Poker Reality #3: Poker Is A High Variance Game

If we want to ride the emotional roller coaster that is Texas Hold'em--and not lose our minds along the way--we have to accept some hard truths about the game. The first two of these "realities" were covered here and here. Today I want to talk about another tough one for beginners to stomach:

Poker is a high variance game.

Poker is a game of probabilities, of getting your money in good, and then ignoring the results. But the results can suck. Let me repeat that for clarity: the results of a poker hand can SUCK. And this sucking sound can occasionally extend for a long, long time, hand after hand, and even session after session, regardless of how well you're playing. Get used to it, because variance happens to all of us, independent of how good we are.

Variance is the difference between how much money you expect to win over the long run (based on your skill) and the actual results you experience in the short term. Said more simply: variance is the luck-based upswings and downswings of the game. Unfortunately, these swings aren't within your control, and they can be big and sustained. In the long run, the up and down variance of the game will equal out, but in the short term the roller coaster effect can be significant. Poker is not for the feint of heart. Here's a chart of my results I took from Holdem Manager from a random month last year playing $50NL full-ring. My journal notes indicate that I felt I was playing solid, ABC poker during this period:

Results from a little more than 9,000 hands of $.25/$.50 ($50NL) full-ring cash. The straight reddish-orange line shows how much was theoretically expected to be won (based on my long term statistics at these stakes). The green line is a plot of my actual results. The difference between the two lines at any point is a measure of the variance. Note that after almost half the hands were played, I was still essentially at zero net dollars won, with a negative variance of about -$250. By the end of the 9K hands, the variance was less, but was still negative.

In the entertaining book The Making of a Poker Player, author and WSOP bracelet winner Matt Matros calculated that for winning players there is still always lurking a 5% chance of losing 300 big blinds due to variance. In the graph above, I dropped over 500 big blinds at one point. Was all of this variance? Probably not; part of it was undoubtedly bad play on my behalf (or maybe even tilt), but my journal indicates I was playing solidly and felt good about the sessions, so I would argue that the majority of all the swings shown in the chart were simply due to the luck of poker. I.e. Variance.

Variance is caused by the randomness of the cards you're dealt, the board cards, and how your opponents play. Having a better hand preflop against a weak opponent is no guarantee you're going to win. For example, let's say you have AK and get your money all-in against an opponent holding AQ. The good news is that your AK is said to "dominate" the villain's AQ, right? Right, except AQ will still win about 25% of the time against your Big Slick by the river. Seriously. Run it in PokerStove if you don't believe me. One out of four times AK loses this battle. Ouch.

This is why bankroll management is so important in poker; it's really easy for a 3:1 favorite like AK against AQ to lose five times in a row, resulting in a five hundred big blind downswing. Hell, AA will lose to KK nearly 20% of the time. Ouch ouch.

Variance is mostly affected by luck (which is obviously outside your control), but it's also a function of some other key factors that are within your sphere of influence. For instance, your playing style can have a big impact; a loose-aggressive style of play generally has more frequent and larger swings than a tighter, more conservative style. Variance is also a function the game type and betting structure. Pot-limit Omaha, for example, is notorious for its high variance, while a game like limit Hold'em will have considerably smaller swings.

What's vexing about all this is that it's not always obvious--especially to beginning players--whether a losing streak is due to the vagaries of variance.... or just bad play. Analyzing your game when on a losing streak is hard... but so is analyzing your game when you're on a winning streak. In fact, it might even be harder when you're winning, because you're human, and that little thing called Ego starts to get in the way.

Separating the effect of luck from chance takes a lot of data. It also takes detailed analysis. Just look at the chart above and tell me what part is due to luck, and what part is due to bad play. You can't without doing an in-depth analysis on each hand played during that 9K stretch. That's a lot of work, but it's necessary if you want to ensure it's luck eating your lunch, and not bad play.

Variance can also be mentally draining to even the most hardened professional player. Losing, session after session, even though you're doing everything right, can take its toll on your psyche. Even when said professional reminds themselves that variance is what keeps the bad players coming back (i.e., if bad players never won due to dumb luck, they'd quit the game and take their money with them). But try telling that to yourself after you've dropped five straight buy-ins and are convinced that the poker gods hate you.

Anyway, the point I'm trying to make in this post is that the reality of variance happens, and if you want to mentally survive the roller coaster of poker you have to accept its ups and downs. In fact you have to embrace it. Otherwise find yourself a nice merry-go-round game to play on. Poker is not for the weak.

All-in for now...
-Bug