The HUD doesn't tell the tale: Positionally-adjusted ranges

[DoanDiggy]

I was thinking about HUD stats and positionally-adjusted ranges today, and in doing so it became clear to me that HUD stats can be pretty meaningless for putting our opponent on a range of hands in a certain position if we haven't seen enough showdowns. This exploration started when a poster was talking about a 6-max 12/9 player who had raised A3s in the CO, which seemed abnormally wide. I started running some numbers, and when you assume a player is positionally aware and is tightening up when people are already in the pot, the results are pretty surprising.

This post is specifically going to address PFR, but I think some of the ideas can be applied to thinking about ranges in other scenarios as well.

So to start, we'll go back to our 12/9 example. 9% of hands, according to PokerStove, is 88+,ATs+,KTs+,QJs,AJo+,KQo. That seems like a somewhat reasonable range for a tight player. Now, our usual assumption for a positionally-aware opponent might be that his range looks like this:

UTG: 99+,AQs+,AKo (4.2%)
MP: 77+,AJs+,KQs,AQo+ (6.6%)
CO: 55+,ATs+,KJs+,QJs,AJo+,KQo (10.3%)
Button: 22+,A9s+,KTs+,QTs+,JTs+,ATo+,KJo+,QJo (15.5%)
SB: same as Button (15.5%)

For an average of 10.4% PFR, give or take a little since there will be people in front sometimes. So basically, we see a 12/9 open raise to 4x from the CO and we look down at a hand like QJs in the Big Blind. We are getting 1.8:1 to call here, but according to PokerStove we only have 37% equity against what we perceive to be his range. When you add in the effect of being out of position, playing our QJs would be pretty -EV, so we fold.

This seems pretty straightforward and correct, but it's wrong! We have taken a basic number like 9% PFR, made some general assumptions about how position might affect range, rounded off a bit, and come up with a range. But we're so wrong that it's not even funny. One of our biggest errors, actually, is in not accounting for the times when Villain is not first in and is tightening up his range. Making some more accurate assumptions and running some numbers, I will show that a positionally-aware 12/9 can actually be much looser in late position (and in general) than we realize.

First, I will start with a "magic" range. Tell me you would ever expect a 12/9 to be playing a range like this:

UTG: 88+,AJs+,KQs,AQo+ (6.2%)
MP: 55+,ATs+,KJs+,QJs,AJo+,KQo (10.3%)
CO: 22+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,54s,ATo+,KJo+,QJo (19.5%)
Button: 22+,A2s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,65s,54s,A9o+,KTo+,QTo+,JTo (25.5%)

The thing is, when you run the numbers, it all works out. Now, I'm going to assume that an average player in front of our villain is likely to come into the pot 35% of the time. There are players who come in more and come in less, and the true average is actually lower than that, but there are also times when players come in for a raise and villain tightens up his reraising range significantly (and sometimes is calling instead of raising). For this reason, I think 35% is a decent approximation. We are going to assume that for each player who has entered the pot in front of him, villain is going to tighten up his raising range as if he were one seat to the right. So if he's on the button and everyone limps, he's only going to raise with his UTG range. If 1 player limps, he'd raise with his CO range. From the SB, he will raise with his Button range if no one else is in the pot. Otherwise, he will raise with his UTG range since he is likely to be playing a pot OOP.

Using those assumptions, let's run the numbers. Each successive number represents the amount of new hands added at the given position. It is multiplied by the percent of times (based on the action in front of him) that villain will be willing to play that range.

