Kelly’s Criterion: When Math Helps Win Bets

We often hear that professional bettors make use of complex mathematical tools to achieve favorable results.
One of these tools (not really that complex) is the so-called Kelly criterion .
John Larry Kelly jr. he was a Princeton scholar who in the 1950s published some studies that proved to be a cornerstone, in the following years, in the management of the investment portfolio . That is, by means of irrefutable mathematical formulas, he successfully theorized what was the optimal portion of his budget to be used in each individual investment.
As you can imagine, the application of his studies in the betting sectorit came almost immediately after.
Thanks to him, in fact, today we can calculate what is the optimal amount to bet in each single bet.

The sentence

As explained in his university treatise , the formula coined by Kelly allows the bettor to calculate the optimal amount to bet taking into consideration the odds offered by the bookmaker and his own personal prediction . According to the author, betting a larger amount would imply too high a risk, while betting less would result in a lower return and at the same time generate a waste of ‘probability’ in one’s favor.
To get the maximum profit it is necessary to estimate the real probability of success of the bet. It is very important that this estimate is more accurate than that of the bookmaker (a problem which we will return to shortly, anyway), because the success of the Kelly criterion depends on this.
The optimal bet is expressed as a percentage of one’s budget (or bankroll ): to calculate the amount of the bet, it is therefore necessary to know the odds proposed on the event by the bookmaker (Q) and precisely determine the probability (P) that the your prediction is winning.

Kelly’s formula:

 % of bankroll to bet on the event = (Q x P-1) / (Q-1)


(((Odd x (Probability / 100)) – 1) / (Odd – 1)) x 100

A practical example

“Oh well, but I don’t understand anything about mathematics!”
It is normal, do not be alarmed. Now a practical example will clarify the ideas.
Let’s suppose that on the next day of the Italian Serie A championship, Gasperini’s excellent Atalanta goes to visit Giampaolo’s equally fierce Sampdoria .
Our reference bookmaker odds 1 (ie the Sampdoria win) at 2.00, the equal to 3.50 and the away win at 3.15.
The day before the game, however, we find out from the press conference of the Orobico coach that due to a sudden flu neither Ilicic , nor Zapata nor Toloi(or perhaps the most representative players of the Goddess) will take part in the away match from Marassi; at the same time, Giampaolo professed to be very sure about the state of form of Quagliarella and his companions.
With these premises, we think that perhaps an odd of 2.00 for the home win (corresponding to a 50% concrete chance of winning) seems a bit tight, and personally we begin to believe that perhaps Sampdoria may have at least 60% of possibility to take home the entire mail. Percentage that would correspond to a share equal to 1.65 (given by the 100/60 transaction).
The discrepancy between 2.00 and 1.65, with the Kelly criterion, can be exploited mathematically: assuming that our betting bankroll amounts to 1000 euros, the formula must be applied as follows:
Kelly% = (2.00 × 60% -1 / 2.00-1) = 0.2%
Therefore, if our estimation assumptions are correct, the optimal amount to bet is 0.2% of your bankroll, so (following the example above) 20 euros must be bet on sign 1.

Final remarks

Kelly’s criterion will allow you to manage your budget efficiently, preventing it from running out in a short time. Obviously, this formula is inextricably linked to the ability to accurately estimate the exact percentage probability that a certain event will occur. In fact, if we tend to make estimates higher than the real ones, the percentage obtained through the formula will be disproportionate and over time the budget could run out. Conversely, if lower estimates than the real ones are made, a lower profit margin would be obtained than what would have been obtained considering the correct probability.
Ultimately, Kelly’s criterion is one of the decidedly more interesting tools for managing, maintaining and developing one’s betting portfolio.


by Abdullah Sam
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