Variance
Variance is the natural up-and-down movement of your results around the average you expect over time. Even a winning player has losing days, weeks and months, because the cards are random.
The simple explanation
If you make the best decisions, you will still lose some hands, sessions and tournaments. Variance is the reason. The more hands you play, the closer your results get to your true win rate, but short-term results are strongly influenced by luck.
A closer look
Variance is measured by standard deviation. In no-limit hold'em, the standard deviation is often about 80 to 100 big blinds per 100 hands, which is large compared with a typical win rate of a few big blinds per 100 hands. This is why a player can lose many buy-ins in a row while playing well, and why bankroll management matters. Tournaments have more variance than cash games, since the prizes are concentrated at the top. Accepting variance is a psychological skill that helps to avoid tilt.
A practical example
A player with a win rate of 4 bb/100 can still lose 10 buy-ins over 20,000 hands because of variance.
Full explanation
Variance is the natural up-and-down movement of your results around the average you expect over time. Even a winning player has losing days, weeks and months, because the cards are random.
Variance is the random fluctuation of results around the expected average.
It affects every player, even the best.
It is larger in tournaments than in cash games.
Bankroll management exists to survive it.