UTG:     6.2 * 100%                                                                            =  6.2% PFR
MP:      6.2 * 100% + 5.4 * 65% (0 in pot)                                                     =  9.7% PFR
CO:      6.2 * 100% + 5.4 * 88% (<= 1 in pot) + 9.2 * 42% (0 in pot)                           = 14.8% PFR
Button:  6.2 * 100% + 5.4 * 96% (<= 2 in pot) + 9.2 * 72% (<= 1 in pot) + 4.9 * 27% (0 in pot) = 19.3% PFR
SB:      6.2 * 100% + 19.3 * 18% (0 in pot)                                                    =  9.7% PFR
----------------------------------------------------------------------------------------------------------
Average: (6.2 + 9.7 + 14.8 + 19.3 + 9.7) / 5                                                   = 11.94% PFR

What does that give us? 12! Since some of the hands in his "raising range" would actually be limp behinds or calls behind a raise, it is actually quite feasible that someone could be open raising as wide as 25.5% from the button while still showing up as a 12/9 on your HUD!

So why does that mean anything? Well, for starters our QJs hand in the BB now has 43% equity against his CO range instead of the 37% equity that we thought before. Since it's not too hard to play QJs postflop, calling and seeing a flop would not be a terrible idea, especially since pot odds say we only need 35% equity; with that and our postflop ability (hopefully) should be able to make up for the fact that we're out of position. We used to think our ATs had 47% equity against his button opening range, but in reality it has 55% equity. By seeing a few showdowns and extrapolating a position-adjusted range from that, we might find that we should probably be 3betting our ATs hand vs his button raise instead of just folding our blind to him.


What about that non-positionally-aware donk who is running like 50/10? Based on the idea that he's raising the same hands from all positions as long as there's no action in front of him (in which case he's only raising QQ+), and otherwise he's calling with a wide range, we can assume his raising range is actually wider than 8%. Let's start with a calling range that is almost 60%. That would be any suited cards, any pair, Ax, K5+, Q8+, J8+, T8+, 98. With a raise in front or any kind of heavy action, the weakest of this range gets folded and brings us to the 50% we all know and love. That 60% is what he would limp with if given the chance.

But what is that 10%? You've seen those 3x raises over limpers that make no sense at all... all it does is build a pot without thinning the field. We are going to assume, then, that other than QQ+ and AK, our donk will only raise if the pot has not been raised yet, but he doesn't care how many limpers there are. Let's assume the average player in front of him will raise 10% of hands if given the opportunity. What number gives us a PFR of 10? It turns out that number is 11.7% of hands, as show below (the % at each position is the % chance that no one has raised yet).

UTG:    11.7            = 11.7% PFR
MP:     2.5 + 9.2 * 90% = 10.8% PFR
CO:     2.5 + 9.2 * 81% = 10.0% PFR
Button: 2.5 + 9.2 * 73% =  9.2% PFR
SB:     2.5 + 9.2 * 66% =  8.5% PFR
-----------------------------------
Average:                  10.0% PFR

A somewhat interesting result is that a non-positionally-aware donk is actually raising more hands out of position than in position. A corollary is that if your PT stats show an effect like this, where you are opening more hands out of position than in position (or even a pretty static amount) it could mean that you need to reconsider adjusting your ranges so that you are opening a narrower range in early position and a wider range in later position. This is especially true if you are losing money in early position (obviously).

So what is a good range for a donk 10% raiser? It turns out that any time no one has raised yet, he is raising TT+,ATs+,KTs+,QTs+,JTs+,ATo+,KJo+,QJo. If someone has raised, he is reraising (probably a minraise ) QQ+,AK. So pretty much what you would expect. If we had gone by the HUD's 10% stat, we would have had to leave out out KJo and QJo. With those hands in there, KQs is 47%. Without them, it is only 42%. Thus we can definitely cold call a donk's UTG raise with KQs because with our position and the extra money in the pot, we should be able to play it in a +EV manner. If our equity were only 42% (a gap 3x greater than our true 47%), we may be less inclined to make such a call.


So far the differences seem minor, but it may really affect the types of hands we play preflop and how we play them postflop. We may think that we can almost always call someone who is a 12/9 with set odds, but if they are raising in late position, this is probably not going to be a profitable play. We may call from the blinds, see a low flop, and think that it really hit villain's range horribly, when in reality low suited connectors, Axs, and all pocket pairs are a pretty big part of his range.

