Analysis of Kelly Criterion: Betting companies' attitude towards game results

Analysis of Kelly Criterion: Betting companies' attitude towards game results

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The several methods of predicting the possible results of the game that we have introduced above are all based on the objective data of the team and the game itself. When these possible data become market odds, they must be considered Enter more constraints that play a role in the outcome. When predicting and analyzing this stage, it has entered a dynamic market analysis process from a static mathematical model analysis, so we call it a dynamic forecasting method. Static prediction is carried out before the odds are formed, while dynamic analysis is actually a method of forecasting and analyzing the whole process of odds formation. The dynamic analysis method is also the analysis of the index, which can be divided into four dynamic analysis models: Kelly Criterion analysis, Betfair index analysis, profit and loss index analysis, and bookmaker odds analysis.

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Article main points


  • Point 1: Understand and master various odds analysis methods, and find out the odds analysis tools that suit your own mode.

  • Point 2: Understand the trading characteristics of bookmakers.

  • Point 3: Master the trading characteristics of various bookmakers in different events.

  • Point 4: Through the understanding of Betfair market analysis, form a market-oriented game analysis awareness.


Section 1 Kelly Criterion Analysis


1. What is Kelly Criterion and Kelly Value?


Kelly Index Kelly Criterion originated in the 1960s. It is a mathematical formula originally invented by American physicist John Kelly to help reduce the interference of noise in communication, that is, the "Kelly Criterion". Later, it was used on the gambling tables in the Las Vegas casino, and swept away a lot of money in the casino. What kind of mathematical formula has such magical power that it can subvert the rule of ten bets and nine losers in the casino?


First understand the application principle of the formula. The Kelly formula proposes a complex calculation formula for events with a small probability. When applied to scientific experiments, it can reduce the possibility of errors caused by noise interference to zero in the process of information transmission. In the same way, when it is transformed into the control and management of investment risks, investors or gamblers can also reduce the probability of possible risks to zero.


The result calculated by "Kelly formula" is called "Kelly value". Since the unpopularity in betting is also an event with a small probability, the concept of Kelly value is introduced into the betting industry. Because of its theoretical advances in anticipating events and avoiding risks, the application of the Kelly Criterion in gambling spreads very quickly, such as the poker game blackjack in casinos and the popular horse racing and greyhound racing in Europe. Its status is as prominent as "rotation matrix" in the field of digital lotto. The application in football betting is mainly based on European odds, which can calculate the best betting amount under the given odds, so that the bettors' bets can be stably, safely and quickly (geometric progression) )increase.


2. Effective Calculation Method of Kelly Value


Many bettors are confused about the Kelly index given by some online gaming companies. The biggest question that arises is, since the Kelly index can predict the game, why does the dealer show us these calculated data? Here we must first clarify a concept: "The Kelly value is not calculated by the gaming company." Just imagine, the reason why bettors value the Kelly value is that it has a great effect on predicting the outcome of the game. If gaming companies share the results of their analysis and calculations with players without reservation, this is contrary to the nature of gaming, and it is tantamount to giving up their right to profit and even survival, and the gaming industry will completely die out. So, who calculated the Kelly value? What is the basis for the calculation? After the calculation, how to predict and measure the outcome of the game and the possible risks? With these questions in mind, we began to study step by step, uncovering its mysterious veil layer by layer.


1. The basic concept of Kelly value


If the odds market is compared to the stock market, then the probabilities and odds that may change at any time are like various public financial data given by listed companies. The Kelly value is the same as the financial data of listed companies. It can be calculated based on the public odds given by each event and the probability of victory, draw and loss combined with the calculation formula of the Kelly index. Since the odds will change with the change of the probability, the Kelly value calculated based on the odds and the probability will also change with the change of the probability and the odds, that is, the Kelly Criterion can be defined as "in the variable Variables". We know that odds and probabilities are the market performance of bookmakers to analyze and judge the results of games in different periods, and the Kelly index, which is variable along with them, can truly reflect the tendency of the data given by bookmakers and the value of chips. traffic trends. The conclusion is: Kelly Criterion is the numerical expression of the attitude of the gaming company to a certain result of the game.


