This is actually a section out of my book, The Ultimate Poker HUD Guide.

I’ve been wanting to write a post on the topic of sample sizes for awhile and decided to kill two birds with one post. Along with a discussion on sample sizes this is a shameless promotion of the book!

The Most Important HUD Stat

I want to introduce you to the most important stat – although it doesn’t tell you a single thing about how your opponent plays. This stat should be included on every HUD and referenced before you make any important decisions… I’m talking about the “# of Hands” stat. Without knowing this number, you won’t know whether or not you have a relevant sample size for the stat you’re looking at.

What’s a “relevant sample size”, you ask? It depends on the stat you’re looking at. Some stats will converge (move closer to the player’s actual stat value) very quickly and others may take thousands of hands.

There’s such a big range because some stats, such as VPIP and PFR, are affected after every hand that’s dealt. Other stats, such as turn C-Bet, just don’t have the same opportunity to collect data. In order to get data on a turn C-Bet stat, the player needs to be the preflop raiser and then C-Bet the flop. Only after those two conditions are met will we have a situation where a turn C-Bet is possible.

Players with higher VPIP numbers see more flops. So, these players’ post-flop stats will converge more quickly than a tighter player’s.

Reads From Any Sample Size

I’ve often read that you need X number of hands before a certain stat becomes significant. I tend to disagree with this logic, at least in part. I suppose it depends on your definition of significant. My definition of a significant stat, in this context, is simply a useful stat. As soon as you have just one hand on a player, you can begin to obtain useful information. While the information may not be statistically significant, it’s the only information you have so it shouldn’t be completely discounted.

As an example, on the very first hand a player from UTG limps in. This player now has a VPIP/PFR of 100/0. It’s only been one hand, so these numbers will surely change drastically during the next few hands, but what can we gain from the numbers right now?

More than you might assume, but we will need to make some broad generalizations. Limping from under the gun is a play regulars will rarely make. So maybe we can assume this player is a recreational player. If we assume that, we can also assume that his range is very wide, given that almost all recreational players play far too many hands.

Maybe we can make some assumptions about how he will play on the flop? Many recreational players that like to limp also play very passively post flop. From just this one hand sample we can really start painting a picture of this guy’s tendencies. It’s no guarantee, but we draw the best conclusion we can from the limited information we’ve been given.

Assume we have AJo on the button and a new player sitting UTG limps in. His VPIP/PFR stats are now 100/0 over a one hand sample. The action folds around to us, what’s the best play? Personally, I want to start building a pot with this opponent, who I assume will be loose-passive. My hand is way stronger than his probable limp-calling range, and I have position. So I pop it up to 4x the big blind and expect a call. Think about how this hand would play if the new player UTG open raised to 3 or 4x the big blind instead of limping. That makes it a totally different situation, right?

Maybe this example is oversimplified. You would certainly be able to come up with the same conclusions even if you didn’t have a HUD. But what if you are playing 8+ tables?

My point here is don’t disregard a particular stat just because you don’t have a good sample. Take the data in context and use it to formulate your plan.

How Different Stats Converge

You should consider the particular stat in question when determining how valid it is, based on sample size. A stat like VPIP will converge near the player’s true VPIP rather quickly. I’d say that the VPIP and PFR stats get close enough between 20 and 30 hands, while a stat like River C-Bet will take a very long time to converge, probably several thousand hands.

With experience you will learn which stats converge quickly or slowly. Holdem Manager’s pop ups display the sample size for a particular action next to the stat value. When you see a stat with a low sample number, while it may still be useful, you know to give it less weight. When possible actions occur more than 20 times or so, you’re starting to get a real meaningful number.

Stats are here to help provide information about your opponent. Don’t be afraid to use the information you’re given, even if you aren’t given “statistically relevant” data. At the same time, employing solid poker principles is really the name of the game, so stat reads should not override them, regardless of sample size.