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Mathematics in poker - II. Range - myth called "NIT"

• Bronze
Joined: 11.07.2010

If you haven't read my first article, please check it first, it will help you understand today's topic. You can find link to that above.

Hi there guys,

it’s weekend and it means more Math in poker! Today we will work on ranges and calculating ranges. I would call this stuff again basic of basics, however, I’ve already met a lot of good players who have really bad picture about ranges – that's just enhanced by using HEM,PT (which I recommend to everyone!)

For me, this is the most extended myth in microgame cashgame, I call it NIT MYTH. We will look closer just in any minute.
At first what really RANGE means for us?

Of course range = some cards which are expressed in percentage (for example 10% PRF).
So well we can count it as COMBINATIONS of 2 cards, which are sorted by their strength.

I guess a lot of people just have NO CLUE about what hands are 10% they really can’t make some range conclusion based on informations, which track programs contains.

Just make your guess! What hands do you think is hidden behind PRF 10% write it below before you read any futher…

I have to say that I’ve been playing long time in NIT MYTH – I thought 10% is something like TT+,AQ+ at the worst scenario! Therefore I was easily giving up +EV spots, because I had bad picture about opponents range!

Well then, let’s count that! What RANGE – combinations of 2 cards, we can assume in 10% PFR.
You can try it on your own and just check it in here, you should all be able to do it on your own if you’ve read my first article!
Again we will need this formula:

At first we need m(A), you all already know it’s

P(A) – probability of phenomenom A
m(A) – positive phenomenoms of A (all combinations in 10%)
m – all combinations

Well we got number 133, but now what? What means 133? We already know that ATC have 16 options to be made and any pair 6 of them. Now, we have to count these to get as close as possible to the number 133. I know it’s kind of slavish, however, it will help you a lot)

We will count it by strength – AA,KK,AK and so on (6+6+16….)

As I suppose a lot of you will be quite lazy and just skip the count part, which is the most important I will write it down here: ))
5,7
AA(6),KK(6),AK(16),AQ(16),QQ(6),AJ(16),JJ(6),AT(16),KQ(16),TT(6),99(6),88(6), KJs(4) , A9s(4) ..

88+, AT+,A9s+,KJs+
So this is our 10% PFR range (of course we don’t have to match in every combination, because sometimes players are tend to play more deped on hand playabilities than real value, however, it doesn’t matter at all. The important thing is if you have learned something new and I hope you have.
Still the counting like this is quite difficult I will show you an easier way … You know that for any pair the probability is ~0,5% for ATC(suited and unsuited) 1,2%... It’s much easier than count 16+6+6+16 etc and in like 10s you can have pretty good image about opponents range.

I can advice you just to try it on your own. I think that after like 10 calculations of different situations you will be able to just look at stats and say pretty accurate range. It will help you a lot in your decisions and game, as you can easily say then, how often he will get for example AT+,66+,A2+

As the time will go, you will make your own „checkpoints“ – your first might be 10% we have done up, for example I have engraved in my mind this + 5% 99+,AJ+ …

Right now, you can count a lot of different situations, which you have to face in your daily sessions. Ranges are very important (and be able to calculate 10% -> combinations of cards and back to percentage)
Even though they look so boring and a lot of people can say they won’t lose their time with that. I’m convinced that more than half of them wouldn’t expect that range for 10/10 player, who is usually cold NIT is same, as we had calculated!…

Therefore, MYTH BUSTED!

Thanks for your time, I hope it helped next time we will make some more serious calculations)

Cya,
KillerFishes
• 30 replies
• Bronze
Joined: 11.07.2010
Write down what was your idea about combinations in 10% PRF, I'm really curious about that!
• Bronze
Joined: 01.04.2009
I dont get the point

A 10% Range can be composed in so many different ways.

