At the beginning of the year my focus was on online poker. I set a specific goal which was that by the end of the year I would be playing 12 tables or more of 25c/50c and beating the level. After a few months of grinding I was on my way. I was feeling confident and thanks to playing tens of thousands of hands of cash game poker. plus the fact that I was working full time and earning a decent salary, I decided to go back to playing live cash game poker. Initially the results were great and for the first time in my life I kept my own and started crushing the live games. I downloaded a great poker app for recording all my sessions and was so happy to see that I was winning 7/10 sessions and making some nice extra cash every month.

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Fast forward 2 months and unfortunately the results haven’t continued on the same trajectory. After 24 sessions over the last few months I’ve won money in 54% of the games I’ve played and only made money in 2 out of the last 10. It is runs like this that test your resolve as a poker player and make you question both your ability and approach to the game. Last week I had another losing session, this time it was a combination of bad play on my end and very bad luck, but it wasn’t the fact that I lost money that upset me, it was how I lost the money.
There is an element of poker which can’t be denied and can’t be ignored and that is variance. People call it different things but variance is very simple to understand. There is the norm, which for example is getting dealt pocket aces once in every 220 hands, or flopping a set with a pocket pair in your hand 11.7% of the time, and then there is what happens in reality over a certain number of hands. The difference in the norm and what happens in reality is called variance. In the long run if you are playing with a regular deck of cards in a regular poker game, you will on average be dealt pocket aces every 220 hands. This is a fact and can be proven easily with mathematical software or by looking in a large database of an online poker player.

Now for interest sake lets say that you play poker with a bunch of friends once a week and on average you play for 5 hours and see 28 hands an hour. In my made up example, you will be dealt pocket aces once every 7.8 hours on average. Now imagine that you have two amazing sessions and within 56 hands you are dealt aces 4 times. This is really positive variance for you and will make you experience a much higher win rate than usual. Unfortunately this type of variance doesn’t last, remember, the stats needs to balance itself out, even though it will almost never be exact, in order for the stats to now balance themselves out, you could go over 6 sessions without being dealt pocket aces. Variance can be a bitch, especially in like poker where it takes much longer to balance things out.

My run of 10 sessions with only 2 wins made me realize this. I had been crushing the game and consider myself to have a decent edge over the average player in the game but a combination of run bad and lack of resolve on my part had resulted in a downswing that has lasted over a month and a half. During the last few sessions I have felt like a prisoner, chained to the outcome of the cards with nothing I could do, a feeling I hate even more than losing. The variance in poker is such that even a winning live cash game player can go many months breaking even or even losing money.

Aggressive Bankroll Decisions. Let’s start with an obvious point: If you don’t have a deep enough.

There are only two ways to beat variance. The first is playing through it. As long as you are a winning player and can control your losses, you will get through the bad spells and show a positive balance in the long run. The biggest problem with playing through the negative variance is that it can last a long time, hence my statement earlier that a winning player can go months without showing his true win rate. The second way to beat variance is having a massive edge over the competition. If you put Doyle Brunson in a poker game with a bunch of first timers, Doyle will almost always have a winning session, even if he is experiencing very negative variance. The reason for this is because Doyle has such a high skill level in poker that he is able to maximize his winnings and minimize his losses. In such a poker game, Doyle’s skill level will be the determining factor over his results, not variance.

Acknowledging these facts has humbled me because it has shown that I’m not as good as I believe. I still find myself making horrible calls and getting desperate when the negative variance comes knocking. I think I handle it better than most but it still eats at me. It really bothers me that at this moment I could go 3-6 months breaking even or losing money, simply because the cards are falling very much against me. I can’t push through it quickly because like the example I used, I’m only playing once a week and seeing around 28 hands an hour. For these reasons I have decided to take a break from live poker and concentrate on reaching the goal I set for myself at the start of the year.

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. These ups and downs of poker are often collectively known as “variance”.

What is Variance?

Live Poker Variance Rules

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.

The total of these seven sessions equals +140 (-11 + 85 – 30 + 144 + 9 + 30 – 87 = 140)

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

Live Poker Variance

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.

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.

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