Understand poker Variance & don’t tilt!

Poker professionals are still all too often tarred with the same brush as gambling addicts: How often do you hear a sports professional being asked if they win or if they are good?? This perception probably not helped by the majority of poker personalities that reach the spotlight. But the main reason for this is because poker is an extremely high variance game.

I’m not convinced the majority of professional poker players realise to what extent. There seems to be something engrained in humans to believe that a 9bb/100 win rate after 100,000 hands is an indicator of being the best player since sliced bread, similarly to a recreational player thinking their 3 buyin win in a session must makes them the best player since sliced bread. Conversely the 0-1bb/100 grinder that’s played 300,000+ hands, and still thinks they need coaching, probably does not understand variance significantly more than the recreational player that has decided that a certain site is ‘rigged’ or that poker is ‘rigged’ in general because they lost a few buyins.

Here is the expected winnings(big blinds) of a 4bb/100 winner(after rake) over 1,000,000 hands:Poker variance graph 4bb/100
Courtesy of Pokerdope.

The difference between the worst and the best run (of the same profitable player) over 1 million hands is 75,000BB’s = 150,000big blinds = 1500buyins.
The worst run that this player will have will give him an actual win rate of around -3.9bb/100 (over a million hands), and the best run of that same player will result in a win rate around 10.5bb/100.
It’s worth noting that the 95%confidence interval is around 0bb/100 and 8bb/100 after 1,000,000 hands. That is quite a difference in actual results, and it really should raise questions about judging a player on their win rate.

For 100,000 hands the bb/100 95% confidence interval is approximately between 16bb/100 and -8bb. Which is even crazier. Are you certain the people who are offering coaching play any better than you?
This is all with a standard deviation of just 100. HeadsUp would have even more variance, and Tournaments even more (as if cash games didn’t have enough!).

Now look at those 8.5bb/100 confidence intervals: So much prettier!Poker variance graph 8bb/100
Courtesy of Pokerdope.

But it’s still plausible that you could lose after 100,000 hands though! That’s the nature of being a poker professional.

It’s also worth understanding that despite the almost incomprehensible variance shown already, standard deviation bb/100 probably doesn’t tell the full extent of the variance story.

Let me explain: There are 1326 combinations of being dealt two cards (a starting hand) in No Limit Texas Holdem, which can be compressed down to 169 non-equivalent combinations given AcAs is of the same starting value as AdAh, and 7d2d is of the same starting as 7h2h etc. There are 52 cards in the deck, minus your two known cards, to the power of 3 gives (50^3=125,000) possible flop turn and river combinations.

It is not possible to play every 169 combinations of starting hands on every 125,000 possible flop turn and river combinations against every opponent. If it was then we would have an objective measure for how good a player is, but that would still not take account for varied strategies in combination. I.e. you may play your AA one way 70% of the time and your AA another way 30% of the time.

In comparison to a recreational player, there are less combinations of boards/starting hands that a professional player will get his whole stack in by the river. An unmeasured form of variance is how often you and your recreational opponents get hands they consider good enough to put significant amounts of money in the pot when yours is better. You can sit all day at a table with recreational players, but if they never flop top pair bad kicker when you flop something better, it’s going to be hard to stack them before they lose their money to some one else. I wonder how much this hidden variance accounts for, relative to the Standard deviation variance?

Professional players would have probably read something similar before and given it little credence. Until one experiences both a significant downswing and a significant upswing, while still playing predominantly the same strategy, one will never truely believe the above graphs and the extent of poker variance. Alas, people will always tend to be outcome orientated.

When you are running bad (or even good) over your relatively tiny sample, come back and comprehend this again. Don’t stray away (Tilt) from optimal play out of frustration because then you lower your average EV line. Keep playing good, and realise that your win rate is not something you can control.