Variance and Bankroll Management

Poker is a game of skill, but that doesn’t mean a skilled player will always win in the short-term. You can be the best player in the world, play flawless poker, and still lose money over 10,000+ hands. That’s just the nature of the game.

When planning your poker career, you have to account for variance. Variance is basically statistical deviation from expected value. That may sound complicated, but it’s actually simple: sometimes you’ll lose as a favorite, and sometimes you’ll win as a dog. It’s when the former happens – and then happens again, and again, and again – that the going gets tough.

Consider the following scenario: you’ve got AA preflop on the button, and a terrible player bets into you. Everyone folds, you 3bet, and your opponent pushes all-in. Obviously you snap-call, since you’ve got the absolute nuts. Your opponent turns over JTo and you quietly chuckle to yourself, expecting to take down the pot.

You’re right to expect a win in this situation. Your aces have about 82% equity in the hand, meaning you expect to win 82% of the time. But this time the board comes down J-T-J-2-3 rainbow, and your aces lose.

Okay, you think, that’s fine–I expect to lose 18% of the time with aces, and this is one of them. No big deal. But the next time you get aces, your opponent outdraws you to a straight. And the time after that, your opponent flops a flush. And the five times after that, well… You get the picture.

Losing with aces more than four times in a row defies mathematical expectation. Your aces should win 4/5 times and lose 1/5. That’s what you expect, because that’s what should happen. But because cards come randomly, sometimes things don’t go according to plan. You can easily lose more than you should in the short term.

That’s variance.

Why Bankroll Management Matters

Variance can send you on some crazy downswings. It can be cruel. Pro players often liken downswings to being trapped on a roller coaster while under the influence of bad hallucinogenic drugs. That’s what it feels like to lose when you should be winning – it’s no fun. And it’s easy to let your game slip when you’re stuck on this roller coaster from hell.

That means you need to plan in advance for large downswings. You want to make sure you can absorb losses you don’t necessarily expect. If you don’t plan for variance, you might end up losing more than your bankroll can handle; that’s a one-way ticket to Bustoville, and it’s really no fun.

Hence the necessity of bankroll management. The idea is to always play with a bankroll that can handle large deviations from your expected winnings. By keeping some extra buy-ins in your bankroll, you avoid going bust. That’s critical to keeping you in the game for the long-term.

This is all just a really complicated way of saying the following: play within your means.

Basic Bankroll Management

The general consensus among online players is that you should have 20 buy-ins for whatever cash game stakes you’re playing. If you’re a tournament player, the rule of thumb is 100 buy-ins.

For example, say you’re a No-Limit Holdem cash game player. Your regular game is $1/2, where most tables have a $200 buy-in. A proper bankroll for you is $4000 (20 x $200). This amount will insure you against downswings, and make sure you can stay in the game for the long haul.

On the other hand, say you’re a tournament player. Your regular stake is $10+1, but you play some $20+2 tournaments as well. In this case, you’ll want to keep at least $2,000 in your bankroll. Keeping 100 buy-ins in your account will prevent you from going bust when variance keeps your ROI under expectation.

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