Another useful datum is that an UTG raise by a donk who raises 10% isn't anything to be particularly worried about. For any non-positionally-aware player, his EP range is guaranteed to be wider than your HUD indicates, not narrower as you might expect. If a donk who raises 4% raises UTG, we should put them on a range of TT+,AJs+,KQs,AQo+ rather than the much tighter range of JJ+,AKs,AKo that we might be tempted to put them on.

In the end, the real lesson to take away from this is that there is no substitute for watching the tables and taking good notes. Your HUD can only take you so far. You are much more likely to put your opponent on an accurate range if you are watching the showdowns and noting what kinds of hands your opponents raise from the different positions on the table.

Hopefully this post was a worthwhile read. Good luck on the tables!

[Erpel]

Methinks someone saw someone with a higher WPP than him and got jealous.

Solid post. Points well made. I've been aware of the general principles outlined, but never actually calculated actual examples.

[Keith]

do any of the HUDs give positional stats rather than average stats?

[DoanDiggy]

Methinks someone saw someone with a higher WPP than him and got jealous.

I've always had a high WPP. I'm often inadvertently wordy. I usually find myself going back and removing whole sections that seem like they're unnecessarily detailed or rambling. I hope I struck a good balance here between explaining myself thoroughly and not being redundant.

Thanks for reading and commenting.

do any of the HUDs give positional stats rather than average stats?

From what I've heard, HEM can do this. I'm not sure though because I went with PT3 before I did much research into my options.

One item of note is that even with a HUD that does give positional stats, the true range will still be slightly wider than the stats indicate due to the effect of action in front affecting the player's raising range (presumably tightening it up). Also, it's still important to see showdowns regardless. One person's 25% button range includes all suited Ks while another replaces those hands with suited 3-gappers. This makes a big difference in how different boards fare on an opponent's range.

[daven]

First, I will start with a "magic" range. Tell me you would ever expect a 12/9 to be playing a range like this:

UTG: 88+,AJs+,KQs,AQo+ (6.2%)
MP: 55+,ATs+,KJs+,QJs,AJo+,KQo (10.3%)
CO: 22+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,54s,ATo+,KJo+,QJo (19.5%)
Button: 22+,A2s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,65s,54s,A9o+,KTo+,QTo+,JTo (25.5%)

I expect that cos that's how i play when i'm running 12-9, and that's my same UTG range when I run 18-13....

i forget that some people haven't got around to doing this sort of thing yet.

nice post

[lolzzz_321]

Yes, HEM can do this when you "mouse over" a player's HUD Stats.

[DoanDiggy]

Thanks for the screenshot. That kind of justifies the idea what I was talking about. According to a basic HUD display, this player is raising 16% of hands. However, the open raising range is actually 26% of hands from the button and 43% from the SB. Obviously this makes a huge difference when we're putting our opponent on a range postflop.

[Micro2Macro]

Very nice work.

I think there may be a lesson in this post, and I know we all may not like this because PokerTracker is a great TOOL...

but that's all it really is. A tool. It isn't a substitute for taking notes on opponets, and taking notes on what opponents are opening with from what positions and how they play certain hands is really important to adjusting.

Stats are great to get a general picture of someones style (i.e. 44/2/0.3 loose passive), but I could easily find someone in my database with literally some of the exact same stats of me, and yet they would still play different under different situations. Just because player 'x' only raises 3% of his hands from UTG doesn't mean he won't limp QQ-AA. Statistics can therefore be a bit misleading without notes to confirm them.

I don't think we should rely on HUD, but rather use it to get the bigger picture. Once we understand the bigger picture, we can find out more about how everyone acts by making note on the little things that we might fail to recognize. Ex, does seat 4 check any flop with AA and raise any turn? Someone could do something weird like this and yet still have identical statistics to someone who doesn not.

Spenda's video where he 4 tables $5NL is a great example, he doesn't use HUD but he takes careful notes on his opponents to help give him an edge. He then uses PokerTracker as a post-game tool to do a check up on how he played. IMO PT is more effective for analyzing your own play than HUD is for having you decide whether to call or fold to a raise. I suppose if someone is playing 24 tables though note taking becomes somewhat impossible.