2. The role of Kelly value in game result prediction


As mentioned earlier, the Kelly Criterion is a variable after the probability and odds variables, and when this variable is expressed in the form of the index, the value can reflect the market compensation risk of the odds, that is The payout difference between a dynamic market and a pre-established payout ratio. And through the comparison of the attitudes of various gaming companies towards profit and compensation risk, we can not only find out the differences between them, but also find out where their identity points are. Calculation value and function of Kelly value.


3. Definition of the degree of recognition among bookmakers


Each company has its own Kelly value, in other words, different companies have their own recognition standards for the difference in compensation. When multiple companies have a high degree of recognition for a certain item in the result, that is, when the Kelly value is relatively close, it can be regarded as that they have a certain degree of recognition for the item, and the conclusion is that the result of this item is out The possibility will be very high. And when the differences between companies are large, the possibility of this item will become smaller. If this item is not favored by the chips, the gaming company's compensation transaction risk will be reduced, and this item is the gaming company's profit safety area.


4. Operation method


Gambling transactions and commodity transactions are based on the same principle, and their processes are all completed under the scope of the law of value. The law of value tells us that prices move around value. The value law of betting is that the odds change around the probability, and the Kelly value for measuring them changes around the change between the odds and the probability. According to the commodity trading formula: transaction price × transaction quantity = total transaction value. Looking at the transaction elements of gambling, if the odds are the transaction price, then the bet volume of the bettors on the three items of victory, draw and loss is the transaction volume, that is: odds × betting volume = transaction value of chips. Through this formula, we found that when we have the trading volume (betting volume) of the bookmaker, we can understand their trading value. However, we cannot grasp the real trading volume and total betting volume of the gaming company, which is also an absolute commercial secret of the gaming company. There is a popular calculation formula nowadays, which is based on the public data given by the gaming company. which is:


Assuming that the betting principal is 1


Kelly Value Formula: Main Winning Odds × Main Winning Probability% × 1 = Banker Payable Main Winning Bonus%

Tie Odds × Tie Probability % x 1 = Banker Payable Tie Bonus %

Main Loser Odds × Main Loser Probability% × 1 = Banker Payable Main Loser Bonus %


Through the formula, it is found that the operating principle of this formula is to regard the probability of winning, drawing and losing as the amount of betting. There is a certain reason for such establishment, but the disadvantage is that although the three probabilities are the probability index issued by the dealer according to the market situation, it cannot reflect the real direction of public betting. You must know that the odds itself is also extremely deceptive. It is originally a market performance to satisfy the profit and risk control needs of bookmakers. If you calculate the Kelly value based entirely on it, it is easy to be considered by the banker first. So far, it is also dissociated from the real player betting trends. And many calculation results are very close to the index given by the dealer, making it difficult to make judgments and comparisons. For example:


FA Cup: Manchester United 0-1 Leeds United


Standard odds


Home win Draw Away win

Ladbrokes: 1.25 6.00 10.00

William: 1.22 6.00 12.00

Probability of win, draw and loss

Home win rate  Draw rate  Away win rate

75%      15.62%    9.38%

76.6%   15.6%      7.8%


Kelly value


Win Draw Loss


0.94  0.96  0.80


0.92  0.96  0.96


The above group of Kelly values are published by the gaming company after calculation. The 0.80 of Liberty Blog wins and the 0.96 of William Hill are very different, and they are also very inconsistent with the actual value calculated by applying the formula. If we calculate according to the above formula, the result will be basically the same as this one. So, how do we do the feasibility calculation?


