1. Introduction
This is Part 7 of the article series "PLO From Scratch". The target audience is micro and low limit players with some experience from limit or no-limit Hold'em, but little or no PLO experience. My goal with this series is to teach basic PLO strategy in a systematic and structured manner.

We finished our discussion of preflop theory in Part 6, and I commented that Part 7 and onwards would be about postflop play. But before we do this, we'll take a break from theory and spend one article discussing:

- The practical part of the article series (building a bankroll from $5PLO to $200PLO)
- The low limit PLO player pool
- Sound value ranges for various preflop and postflop HEM stats
- How to design a simple HoldemManager (HEM) HUD for PLO 6-max

It so happens that since Part 6 was published I have gotten my hands on statistics from a huge HEM database. This database was built by a friend of mine who has grinded her way through the low limits during the last 4 months. She started at PLO25 in January 2010 with a 50 BI ($1250) bankroll, and at the time of writing (April 2010) she's about to move up to PLO200. Her plan is to build the bankroll to 100 BI here, before she moves on to PLO400.

Our friend (who shall remain anonymous) has purchased datamined hand histories and built a low limit PLO database with millions of hands from PLO25, PLO50 and PLO100. Some think this is acceptable, some (and most poker sites are among them) think it's unacceptable, but we won't discuss the ethics of this here.

What's interesting to us is that our cynical friend has made the database available for us to do some statistical analysis of the low limit player pool. I mentioned to her that I would have liked to know more about the general low limit conditions. It's been a while since I played low limit, and I didn't grind PLO below PLO100 when I learned the game myself, so I don't know much about these limits. I was also interested in estimating good values for common HEM stats like VP$IP, PFR%, 3Bet%, WTSD%, etc. under low limit conditions.

When our friend heard this, she offered to extract information from her database so that we could use it. I gleefully accepted the offer, and I decided to base an article on this analysis. We have gone through a lot of heavy theory up to now, so we could use a little break where we talk about more practical things before we move on to postflop theory.

So she purpose of Part 7 is to talk about grinding low limit PLO, study the player pool at these limits by extracting information from a large database, and show how we can design a simple PLO HUD for HoldemManager.

2. The practical part of the article series
Before we do statistical analysis of the database, let's talk briefly about the work done on the bankroll building project for the "PLO From Scratch" article series.

We remember from Part 1 that we defined a bankroll building project for the article series. We started with 50 BI ($250) at PLO5, and our goal was to build our bankroll big enough to move up to PLO200.

We use a move-up scheme we call "50+10". This means having at least 50 BI for the limit we're grinding, and then we can take shots at the next limit whenever we have at least 10 BI for that limit in addition to the 50 BI. For example, we start at PLO5 with 50 BI, and then we grind in 10 BI ($100) for PLO10 and take a shot. If we lose the 10 BI, we drop down to PLO5 and grind in 10 BI more, rinse and repeat. This way we always have at least 50 BI for the limit we're grinding before we start taking shots at the next limit, and our shots are done in a controlled manner.

This gives the following progression.

  • $5PLO to $10PLO: Grind in 20 BI ($100) at $5PLO and build the roll to 50+10 BI ($350) for a shot at $10PLO.
  • $10PLO to $25PLO: Grind in 40 BI ($400) at $10PLO and build the roll to 50+10 BI ($750) for a shot at $25PLO.
  • $25PLO to $50PLO: Grind in 40 BI ($1000) at $25PLO and build the roll to 50+10 BI ($1750) for a shot at $50PLO.
  • $50PLO to $100PLO: Grind in 35 BI ($1750) at $50PLO and build the roll to 50+10 BI ($3500) for a shot at $100PLO.
  • $100PLO to $200PLO: Grind in 35 BI ($3500) at $100PLO and build the roll to 50+10 BI ($7000) for a shot at $200PLO.

If all shots succeed at the first try, we have to grind in 20 + 40 + 40 + 35 + 35 =170 BI. If we (somewhat arbitrarily) assume an average win rate of 7.5 ptBB/100 (ptBB =2 x big blind), we will make 1.5 BI per 1000 hands on average. So we have to play a minimum of 170/(1.5 per 1000 hands) =113,000 hands.

So what has happened with our bankroll building project since the start? This can be summarized in one sentence: There and back again is twice as far. I grinded through PLO5 and almost all of PLO10 while writing Part 2 and Part 3 (October-November 2009), and the plan was to blog about these limits before I moved on to PLO25.

But then my grinding computer crashed and died in December 2009 (merry X-mas!) and everything on the desktop hard drive that wasn't backed up (including the database and hand histories for the article series grind) was lost. This was mildly annoying, so I paused the grind for a while and concentrated on writing the theory articles instead.

Now the preflop part of the series is done, and this is a good time to take up the grind again. If things go smoothly, I should be able to finish the bankroll building project and the remaining theory articles at about the same time. So the plan for the next few months is to finish these two parts in parallel and then end the series with a summary. This will probably happen some time during the summer of 2010.

