In our years of experience providing support help for PokerTracker users, it is our experience that stats filtered to specific situations where the Hero was involved (or as they are commonly referred to as verses Hero stats) are often misunderstood. When the function of how a vs Hero stat actually works is properly understood, then it is easier to understand why the functionality of this type of stat has little value for the situations in which most poker players would like to use them.
We hope to use this blog post to explain why these kinds of statistics are not useful for any serious poker analyst, or any player who desires to become an better at game analysis. In turn, we will explain at least one way you can use PokerTracker 4 to give you real, useful data to help you analyze these aspects of your opponents rather than relying on the false hope of vs Hero stats.
Hang on tight... this is a long explaination, but the results are worth it. We hope that you find this blog posting to be a goldmine of reference information that helps you better understand how to use the built in functionality of PokerTracker 4, while addressing the timeless poker question "does this player alter his play against me?".
The Desire for Versus Hero Stats
The desire to see statistics against your personal play is a very reasonable and understandable thing. As players -- indeed, as human beings in general -- we all want to know what other people think of us. We want to know if an opponent is reraising us more (or less) than the others at the table so that we can use that information to exploit him and make more money. However, we also know that our memories are unreliable devices to help us detect an opponent's tendencies in this way due to the Illusory Correlation bias[1] and Self-Reference Effect.[2] This is why players may tend to look to software to help us overcome these innate memory issues.
In an ideal world we could formulate statistics which would make it clear that a player is playing differently against us and how he (or she) is doing so. To play well against any opponent who does not adjust to our play we do not need extra statistics to characterize and understand them - the basic statistics already available suffice, there is no need to burden players with more information which makes playing in-game more confusing.
So even in the ideal world we would only use these statistics to answer two questions:
- Which players alter their play against me?
- How do those players change their play against me?
It is important to note one more significant feature of the kinds of opponents who do alter their
play.
This blog will attempt to show that in the "real world" vs hero statistics do not provide the answers to these questions, especially regarding these players.
Simple Statistics and the Positional Problem
A typical player, not knowing any better, might say something like "I want to see if this opponent 3Bets me more than he 3Bets other players. Just show me Preflop 3Bet Vs Hero!" For the reasons outlined above, there is an understandable urge behind this assertion, however we will show that this particular stat would be worse than useless - it would be actively harmful. The values that this stat would show bear no resemblance and could not be compared to any general 3Bet statistic.
In the ideal world the kind of player targeted with Versus Hero stats are thinking analytical players who pay attention to what is happening around them. These kinds of players pay attention to table dynamics and generally have more than a very basic understanding of poker. This implies that they also have a grasp of one of the most important features of poker: Position.
For example Sklansky and Miller's No Limit Hold'em: Theory and Practice (©2006 Two Plus Two Publishing) says "Position is an undeniably important factor in every hand. "Having position" often represents an enormous edge."[3] Perhaps instead your opponent has read Professional No-Limit Hold'em by Matt Flynn, Sunny Mehta, and Ed Miller (©2007 Two Plus Two Publishing) which says "position is a truly potent weapon. Whatever your concept of position is, chances are you underestimate its value."[4] Many more authors have commented on the significance of position and it is safe to say at this point that virtually all thinking analytical opponent is at least aware of how position affects a hand to some extent.
This means that the relative position between yourself and a thinking, analytical opponent significantly alters how often he will 3Bet against you, and this presents a real problem for our typical player.Let's say our typical player played a session with a good, thinking, analytical and aggressive opponent whom we'll call Villain sitting immediately on his left. Our typical player played 300 hands at this table with Villain on his left and was 3Bet by Villain several times over the course of this session, say 7 times out of 50 opportunities, leaving our typical player seeing a versus hero 3Bet of 14%. A couple of weeks later, our typical player is sitting across the table from Villain and our typical player opens the pot in middle position. Villain, in the small blind, makes a 3Bet. If our typical player sees a versus hero 3Bet of 14% and a regular 3Bet of 6% he may presume that he could be 3Bet light here - but he has no evidence of that fact! Most of the 3Bets in the earlier situations were in steal situations, most 3Bets previously were when Villain was in position, and most were against open raises our typical player made in the cutoff or later.[5] Since in this situation Villain is out of position and Hero is in middle position and Villain is a good thinking player, we know that Villain's range is going to be different than the ranges he had when he was 3Betting from the button against a cutoff open!
