The definition of "variance".

[EjnarPik]

The question sounds simple: "What is the definition of "Variance"?"

Please be very specific.

Ejnar Pik, Southern-Docks.

[pzhon]

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The question sounds simple: "What is the definition of "Variance"?"

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In mathematics,

Var(X) = E((X-E(X))^2)

Variance is the average square of the difference from the mean.

In common English, variance refers to any deviations from the norm, or any variation, difference, or discrepancy.

[EjnarPik]

Thank you for your reply. I should have stated my question differently, so I'll try again:

What does posters in this forum mean, when they talk about "Variance"?

Ejnar Pik, Southern-Docks.

[dana33]

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What does posters in this forum mean, when they talk about "Variance"?

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The variance is this case is the mean-squared deviation of your hourly (or per-100 hand) winnings from their mean value (EV). (Sometimes when people say "variance," they actually mean "standard deviation," which is the square root of variance and thus has the same units as EV.)

[Smasharoo]

I think when you said specefic you might have meant simple terms, so I'll offer this:

How much money you will win or loose due to random luck, even if you play perfectly.

The more variance a game has the larger the swings can be in either direction.

Chess would have no variance, flipping a coin for your entire bankroll would have infinate variance.

[benfranklin]

If you win an average of 5BB an hour, you don't win exactly 5BB every hour. Some times you win more, some times less, some times you lose. Variance is an attempt to describe a normal range of your results in averaging 5BB an hour.

Your variance is going to depend on how you play and how your opponents play. If you play very tightly, and you play in a tight, passive game, your variance should be low. Let's say for example most of your results in these kinds of games are between -10 and +20 BB/hr.

If you play more aggressively, and in a loose, aggressive game, your variance will generally be greater. Let's say that with the same average win of 5BB/hr, your results are usually between -45 and +55 BB/hr. Your variance is much greater in this case, even though you are still averaging 5BB/hr.

What people are talking about on these forums is how one type of game or style of play compares to another as far as how wide a range of results you might expect over a period of time, how big the "normal" short-run swings are between winning and losing, even though on average you are winning.

[topspin]

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Chess would have no variance, flipping a coin for your entire bankroll would have infinate variance.

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I would be very impressed with the size of your bankroll if it really did have infinite variance in a coin-flip situation [img]/images/graemlins/smile.gif[/img]

[BlueBear]

Variance frequently can also mean "fluctuations" in many contexts.

for example, when I say that short handed poker is game with high variance, I also mean that short handed poker is game with high fluctuations.