The setback for the practical part of the series just goes to show that things don't always go smoothly, and you have to expect problems along the way (a good poker mindset to have if there ever was one). But there's a silver lining. Losing the database and starting over gives me an opportunity to adjust my grinding strategy for the microlimits. I wrote in Blog 2 for the bankroll building project that I wanted to maximize win rate (and not necessarily hourly earn) and not volume. In other words, play few tables with high focus and try to squeeze every drop of value from each table.

In hindsight I see that this attack plan is overkill for the micro limits. After having grinded a few thousand hands at PLO5 and PLO10 and assessed the quality of the micro limit opposition, I have concluded that it's better to go for high volume. It's simply ineffective to spend lots of time and energy studying individual microlimit opponents to find and exploit their biggest personal leaks.

Let me explain what I mean:

Assume you're sitting at a table with 1 known big fish, 1 unknown and 3 solid regs. This is typical for the tables you'll play at mid and high stakes where there are lots of regs and few big fish. So when you find a table with a known big fish, you want to play him (there probably aren't many better tables available). Your plan at this table should be to exploit the fish maximally while trying to break even against the other regs (who we will assume are about as good as you).

For this plan to succeed, you need to pay attention to each player at the table and gather reads. You have to punish the mistakes made by the fish, and at the same time you need to defend against the other regs' attempts to punish your mistakes. You also have to keep an eye on the unknown player at the table and try to quickly classify him, so that you can start formulating strategies to use against him. The work done at this table can have a huge payoff, both immediately (by exploiting the fish) and in future sessions (since you expect to meet many of these players again, especially the regs).

But at the micro limits, things are simpler for several reasons:

- You'll meet so many big fish that you don't need to exploit all of them maximally to have a high win rate
- You'll meet few solid regs who you need to defend against
- You'll rarely meet the same players in future sessions

So even if a grinding strategy of playing few tables with intense focus can give you astronomical win rates at the micros, you can also achieve a very good win rate simply by playing solid ABC poker and not paying much attention to reads. In other words: Standard solid ABC poker punishes the micro limit players' big and frequent mistakes hard enough to give you a high win rate.

Playing with intense focus can mean the difference between winning and losing at the higher limits. But at the micro limits it more likely means the difference between a high win rate and a very high win rate for a good player. Furthermore, the value of gathering reads is reduced when the player pool is very large, since you won't play lots of future sessions against the same players. Therefore, it's much more effective poker to play more tables with a slightly reduced win rate. This means we want to maximize our hourly wage and not the win rate (measured in bb/100).

For example, you can easily make 10 bb/100 (e.g. 1 BI per 1000 hands) playing ABC poker at 8 micro limit tables. Playing about 70 hands per table per hour, our hourly wage is:

(10 bb/100 hands) x (560 hands/hour) =56 bb/hour


Maybe you can manage 15 bb/100 when playing 4 tables with maximum focus (e.g. 4 x 70 =280 hands/hour), but the hourly wage then drops to:

(15 bb/100 hands) x (280 hands/hour) =42 bb/hour


Playing with the highest possible win rate in bb/100 is desirable, since this will lower your swings and give you a more linear profit curve. But even if you can manage 15 bb/100, playing with 10 bb/1000 is still a very good win rate, and you now make (56-42)/42 =0.33 =33% more per hour by playing twice as many tables.

These specific numbers are of course pulled out of a hat. But there will always exist a sweet spot (a compromise between volume and win rate) that maximizes your hourly wage. Maximizing the hourly wage at a particular limit isn't necessarily the best for you in the long run, since you probably will learn more (and prepare yourself better for higher limits) by playing fewer tables and maximizing your win rate. But at the micro limits I now believe the best strategy is to simply drill ABC play, maximize your hourly wage and get out of there as soon as you can. Then you can take your next strategical steps when you reach the low limits where you will find more regs. The less time you spend at the micro limits, the better, and a quick look at the rake you pay per hand should convince you this is correct.

Therefore, when I begin the bankroll building again this month (April 2010) I will play more tables (probably 8). I won't try to gather very detailed reads on my opponents, other than the things I pick up automatically while sitting at a table. Still, my advice to new players is that they start out at few tables so that they have time to think through their decisions. But when you have become skilled at ABC poker, it seems best to go for volume and quickly grind your way out of the micros.

Volume grinding your way out of the micros using ABC strategies will give you valuable practice that will come in handy later. Many standard lines and standard ways of thinking/planning will become automatized, and this frees up your brain to think about more difficult things when the need arises. Then you can reduce the volume and increase the complexity of your decision making processes when you reach higher limits where you'll meet more thinking opponents.