As we have known before, one of the two major elements that constitute the odds is the "probability of public psychological betting". Here we compare this element with another element - the dealer's probability analysis. Through some tendentious survey data we There are three betting volumes that can be understood. For example, in this example, the main win betting ratio is 80%, the draw betting ratio is 12%, and the away win betting ratio is 8%. Then it can be judged that the betting direction of this game has been seriously unbalanced. Assuming that the principal of this market is still 1 yuan, it is calculated according to the following formula:


Odds × Betting Ratio × Total Investment


Home win transaction value: 1.25×80%×1=1


Draw transaction value: 6.00×12%×1=0.72


Away win transaction value: 12.00×8%×1=0.96


Even so, the obtained transaction value is quite different from the actual result. After repeated analysis, the author found that since the probability is the basis for the dealer to calculate the odds, if the odds offered by them do not match the probability, there should be a problem with the item; The lower the possibility will be; from the perspective of gaming companies' profitability, such a setup is also in line with their fundamental interests and operational attributes. Based on this idea, the probability and odds are calculated independently by the player, and then the transaction value is calculated according to the two odds before and after, and then the difference is found from the different transaction value results. Calculate again according to the return rate of this game is 90%, that is:


Actual Odds = 90% ÷ Probability


Home win odds: 90%÷75%=1.20


Draw odds: 90%÷15.62%=5.76


Away win odds: 90%÷9.38%=9.59


After recalculation, we get:


Home win trade value: 1.20×80%=0.96


Draw transaction value: 5.76×12%=0.69


Away win transaction value: 9.59×8%=0.77


The difference between the Kelly value calculated according to the actual odds and the market odds:


Home win difference: 0.96:1 -0.04


Tie difference: 0.69:0.72 -0.03


Away win difference: 0.77: 0.96 -0.19


Analysis: Through this difference, we can find that the "true default value" of the dealer (that is, the transaction value calculated by ourselves, which can also be regarded as the dealer's bottom line) is 0.96 when Manchester United's betting volume is heavily skewed. The calculation result of the market odds is 1.00, and the Kelly value published on the index website is 0.94. Finally, the combination of public betting factors and banker factors is (1+0.96)/2=0.98, that is, the transaction value of this game is 0.98, and the transaction value of 0.98 is obviously high, while 0.77 for customer wins and 0.69 for draws are more beneficial to the banker , In the end Manchester United lost the game.


Tip 1: The comparison order of differences is: the last calculation result minus the initial calculation result.


Tip 2: The betting ratio can be achieved through the "customer survey" or "betting vane" in some domestic and foreign football betting websites. The author's approach is usually to make an average survey ratio of 2-3 companies, which can better represent the universality of betting.


Tip 3: In this calculation method, players not only need to refer to multiple betting direction survey indicators, but also require players to have the basic ability to analyze fundamentals and estimate betting direction.


3. Using the Kelly value to predict several definitions of the game


After obtaining the Kelly value, the final task is to define the relationship between each Kelly value and the result. This also determines how the Kelly value works.


The basic definition of Kelly value:


For an item with a relatively normal betting volume, the dealer's attitude towards compensation is willing to be low but not high. Then, the one with the lower Kelly value will be more likely to be played.


When the amount of betting is abnormal or skewed, and there is a significant difference between the Kelly value calculated based on the market odds and the odds calculated based on the real probability, it is necessary to pay attention to the failure of the favorite team.


When a Kelly value result is greater than 1, the normally stronger (larger betting volume) item may be extremely small.


Conversely, the chance increases when it is less than or equal to 1.


The non-market odds are based on the calculated Kelly value range of 0.89-0.92, which is relatively close to the bookmaker’s break-even point. If the value is lower than this standard, if the bookmaker’s default is obtained, the possibility of this item being played is greater.


The greatest value of the Kelly value is reflected in capturing unpopular matches. The calculation procedure must be strictly implemented: first calculate the Kelly value based on the market odds; then calculate the actual odds based on the probability; and finally make comparisons one by one.