A sufficient poker bankroll is necessary to act as a cushion against variance. Some players may believe that, with just a few positive results at a $1/$2 no-limit hold'em game, they are ready to jump into a $2/$5 or $5/$10 game, regardless of their bankroll size. Variance in poker relates to short-term results, and one of the best ways to describe how it works is to take a shuffled pack of cards and turn the cards over one-by-one – betting on whether the next card will be black or red. If you were to bet black every time, you would break even by the time all fifty-two cards have been turned over. Variance is a standard part of the game of poker, and all players go on good and bad runs. While there are certain activities you can take to reduce the variance or lessen its effects on your bankroll and mental state, there is no way to avoid it completely. It's better to just embrace and more importantly understand the madness of variance than trying to avoid it. In reality, if you aren't ready to deal with the variance of playing poker over a long stretch of time, then it just isn't the game for you. Also just to note, variance is the root cause of.
With this out of the way let me now cover the easiest way to get your bankroll started: 'Bonus Whoring'. A Free Lunch in Sports Betting. If you've heard the saying there is no such thing as a free lunch, well think again. Here are some bonuses that sports betting sites offer to players making their first deposit.
Professional poker players often describe their vocation as 'a hard way to make an easy living'. One of the most difficult aspects of the game that a professional poker player must deal with is the inconsistency in income. Despite employing a strong skill set and the benefits of years of experience, many poker players still come home with less money in their pocket than when they arrived at the tables. Nba basketball betting tips and predictions. These ups and downs of poker are often collectively known as 'variance'.
What is Variance?
In statistical terms, variance is used to examine the differences between an individual result and the average for a set of results. These results can be represented as data points in a set to determine the fluctuations within that set.
We'll demonstrate how to calculate variance with a small sample data set. If you were to track the results for your previous sessions at a $3/$6 fixed-limit hold'em cash game, they could read:
-11, +85, -30, +144, +9, +30, -87
Each of these results represents a data point in a set of seven numbers.
Poker Variance Texas Holdem
The total of these seven sessions equals +140 (-11 + 85 – 30 + 144 + 9 + 30 – 87 = 140)
Parlay definition, to bet or gamble (an original amount and its winnings) on a subsequent race, contest, etc. Parlay synonyms, parlay pronunciation, parlay translation, English dictionary definition of parlay. Parlayed, parlaying, parlays 1. To bet on a subsequent event. Parlay definition is - to bet in a parlay. How to use parlay in a sentence. Parlay entitles its invoker with free passage to negotiate with a ship's captain until the negotiations are complete. Part of the mythical set of pirate laws. Parlay is a discussion-based learning tool and global community of educators who are reimagining class discussions for the 21st Century.
The average of these seven sessions equals +20 (140/7).
The variance is the sum of the squares of the differences between each data point and the mean.
For the first result, (20 – (-11)) = (20 + 11) = 31. 31^2 = 961
Follow the same procedure for each result and you get these corresponding numbers:
961, 4225, 2500, 15376, 121, 100, 11449
Add up these numbers and divide by seven to get the variance:
961 + 4225 + 2500 + 15376 + 121 + 100 + 11449 = 34732
34732/7 = 4961.71
The standard deviation, another measure of volatility, is the square root of the variance:
SQRT(4961.71) = 70.43
The most frequent results lie within one standard deviation (+/- 70) of the mean (+20). With these results, a player should expect to finish a session somewhere between -50 (20-70) and +90 (20+70).
However, many of these data points lie outside that range. Are these results the products of bad luck, bad cards or bad play?
Variance and Sample Sizes
The more data points a sample size contains, the more accurate and reliable the measurements of variance and standard deviation will be. The seven-point data set included here is obviously much too small to give an accurate estimate of how a player performs at a 3/6 limit hold'em game. Also, more data points will give the player more information on how to manage the inevitable ups and downs involved in cash games.
Variance and the Central Limit Theorem
Another important mathematical concept that comes with sample size is the 'Central Limit Theorem'. This concept states that, as the number of data points in a set grows, a plot of those points on a graph will resemble a normal statistical distribution, as seen in the classic 'Bell Curve'.
The guiding principle is that, the larger the sample size, the more data points that will fall at or near the average. This measure of variance gives the player a more accurate idea as to what to expect from his results.
Variance and Luck
Even in the most distinguished poker careers, a player will have sessions where he has wins (or losses) that go two or more standard deviations away from the average. Many inexperienced players attribute these results to luck, but they are within the realm of possibility shown in the Bell Curve. These data points are known as 'outliers' and, individually, have little effect on the variance seen over a career. If these 'outlying' results continue to appear, however, they may signal the start of a new trend.
