Understanding variance in poker: AFS, ABI, the long run and ROI

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Continuation to the article: Drawing up a tournament grid in MTT: how to maximize income

Poker is a game that combines skill, strategy, and a healthy share of luck. While experienced players can consistently make good decisions over the long term, there is an important factor that often disrupts this predictability: variance. Variance is the natural ups and downs of poker results caused by chance. In this article, we look at several key concepts related to variance in poker, including AFS, Average Buy-In (ABI), Distance, and Return on Investment (ROI).

For a better understanding of the topic, I will use a free resource.

This site is a calculator that allows users to calculate the probability of winning a poker tournament. The calculator uses statistical data and mathematical formulas to simulate the game and determine the chances of winning. The user can enter various parameters such as the number of players in the tournament, their bet, game types and other factors to get a more accurate estimate of their chances of winning. 

The calculator can also help players determine the optimal game strategy and make more informed decisions when participating in poker tournaments. 

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Let's analyze the concepts and learn how to analyze the data.

1. Average number of participants in the tournament (AFS) 

In poker tournaments, the average field size means the average number of participants competing in a given tournament. The average field size can affect the level of variance faced by players. Here's how:

Impact on prize pool allocation

The size of the tournament field directly affects the distribution of the prize pool. In large tournaments with a significant number of participants, the prize fund usually tends to become heavier, and most of the money is received by the finalists who took the first places. This prize pool structure increases variance as players have to perform better to receive significant payouts.

Increased competition

A larger average field size means more opponents and increased competition. With more players, it becomes more difficult to go through the tournament and get into the deep stage or to the final table. Increased competition increases variance, as even experienced players can face unpredictable situations due to the different playing styles and strategies employed by a large number of players. 

Large fluctuations of chips in the stacks

In tournaments with a large number of participants, there is a wider range of chip stacks. This leads to large fluctuations in the number of chips throughout the tournament. Scatter becomes more apparent when players experience significant fluctuations in the size of their stacks, driven by both luck and skill. One successful or unsuccessful hand can significantly affect a player's tournament prospects, resulting in greater volatility and variance.

Longer tournament duration

As a rule, tournaments with a large average field size have a long duration sized. Longer tournaments provide more opportunities for variance. As the number of hands played increases, the impact of short-term luck and variance diminishes, allowing skill to play a more significant role. However, it also means that players are exposed to variance over a long period of time, which requires them to have stamina and psychological resilience. 

Potential for higher ROI

While larger average field sizes can increase variance, they also provide an opportunity for higher return on investment (ROI). Due to the large prize pools, finishing in the first positions can bring significant payouts compared to smaller tournaments. Experienced players who consistently perform well in large field tournaments can achieve greater ROI despite their inherent variance. However, it is important to note that achieving consistent success in large field tournaments requires a combination of skill, strategy, and adaptability.

2. How do I watch the AFS I'm playing?

Previously, we analyzed the sharkscope statistics site. 

You can see the average number of participants by adding your nickname. There is no indicator in the standard configuration, how to add it.

1. Tap “Add more stats”

1. Find the "Avg. participants" item, press + to add 

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In the same lists, you can add "Total ROI", the indicator is useful for calculating the variance.

3. Average buy-in (ABI)

The average buy-in (ABI) is the most important metric that measures the middle amount of money a player puts into a poker game or tournament. The ABI is an important factor in understanding variance, as it provides insight into the financial obligations of players over a given period. A higher ABI indicates more significant bankroll fluctuations due to variance, as larger amounts are at risk. On the site, using the ABI selection, you can calculate the amount of bankroll for safe growth in tournaments.

4. the long run

The long run, sometimes called the standard deviation (SD), is a statistical measure used to quantify the volatility or scatter of a player's results over a given period. It helps to estimate the amount of deviations from the expected results. A greater the long run means a higher variance, indicating greater fluctuations in the poker player's scores. The the long run score allows players to manage their bankroll effectively by understanding the potential fluctuations they may face. Try to add a distance of 100 tournaments or 1000 on the site. How will the expected value change if the other indicators remain the same?