3. A simple statistical study of the low limit PLO player pool
As mentioned in the introduction, I recently got access to statistics from a large low limit PLO database with ~15 million recent hands from PLO25, PLO50 and PLO100. A few questions immediately popped into my head:

- What percentage of the low limit players are serious regs, and how many of them just splash around without purpose or direction?
- How many of them are winners?
- What is the rake at the low limits, and what is the overall effect of the rake?

By digging up answers to these questions, we can begin forming a general idea about the conditions at the low limits PLO25 to PLO100. And we can perhaps draw some conclusions about what it takes to establish ourselves as winners there. We will also learn things about the typical low limit PLO player and how he performs.

Before we get to work, here is a disclaimer:

The analysis work done in this article is not meant to encourage anyone to break the rules at the poker sites they play at. If the use of datamined hand histories is against the rules at your sites, it is your responsibility to stay within the rules, or take the consequences of breaking them, should you do so and get caught.

The work done in this article is of a very general nature, and we're trying to extract information about the low limit PLO player pool as a whole. We're not analyzing the play of individual players. Therefore, I find this use of datamined hand histories ethically acceptable. The player who built this database of course had other reasons for doing so, but that is her responsibility and not ours. We're simply using an opportunity to analyze data to draw general conclusions about the low limit player pool.

3.1 Facts about the database

- About 15 million hands gathered at PLO25, PLO50 and PLO100
- 92469 unique players
- All hands come from the same hand history provider
- All hand histories are gathered at the same poker site between Jan 1 2010 and Apr 16 2010.

So we have a sample of 15 million recently played hands from the 3 low limits PLO25, PLO50 and PLO100 over a period of 3.5 months. Since all hands are played at the same site, we expect many of the players to have moved between these limits, but we have 92469 unique players in the database.

3.2 What is the distribution of winners and losers?
We pull this number directly out of the database. We define a winner as a player with at least 0 bb/100 win rate, and we get:

Winners: 24212 (26%)
Losers: 68257 (74%)

Of the players registered in our database about 1 out of 4 has turned a profit. The true distribution of winners and losers in the online poker universe is unknown, but we expect the majority of players to lose. And our data confirms this.

3.3 What is the volume for the typical low limit PLO player?
The first thing we want to investigate is how the player pool is distributed according to number of hands played. Some regulars grind the same limit for months, while some hobby players play a session or two, then leave and never return.

Before we begin this analysis, I want to remind you that all we have is a sample. But we will assume that all players have the same % of their hands registered in the database, and that we therefore can compare number of hands played for different players. In other words, if Player 1 has 5000 hands in the database and Player 2 has 1000 hands, we will assume that Player 1 has played 5 times as many hands as Player 2, even if we only have a sample of their hands in the database.

We note that these hands have been collected over a period of 3.5 months. So most players in the database have had enough time to play a lot of hands, if they wanted to. Therefore, if we find lots of players with, say, less than 100 hands played, we can conclude with a high level of certainty that they don't play much. Of course, in theory they could have played a lot of hands that weren't registered in our database, but this is unlikely to happen over a period of several months. It could also be the case that these players just have started playing (i.e. they haven't had the time to log a lot of hands yet). But if there are many of them, this is unlikely, since we expect the influx of new players to be more or less constant.

Let's start by dividing the player pool (92469 players) into groups according to number of hands played:

less than 100 hands: 49248 players
100-999 hands: 31007 players
1000-4999 hands: 9397 players
At least 5000 hands: 2817 players

Total: 92469 players

Let's illustrate this graphically:



This is a somewhat surprising result. Over a period of 3.5 months we sampled more than 5000 hands on only 3% of the player pool. This indicates that the percentage of regulars is very low. This could of course be because the hand history provider only sampled a tiny fraction of all hands played. But since we have 30 players in the database with 100 000 hands or more (one of them has 500 000 hands) this doesn't seem like a good explanation (those who play a lot of hands seem to get their hands registered)

We therefore conclude that the percentage of regulars at low limit PLO is low at this poker site. How we define a regular player is somewhat arbitrary, but it seems reasonable to demand at least 5000 hands registered in our database over a period of more than 3 months. If we use this definition, we have 3% regs at these limits. To allow for statistical uncertainty we can stretch this limit a bit and conclude that less than 5% of the players appear to be regulars.

Now we turn to the group of players at the opposite end of the spectrum, namely the low volume players. We observe that more than half of the player pool has less than 100 hands registered. Could this be because many of them started playing at the end of the sampling period (for example, maybe most of them started playing in April)? We investigate this by looking at how the database grew from month to month:

January 31: 46716 players (+46716)
February 28: 67112 players (+20396)
Mars 31: 84326 players (+17214)
April 16: 92469 players (+8143)

The influx of new players seems to be fairly stable. And of the 49248 players with less than 100 sampled hands, no more than 8143 of them could possibly have started playing April 1st or later. It follows that most of the low limit players have operated between Jan 1 and Mar 31, and that they have had plenty of time to log hands.