Presuming that a good, thinking opponent will always take the same action against you regardless of your relative position to one another is a grave and serious error. Furthermore, it is not possible to take a simple percentage and reconstruct all of the different positional ranges backwards from them without knowing quite a lot more. We have provided our range assumptions in a footnote here should you like to try to reconstruct them, and even with the ranges chosen in the model we used, the numbers would have come out differently if a third player at the table was very active in opening the pot himself![6]
Without knowing the relative positions of the players we cannot compare a versus hero 3Bet statistic with Villain's normal 3Bet numbers. Without being able to make this comparison, we cannot tell whether or not Villain is raising with a different range against us. Since this is the first and most important question this stat is supposed to answer, we assert confidently that any attempt at a simple versus hero statistic that does not take position into account is doomed to failure.
Positional Statistics and the Sample Size Problem
Any modern tracker must have a wide variety of positional statistics, as position is at the heart of high level poker analysis. As we have seen, for a model of versus hero statistics to have any hope of success, it too must take into account positional factors. Unfortunately, as we will see shortly, these positional factors fragment the actual data we have so much that the amount of data that we would need on a single player far exceeds the availability of even the most dedicated of high volume players.
The most important question we need to answer in this analysis is: "Would the gap between a Versus Hero statistic and a regular statistic on an opponent definitely tell me that the opponent is changing his play against me?"With a large enough gap, we can be confident we can detect the difference even without these statistics - if he 3Bets us 20% of the time in this spot and 3Bets in general in this spot 8% of the time, it will be very obvious even without specialized statistics. So we will concentrate on a gap size that is much more likely to emulate a real world gap.
If we see a Villain with a 10% 3Bet when we 2bet in a specific position of 10% and a 8% 3Bet in general in the same position against the same position of 8%, how certain can we be that he is indeed playing more loosely against us?
As we will see, the number of hands we have on an opponent must be very large or the gap must be nontrivial before we can be certain of anything at all.
By using the mathematical concepts of standard deviation and confidence intervals we can test to see how likely it is that a specific gap could happen by chance. We do this by accepting as a given that Villain will 3Bet a specific range which equates to some percentage of the time. Given that Villain 3Bets that specific range, we can calculate how unlikely it is that the gap between the real percentage and the Versus Hero percentage is due purely to chance. That is, Villain may be "running hot" and getting more 3Bet hands than he otherwise should - we can calculate how likely that is. If it is very possible that Villain could be "running hot", we cannot determine from the gap that Villain is certainly changing his play against us.
For our first analysis, we will assume that we have 3,500 hands on our single opponent played at a 6 handed table, split evenly among all positions at the table. A 3Bet percentage from the button against a cutoff open is often one of the most cited vs Hero statistics that people would like, we will continue to analyze this scenario. Since this sample of 3,500 is split evenly amont all positions at the table, in 20% of our hands he will be sitting directly to our left, and so there will be 700 hands in which he has the button. Assuming conservative open percentages from both players in front of us, we have about 500 chances to open the pot with Villain to our left.[7] Assuming we open 30% of the time from the cutoff this means we will have opened 150 times. Thus our villain has had 150 chances to 3Bet us on the button against our cutoff open.
Let us presume that in this case we are certain that Villain's true 3Bet range button versus cutoff is 8%. This would equate to 12 3Bets against us in these spots over our sample of 3,500 hands. However, let us say that we in fact saw 15 3Bets against us for a 10% value. How likely is it that Villain simply ran hot enough to make 3 extra 3Bets against us out of the 3,500 hands we've played together?
The standard deviation of a random event that happens 8% of the time is .27 times the square root of the sample.[8] So with a sample of 150 we find that the standard deviation is 3.3. We can then divide the actual 3 we got by 3.3 and find out our z-score of .909. What does this z-score tell us? This tells us how likely it is that this amount of deviation was arrived at by chance. With a z score of .909, the chance probability is 18.16% - about one in 6, or about as often as you hit a flush draw with one card to come. Using this model, we have created a charts showing how often different sample sizes are due entirely to chance:
| Hands | Chance Probability |
|---|---|
| 325 hands | 38.74% |
| 1,050 hands | 30.96% |
| 3,500 hands | 18.16% |
| 7,000 hands | 10.02% |
We can see that even with 7,000 hands specifically - well over 100 hours of playing poker together - we are still not even 90% certain he is deviating his play against us. That simply is not good enough. To keep this in perspective, 7,000 hands logged in the cutoff would be be an excess of 70,000 hands logged at a full ring table, with the villain one seat to your left the entire time!
