It’s often claimed that good poker strategy involves a mixture of game theory, probability, psychology and statistics.
How exactly, though, do poker statistics formulate part of a strong player’s outlook?
In this article, we’ll consider 7 ways in which applied statistics can be used in the world of poker.
Let’s start by defining the term - poker statistics.
What Are “Poker Statistics” Anyway?
It’s useful to start with a definition of our term since it helps us to avoid confusing “statistics” with similar topics such as “probability”.
One dictionary uses the following explanation -
“The branch of mathematics that deals with the collection, organisation, analysis, and interpretation of numerical data.”
Note the emphasis on collecting data. Although poker statistics and probability share noticeable links, the term “statistics” has implications towards utilising pre-collected and pre-analysed data.
There are many areas where strong poker players first collect data, then interpret with the intention of deploying upgraded strategies at the tables.
1. Odds of Hitting a Hand
Poker players make estimates regarding how often a particular hand is likely to hit based on the number of potential “outs” left in the deck. For example, in Hold’em, a flopped flush draw will hit by the river roughly 36% of the time. Calculating such values on the fly mostly falls within the realm of probability rather than poker statistics.
However, when players attempt to memorise important values en masse before even reaching the tables, it now falls within the branch of poker statistics.
Rather than look to calculate values mid-hand, experienced players tend towards memorising pre-calculated numbers. Here is an example of a group of statistics a poker player may aim to familiarise themselves with.
The following table shows the chances of hitting hands in Hold’em, based on the number of outs and the current street.
Of course, all these numbers can be calculated on the fly utilising techniques derived from the field of probability. But calculating values mid hand is a waste of valuable time, and many players prefer to “just know” the above essential values.
2. Pot Odds and Break-Even Points
Both “pot odds” and “break-even points” can also be calculated on the fly using probability. However, once again, many players choose to memorise the following vital values.
The above table might prove confusing to those without a background in poker theory.
Here is a quick explanation -
Equity Required to Call – Otherwise known as “Pot odds”. Pot odds are different from the “odds of hitting” outlined in the first application of poker statistics. “Pot odds”, when expressed as a percentage, indicate the percentage of the total pot we would be investing on a call.
This number is identical to the amount of pot-equity required to break even on a call when closing the action.
For example, according to the above chart, if our opponent makes a 50% pot-sized bet, we’d be investing 25% of the total pot if we made a call. Assuming we are closing the action, we’d need at least 25% pot equity to break even on our call.
Break-Even Point of Bluff – This value shows us how frequently a bluff (of a specific size) would need to take down the pot to be directly profitable (ignoring any pot equity). For example, a 50% pot-sized bet would need to take the pot down 33.33% of the time to be directly profitable.
All these values can be calculated directly on the fly using probability, but most serious poker players prefer the statistics-based approach of simply memorising all fundamental values.
3. Using Poker Statistics for DB Analysis
Online poker players typically track their played hands using poker tracking software. Said software essentially stores every hand played and compiles the data to display essential poker statistics, such as “number of hands played” and “total winrate”.
This is really scratching the surface, however, since tracking software typically offers hundreds of stats that also display information on specific aspects of a players game, for example -
- How often a player fires a continuation bet on each street.
- How often a player folds to a continuation bet on each street.
- How often a player 3bets preflop.
- How often a player folds to a preflop 3bet
- How often a player raises the flop
In fact, pretty much any conceivable scenario can be tracked since many poker trackers offer the ability to create custom statistics.
Serious players dedicate significant time to trawling through their various poker statistics and comparing them to the stats of strong winning players. This is a great way to spot leaks because it allows us to analyse an extensive sample of hands quickly.
Many poker players hence have direct experience working with a database of statistics and probing it for weaknesses by applying a range of filters.
4. Using Poker Statistics for Villain Analysis
If we can analyse our own data, we can absolutely analyse our opponent’s data.
We can probe his statistics in much the same way that we do our own. This time we have a different goal in mind, however.
We are looking for weaknesses in our opponent’s game, which we can exploit.
For online players, it’s commonplace to display poker statistics on opponents in real time, using a table overlay known as a HUD (heads up display). Accurate poker statistics usage is a crucial factor in maintaining the highest possible winrate.
There are generally differing opinions on the ethics of HUD usage. Some players will be running a HUD, while others won’t. Naturally, this gives players with a HUD a potential advantage over players that don’t have one.
This is a concern with some poker rooms since strong players destroying the weak players too quickly is believed to cause a weak or non-sustainable poker ecology. Some rooms look to limit HUD usage for specific formats or even ban them entirely.
Other rooms consider HUDs fair game since all players have the ability to load a HUD if they so desire. It’s no secret, however, that poker rooms which allow HUDs are typically tougher than poker rooms that don’t.
5. Using Poker Statistics for Population Analysis
The term “population analysis” describes the technique of analysing average statistics for the entire population of a certain poker-room, limit, or network.
This is very similar to “villain analysis” with the key difference that it does not look to target individual opponents. Instead, it seeks to capitalise on the mistakes that an average player makes. This is useful for playing against unknown opponents since we can assume that an unknown opponent’s strategy will typically mirror the common mistakes of the population (on average).
Population analysis techniques are especially useful for dealing with anonymous poker environments (where the screen names of all players are concealed). It was previously believed (although, it seems somewhat naïve looking back) that exploitative poker was not possible in such environments, and that the only approach was to try and employ some approximation of game theory correct poker.
Using population analysis techniques, it is possible to play exploitative poker in anonymous environments by examining the overall trends of the entire population.
6. Poker Statistics in GTO Play
GTO stands for “game theory optimal”, and it’s the term used to describe a perfect, theoretically correct, game of poker.
Unfortunately, GTO poker is exceptionally complex. It’s often believed that even if we knew what a GTO poker strategy looked like (which we don’t, not entirely), it would be so complicated that only a machine could follow the strategy anyway.
Naturally, there is a lot of data that needs to be considered. This is where statistics come in handy. Game theory solvers (tools which make approximations regarding GTO strategy) generally allow us to output results into a database format (such as an excel document). Players who are actively working on developing game theory optimal strategies often have large amounts of information stored in such formats.
They will peruse this information periodically to recap on the various frequencies and strategies advised by their GTO solver.
7. General Poker Statistics
General statistics on poker demographics, as a whole, help us to generate realistic expectations regarding what we are looking to achieve with an online poker career.
For example, the following (potentially unverified) statistic is often cited -
5% of poker players are winning players.
Less than 1% go on to make big money.
More specific values could be obtained by reviewing the data from particular networks. Having said that, the fact remains that the majority of poker players end up losing money.
This doesn’t mean that poker is not entirely beatable, but it underscores the idea that some measure of hard work will be necessary before we can expect to profit playing poker consistently.
Poker Statistics and You
The above list is not exhaustive. There are plenty of other ways that the mathematical branch of statistics can be directly applied to the world of poker.
While it’s not entirely a prerequisite, many successful poker players have an interest in statistics and understand the critical role it plays in generating sound strategies.