10% UTG Range can look like this:

22+, AJs+, KQs, AJo+

or this:

66+, ATs+, KJs+, AJo+, KQo

a 10% 3 bet Range from the SB will look differently:

TT+, AJs+, A5s-A2s, KQs, T9s, 98s, 87s, 76s, 65s, 54s, AJo+, KQo

or

77+, A2s+, AJo+
• Bronze
Joined: 18.09.2008
Originally posted by m3ta
I dont get the point

A 10% Range can be composed in so many different ways.

10% UTG Range can look like this:

22+, AJs+, KQs, AJo+

or this:

66+, ATs+, KJs+, AJo+, KQo

a 10% 3 bet Range from the SB will look differently:

TT+, AJs+, A5s-A2s, KQs, T9s, 98s, 87s, 76s, 65s, 54s, AJo+, KQo

or

77+, A2s+, AJo+
I think that's exactly the point.
• Bronze
Joined: 11.07.2010
Yep, you're right ... This topic is just first step into ranges as we will make some serious calculations later...

I was pretty sure that a lot of "skilled" players will already know and have the right idea, however, I'm still convinced that new players are often not that sure what does really the "10%" mean .. What cards are they? How can I calculate it in game if I have no pokerstove or w/e opened ?

This is the way

And yes, I realize that we can write down 10% range in many ways. That's why I've written this:
"So this is our 10% PFR range (of course we don’t have to match in every combination, because sometimes players are tend to play more depeded on hand playabilities than real value, however, it doesn’t matter at all. The important thing is if you have learned something new and I hope you have. "

Thanks for reply and cya!

KillerFishes
• Bronze
Joined: 21.12.2010
Great thread, I hope you will keep going This is gold for beginners
• Bronze
Joined: 11.07.2010
Thank you! As we will go further I hope it will be more and more useful even for advanced players
• Bronze
Joined: 01.04.2009
Originally posted by Waiboy
Originally posted by m3ta
I dont get the point

A 10% Range can be composed in so many different ways.

10% UTG Range can look like this:

22+, AJs+, KQs, AJo+

or this:

66+, ATs+, KJs+, AJo+, KQo

a 10% 3 bet Range from the SB will look differently:

TT+, AJs+, A5s-A2s, KQs, T9s, 98s, 87s, 76s, 65s, 54s, AJo+, KQo

or

77+, A2s+, AJo+
I think that's exactly the point.
leveled :'(
• Bronze
Joined: 09.11.2010
you're expanding on/making this topic more accessible for absolute beginners than in Let there be Range by slowhabit and cts. well played sir.
• Bronze
Joined: 18.09.2008
Originally posted by m3ta
Originally posted by Waiboy
Originally posted by m3ta
I dont get the point

A 10% Range can be composed in so many different ways.

10% UTG Range can look like this:

22+, AJs+, KQs, AJo+

or this:

66+, ATs+, KJs+, AJo+, KQo

a 10% 3 bet Range from the SB will look differently:

TT+, AJs+, A5s-A2s, KQs, T9s, 98s, 87s, 76s, 65s, 54s, AJo+, KQo

or

77+, A2s+, AJo+
I think that's exactly the point.
leveled :'(
Ah yes. Flat as a pancake.
• Bronze
Joined: 14.09.2009
Originally posted by KillerFishes

If you haven't read my first article, please check it first, it will help you understand today's topic. You can find link to that above.

Hi there guys,

it’s weekend and it means more Math in poker! Today we will work on ranges and calculating ranges. I would call this stuff again basic of basics, however, I’ve already met a lot of good players who have really bad picture about ranges – that's just enhanced by using HEM,PT (which I recommend to everyone!)

For me, this is the most extended myth in microgame cashgame, I call it NIT MYTH. We will look closer just in any minute.
At first what really RANGE means for us?

Of course range = some cards which are expressed in percentage (for example 10% PRF).
So well we can count it as COMBINATIONS of 2 cards, which are sorted by their strength.

I guess a lot of people just have NO CLUE about what hands are 10% they really can’t make some range conclusion based on informations, which track programs contains.