Most players - even those who play quite regularly - will never have that many hands on most of their opponents. And even in they do have that many hands on an opponent, they still are not certain that their opponent is adjusting.
In order to be 99% certain that the 2% gap is not due to randomness we would need a sample size of of well over 20,000 hands just where the the villain was on the button while the hero was in the cutoff! This requires at least 200,000 hands in a full ring game where the precise position between one specific villain and the hero does not change! Most players with databases that exceed 10 million hands cannot say that this situation has occured over a 20,000 hand sample!The NoteTracker Solution
PokerTracker 4 provides a more robust and effective method for making the determination of whether an opponent is varying his play against you. NoteTracker is an automated note taking tool that will generate notes in a player's database based on situations previously specified by the player. In addition to just taking a note if a situation occurred, NoteTracker can also keep track of what hole cards were shown in the specific situations as well. This provides a much clearer picture of a player's actual play by showing the real data points we have on his hand range in the specific situation that we care about.
Furthermore, NoteTracker's options are robust enough to allow for specific Versus Hero notes to be taken. With this construction, instead of seeing that Villain's 3Bet BTN vs CO value versus hero is 2% higher than his real range, we could see that Villain 3Bet BTN vs CO with {AA, QQ-99, AQs, 65s, 54s, 43s, 32s, AKo, AJo}. We could then compare that to his 3Bet BTN vs CO regular number and get a much better feel for how Villain bluffs and in what way he is expanding his bluffing range. If we saw the above range, we could be pretty sure that Villain is using an 8% range of {99+,AJ+, 65s, 54s, 43s, 32s} - if his real number is 8%, we can be pretty confident he's not bluffing us any more or less than the rest of the field. If instead we saw {AA, QQ, TT, 99, AQs, T7s, 65s, 54s, 43s, 32s, AJo, 84o, 54o, 43o, 32o} with an 8% number we could feel pretty confident that he is in fact bluffing us considerably more - because he would almost certainly still be 3Betting for value with KK, JJ and AK, which results in an 11% range. Also, we can likely infer that T7s and 84o do not follow his normal bluffing range if we see his 3Bet BTN vs CO (non-Hero) range does not include suited two gappers or unsuited two gappers.
NoteTracker is not limited to ranges either, you could create a note like "Caught Me 3Betting Light" - then you would not need to worry if the opponent saw you 3Betting with a weak pair of hole cards at some point, you would know that they did (and even know how many times they had done it). There is no limit to the amount of information you can specify in this way - and this information is clear and can be obviously actionable.
Conclusion
Versus Hero Statistics are an unreliable tool to help answer the primary question "Does this player alter his play against me?" As we have shown, these statistics would require samples of tens of thousands of hands vs one opponent and each positionaly scenario to be meaningful. In contrast, the data provided by NoteTracker and Versus Hero Notes are extremely meaningful and could even be actionable very quickly because they show you the real data as to what hands Villain played against you. We believe that NoteTracker is the next great leap forward for in game analysis of your opponent's tendencies, and that Versus Hero notes are a red herring, serving only to distract from the more interesting and more useful options now available to PokerTracker users.
- ChangingMinds.org, Illusory Correlation.
- Pyschwiki.org, PSY322-Self-Reference Effect
- Sklansky and Miller. No Limit Hold'em, Theory and Practice. Page 91.
- Flynn, Mehta and Miller. Professional No-Limit Hold'em. Page 74.
- Our model has each of these happening six times of the seven 3Bets that occurred.
- To arrive at this number we assumed a 300 hand session of 6-max with a full table for the entire session, opening ranges of 20% first to act, 25% second to act, 30% third to act (in the cutoff), 40% on the button and 45% in the small blind. We presumed that Villain will 3Bet us 5% when we are first to act 7% when we are second to act, 15% when we are in the cutoff, 10% when we are on the button and 40% when we are in the small blind. Using these ranges and reasonable percentages for other opponents to play first we arrived at an opponent who 3Bet us seven times out of fifty opportunities, of which only once was Villain out of position.
- This model has the under the gun player opening about 13% of hands and the player in the hijack opening 18% of hands. We used a more conservative model for opponents opening here to make our point even stronger - with active opponents we would have an even weaker sample.
- The standard deviation of a random event with probability p is the square root of p * (1-p)2 + (1-p) * p2. For more details on how this formula was attained please see http://en.wikipedia.org/wiki/ Standard_deviation#Continuous_random_variable