Variance and Bankrolls
A sufficient poker bankroll is necessary to act as a cushion against variance. Some players may believe that, with just a few positive results at a $1/$2 no-limit hold'em game, they are ready to jump into a $2/$5 or $5/$10 game, regardless of their bankroll size. When the variance swings in the negative direction, as it inevitably will, a depleted bankroll could send the player to either a lower-stakes game or out of the game entirely.
Variance and Structure
Some poker games, as well as some betting structures, are prone to have higher variance than others. For instance, a $3/$6 fixed-limit hold'em game will have much less variance than a $1/$2 no-limit hold'em game due almost exclusively to the betting structure. In the $3/$6 limit game, the maximum bet a player can make on the river is $24 (bet-raise-re-raise-cap). In the no-limit game, a player can bet his entire stack at any time, which may be hundreds of dollars. These bet sizes can cause huge swings in variance.
Variance in Poker Tournaments
Despite the allure of fame and glory presented by televised events, no-limit hold'em tournaments are shining examples of the deceptive power of variance. Most professional players (including many famous faces on the tournament circuit) make more of their living through cash games and only enter the most prestigious (and lucrative) tournaments due to the high variance involved. Most major tournament winners are 'outliers', as up to ninety percent of all tournament players walk home empty-handed.
Variance and Playing Styles
In a previous piece, we examined the four primary playing styles (loose-passive, loose-aggressive, tight-passive and tight-aggressive). Just as the tight-aggressive style has been shown to be the most profitable, it also often results in the lowest variance. Both the loose-passive and the tight-passive players depend on catching cards to win hands (a high-variance strategy) while the loose-aggressive style relies on big bets to push players off hands. The tight-aggressive method relies on strong starting hand selection, infrequent bluffs and a well-founded understanding of probabilities, all of which contribute to reducing variance.
Variance and Emotion
The effects of big wins and staggering losses are not strictly limited to a player's bankroll. The emotional roller coaster that comes with big swings in variance can also affect how a player approaches the game. Players who have become accustomed to big wins may lose their cool when confronted with a crushing loss. One bad session can set a player 'on tilt' and wreck both his skills and his confidence.
How to Deal with Variance
Shifts in variance can be as unpredictable and dangerous as shifts in the weather: everybody complains about them, but no one can do anything to prevent it. The most important aspect of success in poker lies in treating each session or tournament as a continuation in one long game. Experienced players understand that their success or failure as a player does not lie in the results of a single tournament or a handful of cash-game sessions. Each session represents only a single data point: a consistent approach will often reduce (but never entirely eliminate) variance.
Conclusion
Former World Series of Poker Main Event Champion Chris 'Jesus' Ferguson once said that poker is '100 percent luck and 100 percent skill'. The turn of each card is the result of luck, but how a player responds to that unpredictable event is the product of skill, practice and experience. The ability to manage the game's inherent variance is a skill on par with calculating odds and outs in terms of how successful a player can eventually become.
Related Lessons
By Gerald Hanks
Professional poker players often describe their vocation as 'a hard way to make an easy living'. One of the most difficult aspects of the game that a professional poker player must deal with is the inconsistency in income. Despite employing a strong skill set and the benefits of years of experience, many poker players still come home with less money in their pocket than when they arrived at the tables. Nba basketball betting tips and predictions. These ups and downs of poker are often collectively known as 'variance'.
What is Variance?
In statistical terms, variance is used to examine the differences between an individual result and the average for a set of results. These results can be represented as data points in a set to determine the fluctuations within that set.
We'll demonstrate how to calculate variance with a small sample data set. If you were to track the results for your previous sessions at a $3/$6 fixed-limit hold'em cash game, they could read:
-11, +85, -30, +144, +9, +30, -87
Each of these results represents a data point in a set of seven numbers.
Poker Variance Texas Holdem
The total of these seven sessions equals +140 (-11 + 85 – 30 + 144 + 9 + 30 – 87 = 140)
Parlay definition, to bet or gamble (an original amount and its winnings) on a subsequent race, contest, etc. Parlay synonyms, parlay pronunciation, parlay translation, English dictionary definition of parlay. Parlayed, parlaying, parlays 1. To bet on a subsequent event. Parlay definition is - to bet in a parlay. How to use parlay in a sentence. Parlay entitles its invoker with free passage to negotiate with a ship's captain until the negotiations are complete. Part of the mythical set of pirate laws. Parlay is a discussion-based learning tool and global community of educators who are reimagining class discussions for the 21st Century.
