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Variance In Live Poker

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  1. In this video I'm going to debunk some myths about poker variance and share best practices for how to manage your bankroll in tournament poker.
  2. Poker players have a lot of variance in their lives, and tournament players more so than cash game players. Not only do tournament players face financial variance, they also face time variance.

I have written a lot about expectation and variance over the years. Without getting into a lot of mathematical jargon, you should be familiar with these two basic terms.

Variance In Live Poker

Expectation is basically an average. It measures what the average result will be over a large number of trials. Averages can be very deceptive when there are a few extreme (very high or very low) values. The median is another measure that overcomes this problem. It is found by arranging observations in order and then picking one in the middle.

To illustrate this difference let's look at the wealth of a US family. The average net worth is about $700,000, but this includes a few very rich people. The top tenth of a percent has an average net worth of over $40 million. The median net worth is around $100,000, quite a lot less than the average.

Variance In Live Poker Tournaments

Variance measures how much influence extreme values have. A low variance means that there aren't a lot of extreme values. The average is close to the median. A high variance means that there are extreme values that have a lot of influence on the result. Standard deviation is another way in which variation is expressed. It is the square root of variance, but has computational benefits.

Let's see how these apply to two poker players, who both have won an average of $100,000 per year for three years. To make it simple I dropped three zeros, and used sample calculations from an online calculator:

Live poker has variance just like any other form of poker. The thing about live poker variance is that it's much slower and prolonged than what you'll normally encounter in online play. With online poker, a player can swing up or down 5-10 buy ins in a single day. These types of swings are very uncommon in live poker due to the much slower.

Player A is a tournament player, and B is a cash game player.

Year A B
1 -100 +80
2 +500 +120
3 -100 +100
Average +100 +100
Variance 12000 400
Standard
Deviation
346 20

Tournament players have a much higher variance than cash game players. This implies they need a much bigger bankroll or backers to reduce their risk of going broke. The above calculations omit taxes and expenses which are also more punishing on a tournament player. Nothing too novel or earthshaking in the above analysis. Now I'm going to extend the idea of variance away from financial variance and on to life variance.

Most people in the United States have lived lives without much variance. Henry David Thoreau called this leading a life 'of quiet desperation.' Poker players have a lot of variance in their lives, and tournament players more so than cash game players. Not only do tournament players face financial variance, they also face time variance. When I head off to the Rio to play a World Series of Poker event, I don't know if I'll be done in 12 minutes or 12 hours. Obviously, this makes planning social activities, exercise, or anything else a lot more difficult.

The coronavirus pandemic has introduced much more variance, even into lives that are ordinarily extremely uneventful. Work, education, shopping, investing, socializing, and entertainment are completely different than they were a few months ago. Normally, one might try to predict the future by examining current trends and assuming they'll continue forward, but here we have no history on which to base our guesses.

Those of us who were of college age in the ‘60s, remember protesting. We protested against the war in Vietnam. We protested for civil rights, and ending Southern segregation. In some ways, those protests seemed to achieve their objectives: the war ended and the civil rights acts were passed. In reality, the United States has been in an endless series of wars or ‘peace-keeping' efforts. Minorities are still discriminated against. The unnecessary variance that a black person experiences ranges from trivial to deadly. More protests and more upheavals are coming.

Climate is going to be another huge source of variance in our lives. We are probably past the tipping point. Now we will have to learn to deal with more storms, each year's more severe than the last. Coastal cities will flood. Droughts and fires will become more common. Already a lot of areas in the world have trouble getting enough food and fresh water.

My only advice is to try to prepare for rising variance in our lives.

You can also find more ways to entertain yourself. We've been binge watching TV series. I recommend Sneaky Pete, which is about con artists and has some episodes involving poker. I would also recommend studying poker. In the next column, I will get to some specific recommendations of what to study and how to study it.

Steve ‘Zee' Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years and has two WSOP bracelets. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City – The Library near Houston and Doc Holliday's on 9th St. are his favorites.

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Variance In Live Poker

Expectation is basically an average. It measures what the average result will be over a large number of trials. Averages can be very deceptive when there are a few extreme (very high or very low) values. The median is another measure that overcomes this problem. It is found by arranging observations in order and then picking one in the middle.

To illustrate this difference let's look at the wealth of a US family. The average net worth is about $700,000, but this includes a few very rich people. The top tenth of a percent has an average net worth of over $40 million. The median net worth is around $100,000, quite a lot less than the average.

Variance In Live Poker Tournaments

Variance measures how much influence extreme values have. A low variance means that there aren't a lot of extreme values. The average is close to the median. A high variance means that there are extreme values that have a lot of influence on the result. Standard deviation is another way in which variation is expressed. It is the square root of variance, but has computational benefits.

Let's see how these apply to two poker players, who both have won an average of $100,000 per year for three years. To make it simple I dropped three zeros, and used sample calculations from an online calculator:

Live poker has variance just like any other form of poker. The thing about live poker variance is that it's much slower and prolonged than what you'll normally encounter in online play. With online poker, a player can swing up or down 5-10 buy ins in a single day. These types of swings are very uncommon in live poker due to the much slower.

Player A is a tournament player, and B is a cash game player.

