Chris “Jesus” Ferguson, the 2000 World Series of Poker Main Event Champion, once described no-limit Texas Hold’em as “all luck and all skill”.  While each card arises from the luck of the draw, the ways that a player deals with each turn of the cards comes from practice, skill and experience.

The statistical ups and downs that come with the game of poker (both land based and online poker) are collectively known as “variance”, and how players cope with the inevitable variance separates the mediocre ones from the all-time greats.

What is variance?

Variance describes the differences between a set of numbers and the average of that set.  For instance, if the numbers are close to their average, the set has a low variance.  If the numbers are widely spaced, the set has a high variance.

Example of variance

Here are some numbers from recent \$0.25/\$0.50 no-limit Texas Hold’em cash games:\$3.10, \$7.20, \$24.95, \$0.22, \$16.30, (-\$4.30), (-\$19.89)

The total profits from all of these sessions are \$27.58.The average profit per session is: \$3.94.(This assumes all sessions were equal length).

To calculate the variance, we start by subtracting each number from the average, square that result, add all the results together and divide that sum by the number of sessions. By squaring the differences, we make sure that values lower than the average do not cancel out those higher than the average. With this data, the variance is 209.19.

Standard deviation

Standard deviation is the measure of how far the values “deviate” from the average. To calculate the standard deviation, take the square root of the variance. With this data, the standard deviation is 14.46

Note: Most spreadsheet programs and scientific calculators have the capacity to calculate variance and standard deviation automatically.

What do variance and standard deviation tell us?

From the extreme values at either end (-19.89 to +24.95), we should expect a high variance. If each session’s profits were closer to the average of \$3.94, then the variance would be much lower.

The standard deviation can tell us what to expect in future sessions.  The standard “Bell Curve” from statistics shows us that most values will fall within one standard deviation of the mean.  In this case, as we play more sessions, the results should fall between -\$10.52 and +\$18.40 (\$3.94 +/- \$14.46).

Variance and cash games

Why do the best players in the world play fixed-limit mixed games rather than no-limit Texas hold’em cash games? The mixed games require much more skill (and, thus, much lower variance) than no-limit hold’em games. Also, the fixed-limit betting structure cuts down on big bets, which can cause huge swings in a player’s bankroll (and emotions).

Variance and tournaments

While victories in major poker tournaments often bring the big money, the heavy publicity and the shiny trophies, they also happen so infrequently, even for the best players. Veteran players can (and frequently do) get knocked out of the money dozens of times before reaching a TV final table. To curb the variance of tournaments, almost every notable pro poker player makes their living from cash games rather than tournaments.

Part II: The mental game

In Part II, we’ll examine the mental makeup it takes to succeed in the face of the ups and downs of the game. As the pros like to say, “poker is a hard way to make an easy living”.