The average of these seven sessions equals +20 (140/7).
The variance is the sum of the squares of the differences between each data point and the mean.
For the first result, (20 – (-11)) = (20 + 11) = 31. 31^2 = 961
Follow the same procedure for each result and you get these corresponding numbers:
961, 4225, 2500, 15376, 121, 100, 11449
Add up these numbers and divide by seven to get the variance:
961 + 4225 + 2500 + 15376 + 121 + 100 + 11449 = 34732
34732/7 = 4961.71
The standard deviation, another measure of volatility, is the square root of the variance:
SQRT(4961.71) = 70.43
The most frequent results lie within one standard deviation (+/- 70) of the mean (+20). With these results, a player should expect to finish a session somewhere between -50 (20-70) and +90 (20+70).
However, many of these data points lie outside that range. Are these results the products of bad luck, bad cards or bad play?
Variance and Sample Sizes
The more data points a sample size contains, the more accurate and reliable the measurements of variance and standard deviation will be. The seven-point data set included here is obviously much too small to give an accurate estimate of how a player performs at a 3/6 limit hold'em game. Also, more data points will give the player more information on how to manage the inevitable ups and downs involved in cash games.
Variance and the Central Limit Theorem
Another important mathematical concept that comes with sample size is the 'Central Limit Theorem'. This concept states that, as the number of data points in a set grows, a plot of those points on a graph will resemble a normal statistical distribution, as seen in the classic 'Bell Curve'.
The guiding principle is that, the larger the sample size, the more data points that will fall at or near the average. This measure of variance gives the player a more accurate idea as to what to expect from his results.
Variance and Luck
Even in the most distinguished poker careers, a player will have sessions where he has wins (or losses) that go two or more standard deviations away from the average. Many inexperienced players attribute these results to luck, but they are within the realm of possibility shown in the Bell Curve. These data points are known as 'outliers' and, individually, have little effect on the variance seen over a career. If these 'outlying' results continue to appear, however, they may signal the start of a new trend.
Variance and Bankrolls
A sufficient poker bankroll is necessary to act as a cushion against variance. Some players may believe that, with just a few positive results at a $1/$2 no-limit hold'em game, they are ready to jump into a $2/$5 or $5/$10 game, regardless of their bankroll size. When the variance swings in the negative direction, as it inevitably will, a depleted bankroll could send the player to either a lower-stakes game or out of the game entirely.
Variance and Structure
Some poker games, as well as some betting structures, are prone to have higher variance than others. For instance, a $3/$6 fixed-limit hold'em game will have much less variance than a $1/$2 no-limit hold'em game due almost exclusively to the betting structure. In the $3/$6 limit game, the maximum bet a player can make on the river is $24 (bet-raise-re-raise-cap). In the no-limit game, a player can bet his entire stack at any time, which may be hundreds of dollars. These bet sizes can cause huge swings in variance.
Variance in Poker Tournaments
Despite the allure of fame and glory presented by televised events, no-limit hold'em tournaments are shining examples of the deceptive power of variance. Most professional players (including many famous faces on the tournament circuit) make more of their living through cash games and only enter the most prestigious (and lucrative) tournaments due to the high variance involved. Most major tournament winners are 'outliers', as up to ninety percent of all tournament players walk home empty-handed.
Variance and Playing Styles
In a previous piece, we examined the four primary playing styles (loose-passive, loose-aggressive, tight-passive and tight-aggressive). Just as the tight-aggressive style has been shown to be the most profitable, it also often results in the lowest variance. Both the loose-passive and the tight-passive players depend on catching cards to win hands (a high-variance strategy) while the loose-aggressive style relies on big bets to push players off hands. The tight-aggressive method relies on strong starting hand selection, infrequent bluffs and a well-founded understanding of probabilities, all of which contribute to reducing variance.
Variance and Emotion
The effects of big wins and staggering losses are not strictly limited to a player's bankroll. The emotional roller coaster that comes with big swings in variance can also affect how a player approaches the game. Players who have become accustomed to big wins may lose their cool when confronted with a crushing loss. One bad session can set a player 'on tilt' and wreck both his skills and his confidence.