Year A B
1 -100 +80
2 +500 +120
3 -100 +100
Average +100 +100
Variance 12000 400
Standard
Deviation
346 20

Tournament players have a much higher variance than cash game players. This implies they need a much bigger bankroll or backers to reduce their risk of going broke. The above calculations omit taxes and expenses which are also more punishing on a tournament player. Nothing too novel or earthshaking in the above analysis. Now I'm going to extend the idea of variance away from financial variance and on to life variance.

Most people in the United States have lived lives without much variance. Henry David Thoreau called this leading a life 'of quiet desperation.' Poker players have a lot of variance in their lives, and tournament players more so than cash game players. Not only do tournament players face financial variance, they also face time variance. When I head off to the Rio to play a World Series of Poker event, I don't know if I'll be done in 12 minutes or 12 hours. Obviously, this makes planning social activities, exercise, or anything else a lot more difficult.

The coronavirus pandemic has introduced much more variance, even into lives that are ordinarily extremely uneventful. Work, education, shopping, investing, socializing, and entertainment are completely different than they were a few months ago. Normally, one might try to predict the future by examining current trends and assuming they'll continue forward, but here we have no history on which to base our guesses.

Those of us who were of college age in the ‘60s, remember protesting. We protested against the war in Vietnam. We protested for civil rights, and ending Southern segregation. In some ways, those protests seemed to achieve their objectives: the war ended and the civil rights acts were passed. In reality, the United States has been in an endless series of wars or ‘peace-keeping' efforts. Minorities are still discriminated against. The unnecessary variance that a black person experiences ranges from trivial to deadly. More protests and more upheavals are coming.

Climate is going to be another huge source of variance in our lives. We are probably past the tipping point. Now we will have to learn to deal with more storms, each year's more severe than the last. Coastal cities will flood. Droughts and fires will become more common. Already a lot of areas in the world have trouble getting enough food and fresh water.

My only advice is to try to prepare for rising variance in our lives.

You can also find more ways to entertain yourself. We've been binge watching TV series. I recommend Sneaky Pete, which is about con artists and has some episodes involving poker. I would also recommend studying poker. In the next column, I will get to some specific recommendations of what to study and how to study it.

Steve ‘Zee' Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years and has two WSOP bracelets. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City – The Library near Houston and Doc Holliday's on 9th St. are his favorites.

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Variance In Live Poker Games

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What is variance? While we could go into the mathematical details we will explain variance on video poker machines using real world examples. Variance is one of the characteristics that makes a big difference in the short term results between one game and another. Lets compare two popular machines.
Below you have the pay tables for both full pay Jacks or Better (9/6) and a popular variety of Double Double Bonus (40/10/6). We picked these games for the example as both have a total return in the 99% range and compared side by side make a good example of variance in the real world.
Full Pay Jacks or Better (9/6) Dbl Dbl Bonus (40/10/6)
Hand PayoutReturn % Hand PayoutReturn %
Royal Flush40001.98%Royal Flush40001.95%
Straight Flush2500.55%Straight Flush 2000.44%
Four of a Kind 1255.91%Four Aces +2-4 20002.46%
Full House 4510.36%Four Aces 8002.78%
Flush 306.61%Four 2-4 + A-4 8002.29%
Straight204.49%Four 2 - 4 4003.08%
Three of a Kind 1522.33%Four 5 - K 2508.16%
Two Pair 1025.86%Full House 5010.86%
Jacks or Better 521.46%Flush306.77%
Straight205.11%
Three of a Kind 1522.59%
Two Pair 512.31%
Jacks or Better 521.16%
Total Return99.5439%Total Return 99.9577%
Variance19.51468Variance41.96707

Variance Explained

You will notice at the bottom of each pay table we have listed the variance. The first machine shows 19.51468 and the second is over double at 41.96707. The biggest difference when you compare the pays are the four of a kind wins. On the Jacks or Better machine they make up 5.91% of the total return while on the Double Double Bonus machine they make up 18.77% of the total return.
You will also notice that on the Double Double Bonus machine the pay for two pair makes up 12.31% of the total while on the Jacks or Better the same pay contributes 25.86% to the overall percentage. It is these changes in the way that pays contribute to the overall pay outs that alter the variance.
Let's say you play 1,000 hands on both of the machines above and do not hit a royal flush or any four of a kinds. At the end of the thousand hands it is more likely that you will still have a good amount of credits left if you were playing the Jacks or Better machine compared to the Double Double Bonus. This is because one of the more common hands, the two pairs pay is a win on Jacks or Better while it is simply your bet back on the second game.
Comparing the two games you will find that the first game will offer a longer run of smaller pays that keep you going while the second machine will be much harder on your bankroll if you do not hit any of the four of a kind ands. This difference is what variance is all about.
The question then comes to mind - Which machine should I play? In the example above the Double Double Bonus would be a better bet over the long term simply because it has a higher overall pay back. But in the short term you have to ask yourself, do you want regular small wins that keep you playing or do you want to have fewer small wins but the chance at the occasional big hit. This is a personal choice so there is no right or wrong answer - it is totally up to you.

Popular Games Compared

Below is a table showing the variance for several popular video poker machine types. This further illustrates the points made above. Note that the higher the number the higher the variance.
GameVarianceGameVariance
Pick'em Poker 15.0055 All American 26.7998
Jacks or Better 19.5146Double Bonus 28.2555
Bonus Poker 20.9040Double Double Bonus 41.9849
Aces & Eights 21.7259 Deuces & Joker 45.5885
Deuces Wild 25.8346Loose Deuces 70.3054
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