Just make your guess! What hands do you think is hidden behind PRF 10% write it below before you read any futher…

I have to say that I’ve been playing long time in NIT MYTH – I thought 10% is something like TT+,AQ+ at the worst scenario! Therefore I was easily giving up +EV spots, because I had bad picture about opponents range!

Well then, let’s count that! What RANGE – combinations of 2 cards, we can assume in 10% PFR.
You can try it on your own and just check it in here, you should all be able to do it on your own if you’ve read my first article!
Again we will need this formula:

At first we need m(A), you all already know it’s

P(A) – probability of phenomenom A
m(A) – positive phenomenoms of A (all combinations in 10%)
m – all combinations

Well we got number 133, but now what? What means 133? We already know that ATC have 16 options to be made and any pair 6 of them. Now, we have to count these to get as close as possible to the number 133. I know it’s kind of slavish, however, it will help you a lot)

We will count it by strength – AA,KK,AK and so on (6+6+16….)

As I suppose a lot of you will be quite lazy and just skip the count part, which is the most important I will write it down here: ))

AA(4),KK(4),AK(16),AQ(16),QQ(4),AJ(16),JJ(4),AT(16),KQ(16),KJ(16),TT(4),99(4),88(4) .. so far we have 124 so still some place to 133 and our range looks so far like that:

88+, AT+, KJ+ because people usually like more the suited let’s count them down so 124+ A9s(4), KTs(4) = 132
88+, AT+,A9s+,KJ+,KTs+
So this is our 10% PFR range (of course we don’t have to match in every combination, because sometimes players are tend to play more deped on hand playabilities than real value, however, it doesn’t matter at all. The important thing is if you have learned something new and I hope you have.
Still the counting like this is quite difficult I will show you an easier way … You know that for any pair the probability is ~0,5% for ATC(suited and unsuited) 1,2%... It’s much easier than count 16+4+4+16 etc and in like 10s you can have pretty good image about opponents range.

I can advice you just to try it on your own. I think that after like 10 calculations of different situations you will be able to just look at stats and say pretty accurate range. It will help you a lot in your decisions and game, as you can easily say then, how often he will get for example AT+,66+,A2+

As the time will go, you will make your own „checkpoints“ – your first might be 10% we have done up, for example I have engraved in my mind this + 5% 99+,AJ+ …

Right now, you can count a lot of different situations, which you have to face in your daily sessions. Ranges are very important (and be able to calculate 10% -> combinations of cards and back to percentage)
Even though they look so boring and a lot of people can say they won’t lose their time with that. I’m convinced that more than half of them wouldn’t expect that range for 10/10 player, who is usually cold NIT is same, as we had calculated!…

Therefore, MYTH BUSTED!

Thanks for your time, I hope it helped next time we will make some more serious calculations)

Cya,
KillerFishes
question: if for each PP there are 6 combinations, why do you only count 4 of them?
• Bronze
Joined: 11.07.2010
Thanks thazar, I don't like to make exuces, however, I was adding the counting part very late as I've somehow believed people will make it on their own (didn't happend though )

Now it should be ok, fortunately it didn't affect the range very much Still don't know, why I have written it well above and then counted 4 ... pfffff
• Bronze
Joined: 31.12.2010
Really great thread, really enjoying this

Roo
• Bronze
Joined: 11.07.2010
Thank you! More is coming soon
• Bronze
Joined: 03.04.2011
Heh interesting thread. The one problem with it is the premise:

While it's true many people don't realize what 10% range IS,
the true ranges you've given for 10% DO represent a nit!

Anyone who opens only with 88+, AT+,A9s+,KJs+ (or one of the alternative 10% ranges that people have given here) IS a nit, an overly conservative player who can be easily exploited.

Consider that you can open up to ~45% from the button profitably according to many top pros, and quite a high % from the CO as well, and in order for people to not exploit you in the blinds you need to defend them much more often than with that range... A player with 10% VPIP all across the table IS a nit, and is both missing out on many profitable opportunities and can be easily exploited (That's the definition of a int. When you play so few hands that you can be exploited).