How to Deal with Variance
Shifts in variance can be as unpredictable and dangerous as shifts in the weather: everybody complains about them, but no one can do anything to prevent it. The most important aspect of success in poker lies in treating each session or tournament as a continuation in one long game. Experienced players understand that their success or failure as a player does not lie in the results of a single tournament or a handful of cash-game sessions. Each session represents only a single data point: a consistent approach will often reduce (but never entirely eliminate) variance.
Conclusion
Former World Series of Poker Main Event Champion Chris 'Jesus' Ferguson once said that poker is '100 percent luck and 100 percent skill'. The turn of each card is the result of luck, but how a player responds to that unpredictable event is the product of skill, practice and experience. The ability to manage the game's inherent variance is a skill on par with calculating odds and outs in terms of how successful a player can eventually become.
Related Lessons
By Gerald Hanks
Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold'em tournaments at live venues all over the United States.
Our beginners guide to variance explains what it is, why it matters, how you can calculate your acceptable poker variance score, and what to do if you are on the wrong side of it. Our guide is not going to suit every player; but, if it helps you make a few dollars, it should be worth a few minutes of your reading time.
If you read a lot of poker articles, or frequently visit poker forums, you are undoubtedly going to come across the term 'variance'. Variance is generally considered to be the upswings and downswings you experience when you play poker. In a way that is true. However, by better understanding variance and what you can do if you are on the wrong side of it, you could experience more upswings and fewer downswings – or, at worse, fewer financially painful downswings. Let´s start by defining variance.
What is Variance in Poker?
Variance in poker relates to short-term results, and one of the best ways to describe how it works is to take a shuffled pack of cards and turn the cards over one-by-one – betting on whether the next card will be black or red. If you were to bet black every time, you would break even by the time all fifty-two cards have been turned over. However, during your break-even run, there will have been times when you won or lost two, three or four bets in a row – maybe more.
Variance in poker is different because you don´t know you will break even at the end of each session. You can calculate the odds of winning each hand, and only bet when the odds are in your favor, but that is no guarantee of short-term success. In theory, your pocket Aces could get busted five times in a row, or you could win against pocket Aces five times in a row – even though the math says pocket Aces will prevail in four-out-of-five hands at the pre-flop stage.
Poker Variance Analysis
So, if variance in poker only applies to short-term results, why does it matter? It matters because in order to return a long-term profit you want to have more winning sessions than losing sessions, or at least make sure you win enough during your winning sessions to cover your losses during your losing sessions. In order to do this, you need to calculate your acceptable poker variance score and then decide what you will do if you find yourself on the wrong side of the score.
How to Calculate Your Acceptable Poker Variance Score
The primary objective of calculating your acceptable poker variance score is to determine a stop/loss position at which you say 'enough is enough' and end the session. This requires considerable discipline – especially if you are on a sequence of losing sessions – which is why we stated at the very beginning of this article 'our guide is not going to suit every player'. To calculate your acceptable poker variance score, you need to collect a sequence of results and then do a little math:
- Take the results from at least your last six sessions. Ideally they should be consecutive sessions with particularly bad days or good days excluded.
- Add up your winning sessions, take away the losses from your losing sessions, and divide the result by the total number of sessions in the calculation.
- The figure you have now is your average win/loss per session, and what you need to do next is work out how far each session is away from the average.
- This is where it gets complicated. Square each 'how far each session is away from the average' value, add the results together and divide the result by the number of sessions.
| How to Calculate Your Acceptable Poker Variance Score | Total | Average | ||||||
| Take At Least Your Last Six Results | $10 | $15 | -$12 | $20 | -$15 | $36 | $54 | $9 |
| How Far is Each Session from the Average | 1 | 6 | -21 | 11 | -24 | 27 | n/a | n/a |
| Square the Values in the Row Above | 1 | 36 | -441 | 121 | -576 | 729 | -130 | -21.66 * |
* To get the figures on the bottom row of calculations, you have to multiple each figure in the middle row by itself.
So, 1×1 = 1, 6×6 =36 -21x-21 =-441, etc.
Then you add all the figures up along the bottom row to get the total of -130, and divide -130 by 6 (because you have used six sets of results in the calculations) to get -21.66.
Therefore if you had the series the results along the top line of the calculations, you should stop playing once you have lost $21.66.
The resulting figure is your acceptable poker variance score – basically your stop/loss position when you are experiencing a losing session. If it looks a bit high to you, it could be because you are playing at the wrong level or because you are an overall losing player. To get back on the right side of variance you should read our article about Poker Bankroll Management for Dummies, work on improving your game, and have the discipline to end a session when the stop/loss position is reached.
