# Gambling Strategies and Prize-Pricing Recommendation in Sports Multi-Bets

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Processing

#### 2.2. Defining and Labeling Profitable Rounds

## 3. Results

#### 3.1. Market Efficiency of Single Bets

#### 3.2. Single-Bet Gambling Profitable Strategy Is Hard to Find

#### 3.3. Form Ranking

#### 3.4. Choosing the Best Rounds to Bet

#### 3.4.1. Feature Extraction and Engineering

#### 3.4.2. Model Selection

#### 3.5. Proposed Fair Prize-Pricing Mechanism in Multi-Bets

#### 3.5.1. Generalizing the Single-Bet Prize-Pricing Mechanism to Multi-Bets

#### 3.5.2. Risk Assessment of the Suggested Prize-Pricing Mechanism

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Assessing market efficiency for single bets. (

**A**) Density curves of the betting probabilities for the three betting houses considered in this work: William Hill (WH), Bet365, and WINNER. The x-axis shows the expected probability for a single bet. The y-axis reflects the associated densities of these probabilities. (

**B**–

**D**) Single bet observed probability vs. the matching expected probability for WINNER (

**B**), William Hill (

**C**), and Bet365 (

**D**). Each point in the plots corresponds to a set of bets in a range of expected probabilities (x-axis). The y-axis was calculated from the obtained results of these bets.

**Figure 2.**Schematic view of the form ranking algorithm. The table on the left shows the final odds for each game in an example round. The odds are the return for investing 1 dollar. The panels to the right of the table illustrate the ranked forms that are filled according to the strategy. The left-most form is ranked 1st as it has the highest probability to win the big prize, and the right-most form is ranked 43,046,721 as it has the lowest probability to win the big prize.

**Figure 3.**Number of profitable rounds and the mean profitability averaged over all rounds. The x-axis corresponds to the number of filled forms sent in each round according to the described algorithm. The yellow circles correspond to the number of profitable rounds. Each dot corresponds to a single round, and the associated y-axis (to the left in black) is the average profit per form. The average profit per round is indicated on the right y-axis in red. (

**A**) shows the results for ${10}^{3}\le $ N $\le {10}^{7}$, and (

**B**) zooms in on $4\xb7{10}^{5}\le $ N $\le 2\xb7{10}^{6}$.

**Figure 4.**The ranking algorithm vs. random form filling strategy. (

**A**) The cumulative probability to win the big prize (y-axis) vs. the number of top N forms filled (x-axis). The gray shaded area corresponds to the mean probability of winning the big prize (black line in the middle of it) ± one standard deviation over all rounds. The blue line corresponds to the empirical winning fraction in the rounds given that the top N forms were filled (x-axis). The red line corresponds to a situation in which all probabilities equal 1/3. (

**B**) Box plot of the winning form in the form ranking approach. The green line represents the median and the blue line represents the mean. The red line represents the mean ranking of the winning form in a situation where all probabilities equal 1/3.

**Figure 5.**Assessing the selected model’s performance. (

**A**) An example of a typical simulation. Vertical jumps of the curve indicate rounds in which the model output was to place a bet in the specific round (x-axis) by filling the 200 K top ranked forms. (

**B**) Shows the profit distribution of single rounds from 100 simulations of 30 rounds, in which the model output was to place a 200 K forms bet. The mean profit per round of all simulations as a function of the number of submitted forms is shown in (

**C**).

**Figure 6.**Expected house share of the proposed prize-pricing mechanism. (

**A**) A distribution of the maximum probabilities for all single games of WINNER, William Hill and bet365. The x-axis corresponds to the maximum probabilities for all single games provided by the gambling houses, and the y-axis corresponds to their density. (

**B**–

**D**) Histograms of the house share for the proposed prize-pricing mechanism with three levels of $\alpha $. A total of 100,000 simulations were conducted and the house share was recorded in all of them for $\alpha =0$ (

**B**), $\alpha =0.3$ (

**C**), and $\alpha =0.6$ (

**D**). The profitable rounds are shown in light blue and the non-profitable in gray. The f value indicated on the graphs refers to the fraction of non-profitable simulated rounds.

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## Share and Cite

**MDPI and ACS Style**

Pirvandy, O.; Fridman, M.; Yaari, G. Gambling Strategies and Prize-Pricing Recommendation in Sports Multi-Bets. *Big Data Cogn. Comput.* **2021**, *5*, 70.
https://doi.org/10.3390/bdcc5040070

**AMA Style**

Pirvandy O, Fridman M, Yaari G. Gambling Strategies and Prize-Pricing Recommendation in Sports Multi-Bets. *Big Data and Cognitive Computing*. 2021; 5(4):70.
https://doi.org/10.3390/bdcc5040070

**Chicago/Turabian Style**

Pirvandy, Oz, Moti Fridman, and Gur Yaari. 2021. "Gambling Strategies and Prize-Pricing Recommendation in Sports Multi-Bets" *Big Data and Cognitive Computing* 5, no. 4: 70.
https://doi.org/10.3390/bdcc5040070