So it's not the "NIT" myth that you've busted, but rather,
your view of good opening ranges and bad ones, as well as what ranges constitutes a nit. The real 10% you've discovered and now know DOES represent a nit...

The range you initially thought was 10% (TT+,AQ+) does not represent a nit at all...You can call him a super nit or invent your own name... It doesn't matter, since this range usually represents a horrible horrible player...

A nit doesn't have to be that horrible, but he's missing out too much value and is way too exploitable.

The only way in which super tight ranges like these can be profitable is if you heavily manipulate the mathematical odds, such as Mid Stack Strategy and Short Stack Strategy here on pokerstrategy. But it's very easy to recognize such players quite fast.

I've left the mathematical part as to (part of the reason. The whole reason is related to even more spots) WHY a 10% vpip player IS a nit and is playing very poorly and in an exploitable way for the next post, to prevent a super long one ...

Sorry for all the math that is about to appear.
• Bronze
Joined: 03.04.2011
Here's for a bit of math to explain it (a bit technical):

Suppose a player defends even as many as ~15% of his hands from the Big blind (which is just about right for a player with an overall 10% range. I assume he's aware of position and plays less from early etc.)
I'm the small blind... it's folded to me. With what hands would it be profitable for me to raise with?

Suppose I raise to 4BBs. I'm putting 3.5 BB to win the 1.5BB already there when you fold, or the 1.5BB + the 3BB you'll call with for the times you call. So I'm getting 1.285:1 on my money when you call(I'll deal with 3bets in a bit). That means that when I do get called I need about 43% equity in the hand.

so my EV from the times you fold is 0.85*1.5 = 1.275.
my EV from the times you call is 0.15*(relative hand equity).

Suppose I open a ridiculous amount of 70% of my hands in that spot! put them in a range comparison tool, and you'll see that a 70% range has about 37% against different 15% ranges (which a 10% vpip player would probably defend the blinds with).

we get my EV (roughly...there are many slight changes but that's the gist of it) as:

EV = 0.85*1.5 + 4.5*0.15*0.37 (I'm ahead 34% of these, and stands to win 4.5) - 3.5*0.15*0.63 (I'm behind the rest, and will lose the 3.5 I've put in) =

EV = 1.275 + 0.25 - 0.33 = 1.195

That means opening 70%!!! of my hands in that spot is profitable! and that happens every time it folds to me just because you're sitting next to me!
That happens at least twice in 100 hands (once in ~6 orbits it would fold to the big blind...) giving my winrate a +2.4 bb/100 addition! and in case that wasn't obvious, decreasing the nit's winrate...

Of course, it's probably a bit lower than 1.195, because I hope (for the nit's sake), that he's 3 betting his super strong hands in that spot.
Note something curious: EVEN if I choose to raise 100% of my hands in that spot and fold EVERY time on the flop when you call preflop. we get: my EV =

1.275 - 3.5*0.15 (I always lose the 3.5 I put in when you call) = +0.75 !!!

STILL profitable! to raise with EVERY hand and fold post flop... heh Are you beginning to see just HOW exploitable a Nit's game is (and why a 10% player IS a nit)?

Such is the power of fold equity.

Also nits lose lots of value from late position: they fail to leverage fold equity in that same way, and they miss many value raises when the odds of the blinds having worse hands are quite high.

So, glad you now know what a 10% range looks like, but make no mistake, such a player is most definitely a nit... It's a bad range to play (unless you're manipulating the odds with something like the midstack strategy... but again, easy to know who these are).

Good luck exploiting the nits
• Bronze
Joined: 23.06.2008
10% can be a good range to play for me if the others are playing 85/48; and don't tell me there aren't any of those or I'll laugh...a lot.

This is good stuff and I think you should be commended for your efforts here.