Just my 2 cents..ever since I stopped relying on HUD to play I've been felted less often and am beginning to improve things like betting for thin value etc. because having written notes makes it easier to deduce what my opponents are holding in a given situation.

[bigspenda73]

With out a doubt (in my mind) the most important HUD/PT stat is ATSB (attempt to steal blinds). It not only tells you how positionally aware a player is but also helps to type-cast a player.

[PlayToWin]

With out a doubt (in my mind) the most important HUD/PT stat is ATSB (attempt to steal blinds). It not only tells you how positionally aware a player is but also helps to type-cast a player.

I bet you could put together a very informative post regarding ATSB percentage and how that relates to different types of players.

[DoanDiggy]

Some basic uses for ATSB.

1) If someone's ATSB is higher than their PFR, they are positionally-aware. We can give their UTG and MP raises decent credit (assuming they have a reasonable PFR) and judge their late-position raises based on ATSB alone.

2) If someone's ATSB is higher than like 30%, they are a good candidate to 3bet lightly against. Axs, suited broadways, and SCs are good candidates (IMO) to 3bet with because if called, we can put a lot of pressure on them postflop with our good draws. Of course we should also be 3betting hands like AQo+ and 88+ (or so) for value. AJo and KQo are doing quite good against their range as well, but they don't play great postflop OOP against someone who calls a 3bet. Of course if they are opening from the CO and we are the button, we could potentially 3bet or flat with these hands.

3) If someone's ATSB is >15 or so, it's really a bad idea to flat their late position raises out of position with low pocket pairs, regardless of what their PFR tells us. We will rarely get paid off when we hit, so all we can do is pick a board that doesn't look like it hit them and either lead or check/raise. We end up being put in a lot of tough spots where we have to fold a better hand or we're chasing 2 outs to a set or some kind of straight draw.


That's a start at least. Any other ideas we can add?

[Robb]

HEM's standard popup menu for stealing separates steal% from the CO, BTN and SB. Over a reasonable sample ( > 200 ), if these numbers show BTN steal > CO steal > PFR by about 5%+ jumps, I know the guy's positionally aware.

Also, everyone steals from the button. Knowing the CO steal% can give you a read on actual "think stealing" rather than something auto-learned from a book or poker pro's blog.

Generally, steal% < 20 shows weakness and lack of positional understanding, especially for 15 and lower. Steal% ~ 28 - 30 is standard TAGG. You have to learn to deal w/ them as they make a greater part of your competition as you move up past 25nl. Steal% > 30 means he's getting out of line a lot and can be value 3bet (or flatted for value) pretty wide in stealing situations.

[Robb]

I was thinking about HUD stats and positionally-adjusted ranges today, and in doing so it became clear to me that HUD stats can be pretty meaningless for putting our opponent on a range of hands in a certain position if we haven't seen enough showdowns.

Like Daven, I forget some folks haven't worked this out. Positional awareness is by far the best way to "beat your own HUD stats" by being MUCH stronger than your HUD range in EP and much weaker in LP. This was easier in PT2 than w/ PT3 and HEM.

In HEM, I have tweaked the popups so that when I roll over someone's VP$P, I see his by position BP$P (instead of cluttered "preflop" std. popup). When I roll over PFR, I see his PFR by position. Same for Agg% street by street, etc. Generally, as spenda noted above, positional awareness is first "HUD visible" w/ high steal% stats, but you can develop a reasonable picture of exactly what the player opens on each street with ~ 200 hands.

[bode]

With out a doubt (in my mind) the most important HUD/PT stat is ATSB (attempt to steal blinds). It not only tells you how positionally aware a player is but also helps to type-cast a player.

I bet you could put together a very informative post regarding ATSB percentage and how that relates to different types of players.

i think this was a "triple-dog dare" spenda

[bigspenda73]

I have a lot on my plate at the moment but if I can find an hour I'll try to write something up.