Understanding Variance to Improve Poker Strategy

Jason Lake

Tuesday, August 19, 2014 8:16 AM GMT

As of this summer, nobody is allowed to share bad beat stories except for one man: Connor Drinan. The fact of the matter is, though, this can and probably will happen to you, too.

Don’t tell me

Hard luck stories

And I won’t

Tell you mine

            – Neil Young, “Hard Luck Stories” (Landing on Water, 1986)

 

You may have seen him on TV earlier this month at the Big One for One Drop, the World Series of Poker tournament with the $1-million buy-in. Drinan was one of 18 players left from the 42 who started the event, with the final eight scheduled to finish in the money, and he found himself in the big blind with the best two cards in no-limit hold ‘em: a shiny pair of aces. 

Imagine Drinan’s disappointment when Cary Katz opened, 4-bet, and called Drinan’s 5-bet shove with: pocket aces. This scenario leads to a chop 96 percent of the time, but the One Drop was not one of those times – the board produced four hearts, and Katz had the Ace of Hearts for the flush. Drinan was knocked out of the tournament. Katz went on to finish eighth and “min-cash” for $1.3 million. Sad trombone.

 

Your Mileage May Vary
If you play enough hands, this will eventually happen to you, too. Maybe not with millions of dollars on the line, but still: You will have your pocket aces cracked by pocket aces. That’s on top of all the times your nut flush will get beaten by a straight flush, and your boat sunk by a bigger boat. And you haven’t really lived until you’ve lost a tournament heads-up on a one-outer.

There are three things you can do to deal with these bad beats:

1. Stop playing poker.

2. Fold every hand that comes to you.

3. Get over it.

We’re recommending Option No. 3. As the Stoic philosopher Epictetus once wrote, some things are up to us, and some things are not up to us. That’s poker in a nutshell. Make no mistake, this is a game of skill, but there’s also a built-in element of randomness over which you have no say. The general consensus is that NLHE poker is about 70 percent skill and 30 percent luck – although we hate to use that word. We prefer variance.

 

Sim City
Unless you’re keen on losing your bankroll over and over again, you need to wrap your head around the concept of variance. One great way to do this is to go online and look for a variance simulator. There are plenty of good ones out there. Plug in a winrate and a number of hands, plus a standard deviation. Don’t worry if this is a bit too statisticky for you. The simulator should have some default numbers already chosen for you.

Just to give you a taste, we ran a sim of 1,000 trials with a very healthy winrate of 8BB/100 played over 100,000 hands, with a standard deviation of 80BB/100. In other words, imagine 1,000 excellent players, all playing at exactly the same level of skill over the same number of hands. The results may surprise you. One player ended up with just over 15,000BB in profit. Another ended up with under 1,000BB. If they were playing 100NL, that would mean a difference of $14,000 in earnings between those two players. All of it out of their control.

That doesn’t mean you’re totally helpless against variance. There is always a risk of ruin in any investment, but if you exercise smart bankroll management and only put a small portion of your bankroll on the line at any one time, you can maximize your chances of cashing in. Meanwhile, keep studying. The better you are at poker, and the better you are at finding the fish, the bigger your winrate will be. One last thing: as always, don’t tilt. Tilt is for suckers.