Anyway, my question is; 'Why do I need to know how many combinatoins there are of, say, AK for example? How does this help during playing a hand?
• Bronze
Joined: 01.04.2009
Originally posted by gadget51
Anyway, my question is; 'Why do I need to know how many combinatoins there are of, say, AK for example? How does this help during playing a hand?
during ur session u might want to calcualte whether u have a valuebet or not. it's much more practical to think in combos than X% range.

example:

hero AA

board 229TJ

viallians range 99-KK, he will call all of those to ur shove on the river.
there are 9 combos of sets and 12 combos of overpairs, therefore the best play is to shove.
• Bronze
Joined: 03.04.2011
Originally posted by gadget51
10% can be a good range to play for me if the others are playing 85/48; and don't tell me there aren't any of those or I'll laugh...a lot.
Heh I won't only agree with you, I'll also state that you've found one of the only exceptions. Because while there are lots of these super loose players out there, it's rare to find a table FULL of these... at least not on full tilt and pokerstars... (if you know a place where finding tables with many of these players is common, please tell me!!!)

and with just 1 or two at the table... you'll get exploited by all the others too much...

So yeah, of course there are rare situations where playing 10% is ok, but most of the time (the vast majority of the time), it's just the play of an easily exploitable nit.
• Bronze
Joined: 03.04.2011
So now that (thanks to the thread starter) everyone here knows what does a 10% range consist of, I'd like to complement the information given by answering a few questions that any aspiring poker player interested in improving his game would probably like answered (or have already answered...):

1) How can I use that knowledge of what is a 10% range?

2) What other useful information have I gathered from the original thread starter's post (which was quite detailed!) ?

3) What about other ranges? do I have to memorize every range? how to handle other ranges?

Answers:
1) Every exploitation (and that is what you should constantly be looking for - ways to exploit your opponents' style of play) has two parts - preflop and post flop.

Preflop - exploiting a 10% vpip player preflop is easy, the examples I've given of leveraging fold equity against these types of players are the most basic way of doing it.

Postflop - now that you KNOW what his range is, you know how likely he is to have hit the board or have an overpair. Tight ranges are easy to predict, and knowing where you're likely ahead or behind is a huge help. Hard to do well without knowing his range...

A word of warning though - make sure you're actually playing against the correct range: A 10/5 player may be playing 10% of his hands preflop, but open raises with only 5%.

Also his range will most likely be a bit wider from the button and a bit tighter from early position, so important to take note of that. Know which hands of his range are more likely and which are less (and which hands can be added to his range from late position).

Going over these possible ranges is essential in exploiting any type of player.

2) In the original post, the thread starter did a good job of explaining how many combinations are there for each hand. That can be used for calculating how likely is it that you're ahead/behind, as was mentioned by m3ta in his post. It's a very useful conclusion from a post seemingly related to another topic, and is a good thing to notice and use.

3) So what is a 5% range? 15%? 27%? of course, I don't know a single player who memorized every possible range... That's too difficult, and quite useless... You'll get used to assessing ranges with time and experience, but you need a place to start from, don't you?

Here's what I do: I just used equilab for some ranges, in 5% increments: that is, 5%, 10%, 15%, 20% and 25%. That was it... All I needed to learn. Not much. If you face a 22% player after many hands and treat him as a 20% player, you'll probably be doing great.

Then, I started changing the ranges by using what I know about counting hands (how many combinations does a pair represent (6), and what % does these 6 combinations add to the range? (0.45%, which we can round up to half a percent in real time calculations. Makes it easier and is usually enough).

When we can answer such questions, we can make small adjustments to the ranges we're facing, that is, suppose we know what a 20% range is, and an opponent has 23% after many hands. Of course we can treat him as a 20% and still be ok, but what if we treat a 13% player like a 10%? That's a much more serious error, since the addition of these 3% are actually a significant part of his range (provided he has that range after many hundreds of hands).

We just take the closest range we have already learned, and add or remove combinations to it. Obviously the next strongest hands... until we reach close to our desired range....

Note that the goal is not to do this calculation each time at all! but to get used to making quick range assessments at the table, and by testing yourself with equilab after each session, this method will make you recognize different ranges very quickly. I know it helped me!