So more than half (53%) of the player pool seems to have barely played low limit PLO at all. They have played a few hands and then (probably) moved on. Again, we only have a sample of all the hands played, but if a player has less than 100 hands registered in the database, he most likely is a low volume player (again, we have many players with 100 000 hands or more, so those who play a lot of hands seem to get their hands registered).

So we conclude:

The majority of players at low limit PLO on this poker site play a very low volume of hands. The percentage of regular players appears small. It seems that most players either only test the game over a few hands, or they play regularly but very sporadically

This means that most of the players you meet will be weak with a limited understanding of the game. Of course, the regular players play more often and they play more tables, so you will bump into an individual reg more often than any other individual random non-reg player. But you will mostly be playing against opponents who are easy to beat. This is encouraging (and not totally unexpected). However, it was surprising to see that the percentage of one-shot-and-done players (those with extremely low volume) was so high.

But having fish to play against is only one part of the equation. To win, we also need to beat the rake, so let us calculate it for each of the 3 limits:

3.4 What is the rake at PLO25, PLO50 and PLO100?
First, lets find out how much the total player pool has lost in rake. We pull the following data directly out of HEM:

- 92469 players
- Total profit: -$6071161.70
- Average profit: -$65.66
- Average win rate: -13.28 bb/100

Since the total profit for all players per definition equals the rake, we see that each player has paid -$65.66 in rake om average. Our sample gives a total of more than $6 millions in rake over 3.5 months, and our sample only contains a fraction of all hands played on PLO25, 50PLO and 100PLO during this time.

Conclusion: If you want to get rich off poker, start your own site

Now to the rake for each limit. We pick the 3 players with most hands played on each limit, calculate their rake and take the average:

$25PLO:
Player 1: 175466 hands and -$7161.15 in rake =-16.32 bb/100 in rake
Player 2: 150728 hands and -$5886.37 in rake =-15.62 bb/100 in rake
Player 3: 134534 hands and -$5126.66 in rake =-15.24 bb/100 in rake

Total: 460728 hands and -$18174.18 in rake =-15.78 bb/100 in rake

$50PLO:
Player 1: 349427 hands and -$22575.55 in rake =-12.92 bb/100 in rake
Player 2: 259214 hands and -$19811.55 in rake =15.29 bb/100 in rake
Player 3: 122772 hands and -$8698.48 in rake =-14.17 bb/100 in rake

Total: 731413 hands and -$51085.58 i rake =-13.97 bb/100 in rake

$100PLO:
Player 1: 295804 hands and -$33417.86 in rake =-11.30 bb/100 in rake
Player 2: 280966 hands and -$32858.25 in rake =-11.69 bb/100 in rake
Player 3: 218506 hands and -$27374.52 in rake =-12.53 bb/100 in rake

Total: 795276 hands and -$93650.63 in rake =-11.78 bb/100 in rake


Estimated rake
$25PLO: 15-16 bb/100
$50PLO: 13-14 bb/100
$100PLO: 11-12 bb/100

The rake is more than 10 bb/100 at all limits, e.g. more than 1 buy-in per 1000 hands played. Relative to PLO25, the rake drops ~12% at PLO50 and ~25% at PLO100.

This steep rake is a huge obstacle to overcome for new players, and this is obviously the biggest reason why so few players come out ahead. Rake is partly a function of playing style. For example, if you play lots of hands and get involved in lots of small pots, you pay more rake. If you play less hands, and let more small pots go and instead focus on maximizing value in big pots, you will pay less rake.

An important effect of the rake is that it might turn marginally profitable situations into break even or losing situations. If you get involved in many of these situations, two things will happen:

- You reduce your win rate
- You introduce (even) more variance into the game

So keep in mind the rake when you have a close decision at the low limits. If it's a marginal play at best, it might be the case that the rake will turn it into a losing play. So you might want to make the rake a factor in the equation when you're in doubt.

We know that PLO is a game that allows for a lot of variation in style (you can win with many very different styles), but I suspect that the low limit rake severely limits our options with respect to style. At the high limits, where the rake is almost negligible, you will find winners who play very loose (more than 40% VP$IP), but I doubt this is optimal at the low limits. You might be able to pull it off if you're a good player, but if you're that good you won't stay long at the low limits anyway. And even though a very loose style of play is profitable for you at the low limits, it might not be the most profitable way to play these limits.

So let's use the database to estimate reasonable values for some common preflop and postflop HEM stats. This should give us an idea about which playing styles work best at low limit PLO.

4. Estimating reasonable HEM stats for low limit PLO
We'll use the database to estimate sound ranges for the values of following HEM stats:

- VP$IP
- PFR%
- 3-Bet%
- Postflop Aggression Factor (AF)
- Flop CBet%
- Turn CBet%
- WTSD%

In other words:

- How many hands you play voluntarily
- How often you raise preflop
- How often you 3-bet preflop
- How aggressive you are postflop
- How often you c-bet the flop
- How often you c-bet the turn (2-barreling)
- How often you go to showdown

Many other interesting stats exist, so we have only picked a handful of the most commonly used ones.

