Variance and the long run

Egotistical delusions aside, the best measure of this is results. However, results can be a fickle friend. World class players can crash out of 25 WSOP tournaments in a row while watching complete novices take down major prizes. So how big a sample of hands or tournaments do you need to know that you are a winning player? And how does that inform your bankroll considerations?

The answer depends on the various factors mentioned in the previous article in this series (‘Variance and game selection’). Playing at a level where you have a big edge, at full-ring tables, and in deep cash games or tournaments with structures that give a generous stack-to-blind ratio, you will need to post a smaller sample of results to know how well you’re doing than if you are multi-tabling a bunch of turbo tournaments against good players.

The bad news is that even in the first scenario – where you stick to low-variance games – the required sample size is larger than you might expect. Your results should start showing defined long-term patterns (good or bad!) within about 500 tournaments or 50,000 hands at cash games. Depending on the aforementioned factors, it takes around two to eight times that amount before the fluctuations settle enough to show a convincing long-term picture. That’s a lot of hands! So in high-variance situations, you could be looking at anything up to 4,000 tournaments before you start posting your results on the forums with pride.

Bankroll and variance

Variance is what informs correct bankroll management. If even solid, profitable players have to wait thousands of hands for the luck factor to even out, it’s a sure bet a healthy bankroll is needed in order to stay afloat.

Indeed, the received wisdom is that you should not buy into a cash game or multi-table tournament for more than 2% of your bankroll. In other words, if you regularly play $20 multi-table tournaments, you should have a bankroll of around $1,000 set aside to cover the up and downs.Many players use different bankroll structures, however. For example, to take ‘shots’ at higher levels, they might set aside 20 times the buy-in at that level, and if they bust that bankroll drop down to the previous level.

Either way, be sure to take into account all the factors that affect variance. Remember, the more variance in the game you play, the bigger the bankroll you’ll need to overcome the swings, and the larger the sample of results you’ll need to know how well you’re doing.

Read Part 1...

Read Part 2...