5. Return on investment (ROI)

Return on investment (ROI) is the percentage that measures a poker player's profitability. It is calculated as the ratio of net profit to total investment, expressed as a percentage.

ROI provides a valuable insight into a player's long-term success and helps mitigate the impact of short-term fluctuations. By focusing on ROI, players can assess their overall performance and identify areas where improvement is needed. We have considered the main indicators and terms that can be found in sharkscope to assess the variance under its parameters. Let's see what variance fluctuations are waiting for us at different distribution levels (Confidence Intervals (simulated) on the website ). The distribution shows the likelihood function for the results, the confidence intervals in which the results fall with a probability of 70%, 95% and 99.7%

6. What are confidence intervals?

A distribution that shows the likelihood function for results and is used to determine confidence intervals is called a probability distribution. Confidence intervals indicate a range of values that contains the true value of a parameter or result with a certain probability. For example, consider the normal distribution, which is widely used in statistical analyses. The normal distribution is characterized by a mean value (μ) and a standard deviation (σ). Knowing these two parameters, it is possible to construct confidence intervals.

1. The confidence interval with a probability of 70% is in the normal distribution, approximately 70% of the values lie within one standard deviation from the mean. The confidence interval in this case will be between μ - σ and μ + σ.
2. The confidence interval has a probability of 95% - approximately 95% of the values lie within two standard deviations of the mean. The confidence interval will be concluded between μ - 2σ and μ + 2σ.
3. The confidence interval has a probability of 99.7% - about 99.7% of the values lie within three standard deviations of the mean. The confidence interval will be concluded between μ - 3σ and μ + 3σ.

These confidence intervals allow you to estimate the uncertainty of the results and provide information about the probability that the true value of the parameter or result is in a certain range.

7. Which confidence interval is more accurate?

The confidence interval is considered more accurate when it is narrower. A narrower interval indicates that the estimate of a parameter or result has less variance and is more accurate.

In the case of a normal distribution with the same standard deviation, the higher the probability of hitting the confidence interval, the wider the interval. Therefore, the confidence interval with a probability of 70% will be narrower than the interval with a probability of 95%, and the interval with a probability of 99.7% will be even wider. However, it is not always possible to say unambiguously which confidence interval is "more accurate". This depends on the context of the task and the degree of confidence required in the assessment. 

If you are more interested in a narrower interval with a higher probability of hitting (e.g. 99.7%), this may be the preferred choice despite its width. However, narrow intervals may be less reliable, especially if the sample is small or the data is asymmetric. Thus, the choice of the most "accurate" confidence interval depends on the goals and limitations of a particular task.

Example:

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To calculate, let's take indicators from the sharkscope website:

• Average bet – $4.49
• Total ROI 24% 

To calculate, we still need to know the payout structure (the person in the prizes). This indicator, depending on the room, changes 12-15% Rake – a contribution to the organization of the game, is charged by the room 10-11% of the buy-in amount. Indicators can be found in the tournament lobby. 

Let's look at the effect of the variance and the results on the current hero parameters. Cf. participants 1052. Compare with the indicator Avg. participants 500 and 3000

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Confidence intervals play an important role in statistics and conclusions based on data, as they allow to take into account the randomness of the sample and the uncertainty of the data in the estimates made. Play a smaller AFS if you want more stable results. For myself, I choose a 50/50 ratio to use different types of tournament structures.

8. Conclusion

Variance is an integral part of poker that challenges players with its unpredictability.

Understanding key concepts such as Average Attendance (AFS), Average Buy-In (ABI), Distance, and Return on Investment (ROI) allows players to navigate high and low levels of the game. By applying proper bankroll management, maintaining a strong mindset, constantly improving skills and increasing the volume of play, players can mitigate the negative impact of variance and strive for long-term success at the poker tables. Here are some strategies to help deal with ups and downs:

Bankroll Management

Mentality and Emotional Control

Skills development

Scope of the game