4.1 Defining our method
To estimate reasonable stat values from the HEM database, we'll use a method outlined in the article Article 1) Plugging Leaks - Determining typical bb/100 based on Stat Ranges that you can find on the HEM menu ("Help" and then "Articles"). The essence of the method is that we study how the win rate (bb/100) varies as a function of the stat value. Then we use this to estimate an optimal stat range.

We start by filtering out all players with at least 5000 hands in the database (i.e. the regular players). We need some minimum sample size, so we use the same sample size as in the article. This gives us a sample of 2817 players with 5000 hands or more. 5000 hands isn't a big sample, but we are going to study groups of players, not individual players.

For example, let's say you choose 1000 players with 5000 hands each and a VP$IP more than 80%. Now compare these players to 1000 players with 5000 hands each and a VP$IP below 30%. Even if each player only has 5000 hands played, it's virtually guaranteed that the second group of players will outperform the first group. So we will be able to conclude with great certainty that VP$IP below 30 is much better than VP$IP more than 80. Our analysis will work like this (and let's not forget that many players have much more than 5000 hands played).

For example, we'll investigate how VP$IP influences win rate. We then list all the 2817 players and sort the list according to VP$IP. Then we divide the player pool into 5 groups with an equal number of players in each group (the 1/5 with lowest VP$IP values go into group 1, the next 1/5 into group 2, etc).

For each group we note the upper and lower bounds for the VP$IP values in the group, and then we find the median for the win rates in the group (the median is the value that divides the group exactly in half). The higher the median, the better the players in the group perform on average, and the more optimal the group's VP$IP range. So we choose the VIP$IP range of the group with the highest median as our estimate of the optimal VP$IP range.

To make this method perfectly clear, let's illustrate it with a toy example where we use two groups. Let's say we have 6 players in the database with the following VP$IP values and win rates;:

Player 1: VP$IP =14 and bb/100 =-1
Player 2: VP$IP =44 and bb/100 =-3
Player 3: VP$IP =27 and bb/100 =4
Player 4: VP$IP =88 and bb/100 =-5
Player 5: VP$IP =19 and bb/100 =2
Player 6: VP$IP =37 and bb/100 =0

Then we sort the players according to VP$IP:

Player 1: VP$IP =14 and bb/100 =-1
Player 5: VP$IP =19 and bb/100 =2
Player 3: VP$IP =27 and bb/100 =4
Player 6: VP$IP =37 and bb/100 =0
Player 2: VP$IP =44 and bb/100 =-3
Player 4: VP$IP =88 and bb/100 =-5


Now we divide this player pool into two equally sized groups (3 players in each) according to their VP$IP values (the 3 lowest in group 1, the 3 highest in group 2) and find the win rate median for each group. The median is defined as the data point that divides the group in half. This means that half the players in the group have win rates lower than the median and the other half have win rates higher than the median. It's obvious that the higher the median, the better the players in a group perform on average.

Group 1
Player 1: VP$IP =14 and bb/100 =-1
Player 5: VP$IP =19 and bb/100 =2
Player 3: VP$IP =27 and bb/100 =4

VP$IP range: 14-27
Median bb/100: 2

Group 2
Player 6: VP$IP =37 and bb/100 =0
Player 2: VP$IP =44 and bb/100 =-3
Player 4: VP$IP =88 and bb/100 =-5

VP$IP-range: 37-88
Median bb/100: -3

Conclusion for toy example
The optimal VP$IP range in this toy example is 14-27 (the rang for group 1). The win rate median for group 1 is +2 bb/100. The VP$IP range for the players in group 2 is 37-88 and their win rate median is -3 bb/100. We conclude that a VP$IP between 14 and 27 is better than a VP$IP between 37 and 88, and 14-27 is our estimate of the optimal VP$IP range based on this data set.

What we'll do next is to use this exact method for each of the HEM stats listed earlier. The difference is that we now have 2817 players instead of 6, and we will divide them into 5 groups instead of 2 (so we will have three groups with 563 players and two groups with 564 players).

For each HEM stat we do the data processing and computations in Excel, and then I paste a screenshot with the results here. Optimal ranges are marked with a grey field.

4.2 Estimating optimal VP$IP



Note that the median is negative for all the VP$IP ranges. This is not unexpected, since the majority of the players in the database lose, and the losers are distributed over all possible playing styles (and the brutal rake is an important reason for this). But this doesn't mean anything for our analysis. We simply want to find the range with the highest median, regardless of what this median is. We just assume that the stat regions with the highest median is a good estimate of the optimal range.

