it is proven that it works, why doesn’t everyone use it?

It takes discipline to follow Kelly Criterion. The system only works if every single bet is placed in the same way. This has been the challenge for most people who have ever attempted such system.

Although the formula shows it is impossible for the player to lose all his/her bank roll, there is always a minimum bet set by the bookmakers. Hence if the calculated fraction of the bank roll falls below the minimum bet limit set by the bookmakers, the formula can no longer be followed. Or it requires the player to raise the defined budget.

The system involves higher wager if the player is on a roll. After a winning streak, the player risks losing more. The calculated wager can exceed the psychological threshold of the player. Hence prompts the player to give up on following the process.

Furthermore, there is no end to the betting process. The formula assumes the player will continue on betting with infinite amount of bank roll, when the bookmakers all have betting ceilings.

Some people argue it is better to bet with a third or half as much as suggested by Kelly Criterion, as it reduces the massive fluctuation of wager. But at the end of the day it is up to each individual. Everybody has different mental threshold to the acceptable wager in betting. This could depend on the personal income, culture or personality.

Each individual has his/her own likings of how he/she likes to bet. Some people like to bet on long odds in order to obtain higher profit, some people like to bet on short odds for higher probability of the bet being paid off.

It does not matter on each individual’s betting habbit, scientific research in Kelly Criterion has proven that by sticking with the formula, the players are almost certain to profit from gambling.