Am I Crushing or is it Poker Variance?
“I can win $1,500 to $2,000 on any given night…. Is that considered crushing?”
Someone recently posted this on my facebook page. And it’s a perfectly reasonable question.
How do we truly know if we’re crushing our game or if it’s just poker variance?
To answer that, first we need a definition for “crushing”:
Achieving a win-rate (over a statistically significant sample size) that is better than most of the other regulars in your game.
Now I’ll break down the operative parts of that definition.
Win-rates in cash games can be described in different ways (insert currency of choice): $ per session, $ per hour, or big blinds per 100 hands. Win-rates per hour and per session, while personally meaningful, cannot easily be compared among players since individuals may be getting more or less hands dealt per hour or may be playing sessions of varying lengths.
Big blinds per 100 hands (i.e. bb/100) works best because it removes any dependency on the rate of hands dealt as well as the stakes.
The Role of Variance in Poker
Let’s discuss what constitutes a “statistically significant sample size”. In the field of statistics, any quantitative observation is usually qualified with a confidence interval if it is to be given any merit.
We can do the same with our win-rates. For example, Pete Poker might claim he’s 95% sure that his win-rate is 5 bb/100 plus or minus 0.5 bb/100.
How many hands does Pete have to play to be 95% confident with such a tight margin of error?
For this we need Pete’s standard deviation (which is also the square root of Mr. Poker’s variance). Taking 6-max as an example, you’ll often see standard deviations around 9 bb/hand. Both Holdem Manager and Poker Tracker will give you this value.
This is the equation needed to find the solution (taken from that same wiki page):
For a confidence of 95%, our “z value” is 1.96. And if we plug in the numbers and solve for n, we get …wait for it… 12,400,000.
We need 12.4 MILLION hands to be 95% confident that a typical 6-max win-rate falls within 0.5 bb/100 of our estimate.
Sorry Pete, I don’t buy it.
Let’s look at this another way. How confident can we be after 200k hands?
Using the same equation, with a 95% confidence interval, your margin of error is 4 bb/100.
If we reduce the confidence interval to 67% for 200k hands, we can get the margin of error down to 2 bb/100, but that’s not really sounding very confident to me.
(Check out NoahSD’s post for a deeper exploration which also touches on risk of ruin.)
Note as your style or game gets wilder, you will be even less confident for the same sample size since your standard deviation (i.e. poker variance) is higher. If you play in a more conservative game (e.g. live full-ring), then either your confidence would be higher or you could get by with a smaller sample size for the same level of confidence.
For those of you that do play live, how long would it take you to play 200k hands? Optimistically assuming you get dealt 33 hands per hour, you need to play 6,000 hours. If there are 2,000 hours in a typical work year, that’s 3 years playing full time!
Better than the Other Regulars
Let’s look at the last part of our crushing definition. How do we compare to the other regs?
In my article, How Much Money Can You Make If You Play Online Poker, I stated that a good win rate for regs is about 5 bb/100.
To be crushing then, you would want to be confident that you’re making at least that much.
Returning to our 95% confidence interval for 200k hands, our margin of error was 4 bb/100. Thus if you wanted to be “confident” that you were doing better than the other regs, you would need a win-rate of 9 bb/100. Thus…
To be crushing, you would need to sport a 9 bb/100 win-rate for at least a 200k hand sample.
What if I Don’t Have that Many Hands?
My short answer: just let it go. If you’re trying your best, then that’s the best you can do!
Move up when proper bankroll management dictates you can, and move down when your roll dwindles too far.
My approach is that I apply steady, ongoing effort towards studying the game and gaining experience at the table. Over time, my bankroll tends to trend upwards. If it starts trending down for an extended period of time, I re-evaluate things and usually make some changes.
If you’re just dying to know how you stack up against the competition, then consider this. You will know when your skills have reached the level that you are better than most of the others in your game. At some point, their leaks will become obvious. Your sessions will be relatively stress free, and you’ll post wins FAR more often than losses.
Any Other Questions about the Effect of Variance in Poker?
We got into some maths in this post, so by all means, do not hesitate to ask for clarification in the comments below. I’m happy to walk you through any of this.
Or if you have other techniques you use to assess skill advantage, I would love to hear them!