From the data above, we conclude that an optimal VP$IP range for the low limits is 21-27% (rounded to the nearest whole number). This is the typical tight-aggressive (TAG) region. This should not surprise us after the work we did computing the low limit rake. Playing a looser style can certainly also be profitable, but I'm guessing we won't find may low limit players who are able to turn a profit using a very loose preflop strategy. And those who are good enough to pull this off, will tend to move up quickly.

These data also tell us that splashing around with a VP$IP higher than 45% is definitely not recommended. Most players trying this are probably fish (who have other leaks in addition to overly loose preflop play), but the rake will probably make it difficult to win with such a style also for competent players. It's a popular assumption that you can play very loose in PLO, but it's likely not a good idea to move far beyond 30% in a high rake environment.

4.3 Estimating optimal PFR%



It's difficult to estimate an optimal PFR% range accurately based on these data, since all the ranges more than 10% perform about equally well. This means we don't find a clearly defined optimal region surrounded by suboptimal regions on both sides like we did for VP$IP.

We're not able to estimate an upper bound for an optimal PFR% range, but we do find a lower bound. It seems clear from the data that a PFR% higher than 10% will perform well. And the range that performs best (although the differences are small) is PFR% higher than 17%. This is a typical TAG value. A standard PLO TAG will have a VP$IP in the 20-25% region and a PFR% in the 15-20% region, and we have now confirmed that both these stat ranges work well for low limit PLO.

But note that a PFR% as low as 10% also seems to work well. An optimal stat value for an individual player can not be decided precisely in a vacuum, since it's also a function of how it works together with the other components of the player's style. For example, one can choose to overlimp more behind limpers and play small pots in position instead of raising them and playing big pots in position. Both lots of overlimping and lots of isolation raising can work well, as long as we choose the right types of hands for these actions, and as long as the postflop play is adjusted according to what happened preflop.

4.4 Estimating optimal 3-Bet%


We see the same trend as for PFR%, namely that the three highest 3-bet ranges have similar median values, so it's difficult to determine which is best. We don't find a clearly defined optimal range, but we do find a lower bound (above 3% clearly performs best) and it seems reasonable to us 3-6% as a starting point for an optimal 3-bet% region.

We remember from Part 6 that a 3-bet range of premium AAxx, premium Broadway hands and premium speculative hands is about 5%. The database analysis indicates that this is a reasonable range to use in a vacuum. But we need to keep in mind that optimal 3-betting frequencies are highly opponent dependent, and that we can get away with a lot of loose 3-betting on the button, particularly against weak-tight opponents.

One thing worth commenting on is that the generally passive conditions at the low limit probably causes sub-optimally low 3-bet% values to be overrepresented in the database. We see that a 3-bet% in the 3-6% region seems to work best, but more than 6% might work even better (the 6+% region performs almost as well as the 3-6% region). But since few players 3-bet as much as 6+% at these limits, we don't get much data for this region. As a result, we don't get a clearly defined upper bound for an optimal 3-bet% range like we did for VP$IP (where we clearly identified an optimal region in the middle).

So we note that 3-betting somewhere above 6% is probably better than 3-6% for a strong player, especially when he faces weak opposition. But as a starting point, a 3-bet% in the upper part of the 3-6% range should work well (again, premium AAxx + premium Broadways + premium speculative hands gives us ~5%).

4.5 Estimating optimal AF



Like PFR% and 3-Bet% we don't find a clearly defined optimal region for AF either. But we find a lower bound (more than 3). We don't know how far up we can go before we reach suboptimal AF-values, but we definitely want to stay above 3.

4.6 Estimating av optimal Flop CBet%



Here we have a clearly defined optimal region. It appears an optimal Flop CBet% lies somewhere between 56-63%. Going lower than 50% or higher than 60% is clearly suboptimal.

4.7 Estimating optimal Turn CBet%



We see the same pattern as for Flop CBet%. We have a clearly defined optimal region 45-51%. It's clear from these data that too much c-betting on the turn gets punished severely.

4.8 Estimating av optimal WTSD%



WTSD% is not a stat we use a lot when playing, since there are other and better stats to use if we want to know if we can bluff an opponent out of the pot postflop. But it's a nice stat to include in a simple HUD layout.

We don't find a clearly defined optimal region, but we get an estimate of an upper bound. The data indicates that an optimal WTSD% lies somewhere below 27%.

5. We design a simple HUD layout for low limit PLO
The last thing we'll do in this article is to design a simple HoldemManager HUD layout to use when grinding low limit PLO. We'll base this work on the optimal stat ranges we found previously.

Before we begin, I'll say that I don't use HUD stats much when I play. I prefer to pay attention to find out how my opponents are behaving here and now, and I often play without a HUD altogether. But I of course understand that people like to use HUD stats when they play. So let's play around with the stat ranges we found previously and use them to construct the "skeleton" of a low limit PLO HUD.

