Be Wary of Poker Statistics: Part 1

I get requests to split the Poker Copilot HUD statistics into streets and positions. People want to know how often their opponent Bob folds to 3-bet on the river when on the button.

There’s no technical challenge to offering this. But I’d be doing you a disservice by giving you this information. Because it would be of no use. Unless you spent too much time reading statistical textbooks, you might try to use the info. Making decisions with bad info is not good.

Here’s the basic principle: Statistics are only reliable if they are based on a large enough sample space. The larger the sample space, the more reliable the stats.

Let me try to explain. Consider the “folds to three bet” statistic. Imagine Bob, in the long run, all else being equal, folds to a three bet 50% of the time.

If we have data for Bob being in this situation only once, he either folded or he didn’t fold. So the statistics would show that he “folds to three bet” either 0% or 100% of the time. Both of these stats are as wrong as it is possible to be. Whatever conclusion you draw from this data is baseless.

So we keep playing against Bob and collect more data. Now he’s faced a 3-bet four times. He folded either once, twice, three times, or four times. So his stat will be 0%, 33%, 67%, or 100%. These numbers are still unhelpful. Remember Bob’s true tendency in the long run is to fold to 3-bet 50% of the time, but the closest we get with these stats is still way off. A casual look at, say 67% will give the impression that Bob is scared of 3-bets. If the stat shows 33%, you’ll think he is quite brave. Any decision you make based on this data is working from false assumptions.

How many times would you need to play against Bob to get a reliable stat? Lots. If you want the stat to be accurate within 5% at least 50% of the time, you’d need to see Bob face a 3-bet 21 times. Based on my Poker Copilot database of 9-player ring game no-limit hold’em, people face a three-bet preflop once every 23 games on average. To gather enough data on a player to have a “within 5%” accuracy for half the time, you’d need to play against that player almost 500 times.

Play against Bob 500 times and you’ll have a sort-of, but not-quite reliable “folds to 3-bet” stat.