5.1 Our main HUD philosophy
We'll apply the KISS principle (Keep It Simple, Stupid) and use broad generalizations when we define the ranges in our HUD. We start with the 7 stats studied previously:

- VP$IP
- PFR%
- 3-Bet%
- Postflop Aggression Factor (AF)
- Flop CBet%
- Turn CBet%
- WTSD%


We also include the name of the player, and the number of hands he has in the database. We first put name and number of hands on one line, then VP$IP, PFR%, 3-Bet% and AF on a 2nd line, and finally Flop CBet%,Turn CBet% and WTSD% on a 3rd line.

In the HEM HUD layout manager (Menu: "HUD Options" and then "Player Preferences...") it looks like this:



For each of these stats we will distinguish between optimal and suboptimal regions using a simple color coding system:

- Yellow =tight/nitty
- Green =loose/passive
- Red =aggressive
- Blue =solid/neutral

For each stat we will define 3 regions using these color codes. This will provide us with simple guidelines for how to interpret stat values for the players we meet. We'll now go through each stat, define stat regions and comment briefly on how these stats can be used while playing.

5.2 VP$IP
3 categories based on previous analysis:

Nit (yellow): below 21
Solid (blue): 21-27
Loose (green): above 27



Note that we have bunched a lot of players together in a very broad category called "Loose". We could have defined a 4th category (semi loose), for example in the 27-35% region, and reserved "Loose" for players that are really loose (35+%). But we sacrifice precision for a simple 3-category-system.

Using VP$IP while playing is straightforward. VP$IP is the stat we start with when classifying an opponent, and it is the basis for all estimates of his range on all streets. The color coding system lets us easily identify nitty and solid players just by looking at their colors. The "Loose" category is very wide, so here we need to look at the numbers as well to see if we're dealing with a semi-loose (27-35) of truly loose (35+) player.

As for ourselves, we want to place ourselves squarely in the middle of the "Solid" region with a VP$IP a little below 25%. This is a solid TAG style that will perform well under low limit conditions.

5.3 PFR%
3 categories based on previous analysis:

Passive (green): below 7
Neutral (blue): 7-10
Aggressive (red): above 10



A straightforward categorization based on the previous analysis. The "Aggressive" category is broad, and we want to place ourselves around the 16-17% mark when using a VP$IP around 25%

5.4 3-Bet%
3-Bet% is a bit more tricky to categorize than the previous stats, since the optimal region was so poorly defined. But let's try this:

Passive (green): below 3
Solid (blue): 3-6
Aggressive (red): above 6



We remember from the analysis done in Part 6 that a strong 3-betting range of premium AAxx + premium Broadway hands is around 2.5%. A wider range of premium AAxx, premium Broadways and premium speculative hands (the best rundown hands and the best suited ace + rundown hands) is about 5%.

So it makes sense to define the 3-6% range as "Solid", while everything below it is "Passive" and everything above it is "Aggressive". When we move below the 3% mark, our range becomes mostly premium AAXX + premium Broadways (alternatively, a range of all AAxx hands and no other hands, which is 2.5%). At the opposite end of the spectrum, if we move beyond 6%, there has to be a lot of speculative hands in our range, which is consistent with the 3-betting range of an aggressive and tricky player.

When we get 3-bet by a passive player, we can throw away our weakest hands and run for the hills, especially when he has position on us. He isn't splashing around, and trying to outplay a strong range with a weak hand from out of position is just silly. So we mostly fold our weak hands from out of position, plain and simple. When we 4-bet this type of player, we will mostly have AAxx.

In position we can call with lots of weak hands, since we now have better control over the pot postflop, and since we will get more opportunities to use the information we have about his tight range to our advantage. For example, it's now easier for us to get the money in good when we hit, or steal the pot when we miss, but we know that he has also missed.

Against a very aggressive 3-bettor we have to fight back a bit more from out of position. Our 4-betting range will also be wider, and we will start 4-betting premium AKKx, AQQx and AKxx hands as discussed in Part 6.

But don't go overboard with fighting back against an aggressive 3-bettor from out of position. You will still have to fold lots of weak hands in this case, and simply accept that a player with position on you has a certain amount of power over you.

When it comes to our own 3-Bet%, I recommend that you don't try to push it up to some predetermined value. Just analyze each 3-betting scenario using the decision making processes we have discussed previously in the article series. When you consistently find good opportunities to 3-bet for value, as a speculative 3-bet or as a bluff 3-bet, your 3-Bet% will take care of itself.

5.5 Postflop Aggression Factor(AF)
We define 3 broad categories:

Passive (green): below 2
Neutral (blue): 2-3
Aggressive (red): above 3



Using this parameter while playing is straightforward. When a passive player bets or raises, he usually has it. When an aggressive player bets or raises, he doesn't necessarily have it. Take it from there

We'll aim for an AF above 3, but we're not sure where the optimal region ends and the suboptimal region begins. But as long as we don't fall down to passive play, we should do just fine.

5.6 Flop CBet%
3 categories based on previous analysis:

Passive (green): below 55
Solid (blue): 55-65
Aggressive (red): above 65



This stat is relatively simple to use. The c-bet of a player who often checks weak hands, should be respected more than the c-bet of a player who c-bets most of his range on the flop. We fold more against a passive c-bettor, and we call and raise more against an aggressive c-bettor.

If you feel that your c-bets with weak hands always gets called or raised, you might be c-betting too much. If your opponents pick up this read on you, they will adjust by fighting back against your frequent c-bets, since they know you often have nothing.

Conversely, if your c-bets get a lot of respect, and you feel like you're never getting any action when you flop a big hand, you might be c-betting too little. If your opponents realize that you check a lot after missing the flop, they will respond by giving you more respect when you bet. So remember that you should c-bet a lot of air hands on the flop. It's profitable in itself (as long as you don't overdo it) and it balances your range and makes you harder to read postflop.

5.7 Turn CBet%
We define 3 broad categories:

Passive (green): below 40
Solid (blue): 40-55
Aggressive (red): above 55



Players who rarely c-bet the turn without a hand can be exploited by:

- Folding more marginal hands on the turn when they bet
- Floating more on the flop to see if they give up on the turn

Here you can look at both the Flop CBet% and the Turn CBet%. Against a player who c-bets too much on the flop, but rarely c-bets the turn without a hand, you can float a lot on the flop. An aggressive flop c-betting strategy can of course also be exploited by bluff raising more on the flop. But if you know he is going to give up on a lot of turns, it's better for you if you wait to see what he does on the turn. You can gather more information about his range before you bluff, and you also get to see a turn card (you would have to fold to a reraise if you bluff-raised the flop and he raised you back).

5.8 WTSD%
An optimal region was not clearly defined, but we found an upper bound (27%). We stretch this limit a bit to be on the safe side, and try the following categories:

Nitty (yellow): below 24
Solid (blue): 24-28
Loose (green): above 28



Use this stat to paint a broad picture of whether or not a player is showdown bound. But if you want to exploit a nitty player, there are better and more specific stats to use (for example "Fold to flop CBet", "Fold to turn CBet", or "Fold vs river bet"). But we include this stat to have a crude how-likely-is-it-that-I-can-steal-this-pot-from-him parameter in our HUD.

WTSD% is obviously very dependent on the cards we're dealt in the short run (when we make hands, we go more often to showdown), so don't rely on it when the sample size is small.

5.9 Summary of our HEM HUD design
The final HUD can be downloaded from the link below:

plo6max.xml (right click and choose "Save as")

You can construct much more refined HUDs that this one, but my philosophy is "less is more". I also like to know why I have included a certain stat in my HUD, and I want to know how to use the information it provides. If you don't know what to do with a piece of information, it stops being information and turns into noise.

Furthermore, I don't claim these HUD stat ranges are optimal for all types of game conditions. But I hope this work has given you a better understanding of how to organize the information that floats all around us when we play. Organizing it makes it easier to gather and process it.

One can use other methods than the one used here, but it all comes down to the same: We want to know approximately where the reasonable stat ranges lie, and then we define various categories ("tight", "loose", "passive", "aggressive", "solid", "nitty", etc.) based on this.

I recommend that you experiment a bit on your own with the borders between the categories. Use the work done here as a starting point, and adjust the borders up or down a bit as you see fit. You can also introduce more categories if you see the need for it. For example, you might want to define a "Semi-loose" category for VP$IP in the 27-35% region as mentioned previously (it's a bit misleading to group a VP$IP 30 player with a VP$IP 80 fish).

Just keep in mind that all HEM stat classification systems that attempt to distinguish "good" stats from "bad" stats are approximate, and that there is no unique way to define categories of players based on their stats. We want reasonable and simple categories that can help us process and utilize information while playing. A HUD should help us, not confuse us. Always remember this, and you will see that designing and using HUD layouts is simple

6. Summary
We have discussed the progression (or lack thereof) of the article series' practical part, and estimated a time frame for the bankroll building project and the rest of the article series. We expect to finish the work some time during the next 4-5 months.

Then we performed some simple statistical analysis on a big HEM database and drew some conclusions about the conditions and player types found on low limit PLO. We also estimated low limit PLO rake.

Finally, we used the database to estimate optimal ranges for a selection of commonly used HEM stats, and we used these to design a simple HEM HUD for PLO.

This article was a little "practical interlude" in the middle of all the theory, and I hope you got some ideas about general low limit conditions, the processing of information from HEM databases, and HEM stats and HEM HUD. The next phase in the article series is to discuss postflop play, and by my estimation we have 3-4 articles left before we're finished.

Good Luck!
Bugs