Hallo micronlers,

im actually still not a pooh-bah, but i decided i wanted to post about something valuable. The only problem is that it's very hard to find topics that haven't been covered yet and what I'm going to be writing about actually is well covered teretory but it`s not solely about playing from the blinds. i hope this will show a couple of posters that you have to think about the game, not only copy ranges you`ve heard and play according to those.

I´m starting with a very simple, specific exmple and am going to apply the results to get a general answer. This is a strategy Isura recently posted about and its a really good way to solve problems.

We´re assuming villain is otb, has a preflop steal of 38,9% (total of 502 combos)
for a range of: 22+, Axs,Kxs,Q8s+,J8s+,T7s+,96s+,As+,QTo+,56o+

→ The frist thing we have to keep in mind here is that villain can pick his spots. He will only be stealing the blinds when he has a hand with at least some potential. That puts the blinds at a general disadvantage because they have 1248 possible combos each and btn has the top 3rd of that range because he folds the (1248-502) 746 combos he doesn´t like.

→ The second obvious fact is that btn is laying 4bb, his preflop raise, in order to win 1,5bb(sb+bb)
so 4 to 1,5 equals 2,66 to 1. So basic pot odds tell us that btn has to win 2,6 times in order to lose
once.

I) We assume sb folds every time villain steals from the btn, hero is in the bb and villain folds his entire range against a 3bet.

As pot odds told us villain is laying 4-1,5 so he has to win 100%-1/3,66=73% of the time.
So for this hipothetical proposition hero would have to raise 27% of all hands in order to prevent villain from making money of his steals.
This would give hero a range of 0,27*1248=337 combos.
This is a redonkulous range of Ax,22+,KJ+,QJ+,QTs,KTs,J8s+,T8s

II) Now we`re going to let the sb participate in the game. He`s a nit and only 3beting 6,8% of his hands, which actually is a reasonable 3 beting range of a unl reg i think...

So sb range will be 88+,ATs+,AO,AK,KQs in total 86 combos.
Btn is still folding to every raise and opening his 38,9% of hands.

How many hands does hero need to be 3beting in order to make villain be?
(For the sakes of keeping this easy we will ignore the fact that hero and sb will sometimes be dealt premium hands (kind of an overlay) at the same time and regard them as 1 player basically)

that said in the anterior example hero had to raise 337 combos to prevent villain from winning. In this example it is 86 combos less which gives us a total of 337-86=251 combos, which is 251/1248=20,11% of all hands dealt. Which is still a huge range to be 3beting obv.

III) Last but not least we will assume that btn does indeed have half a brain and can decide between calling, 4beting and folding.

Sb will still only be 3 beting his nity range.
Btn is a little bit more complicated now. He´s folding the bottom part of his range, 4beting the top and calling the rest.
Hero is still 3beting to 16bb, 20,11% hands and stacking off with with a range of 4,2% which is JJ+AK and AQ (hero stacks off 56/251=22,3% of the time he 3bets thus he folds 77,7% to 4 bets)

So how does this work out with the old raises if villain is only going to 4bet with a range of 4,2%(56 combos) calling with 7,5% (4beting range + 48 combos) and folding the rest of his hands to 3bets?

Ok now we have to find out what his 4beting propability is:
56/502=11,2%

and the calling range:
48/502=9,5%

the probability of folding:
(502-56-48)/502=79,3%

hero`s EV vs villain`s calling range= 48,5%
0,793*4bb-0,112*0,77*15bb+0,112*0,23*0,5*100,5bb-0,112*0,23*0,5*99bb+0,095*0,485*16-0,095*0,515*15=3,172-1,29+1,42-1,27+0,74-0,73=2bb


79,3% villain folds → hero wins 4bb each time
hero folds to 77% of villain´s 4 bets and loses 16bb each time
23% of these times hero has a hand though and stacks off and wins these stack offs half the time
and loses the other half
9,5% villain has the middle of his range and calls, hero has 48,5% equity
villain has 51,5%

So like this you can actually make money playing from the blinds?
Why is this?

Ok well i´m not sure this really belongs into unl anymore because the math is prob difficult for someone who starts out. But what this shows you is how lethal many mistakes are that unl regs make and there is noone exploiting them.
Would anybody have thought before this post that you can make 1bb per hand that btn opens if you start 3beting a wideish range and villain is unable to adapt?
This post was more about showing people how to aproach poker in general though and starting to solve specific problems in order understand the bigger picture. Especially the preflop game is mathematically pretty easily solveable, so just invest the work, its worth it. Plus those aspects of the game that you have thought about this way are carved in stone and you will never doubt them because hey it´s math!

I hope i´ve helped someone with this post and it won´t just fall off the first page immedeately...

gl monk

thanks, look forward to reading this

nice post monk

ok thats how its was supposed to be



hero`s EV vs villain`s calling range= 48,5%
0,793*4bb-0,112*0,77*15bb+0,112*0,23*0,5*100,5bb-0,112*0,23*0,5*99bb+0,095*0,485*16-0,095*0,515*15=3,172-1,29+1,42-1,27+0,74-0,73=2bb


79,3% villain folds → hero wins 4bb each time
hero folds to 77% of villain´s 4 bets and loses 16bb each time
23% of these times hero has a hand though and stacks off and wins these stack offs half the time
and loses the other half
9,5% villain has the middle of his range and calls, hero has 48,5% equity
villain has 51,5%

Pretty basic theory-wise and the examples were a bit extreme.

That said, I'm sure the general ideas of what to consider when faced with a stealer will be very helpful to many. Maybe you should have put more emphasis on the general thought process though.

Thank you monkover, very nice post. I'm usually too lazy to this kind of math myself. Now, I'm going to push myself to actually do the math. Hopefully I will develop more solid, +EV reasons for my actions other than "I think I'm ahead of his range."

well the idea was to start out with an easily solvable example and then make the situation more complex/realistic.
about the basic math part. more or less every situation in poker can be solved with basic/easy math one just has to sit down and make the effort because it does take time.

Definitely pretty typical of a tag "good" regular, a lot of opponents steal quite a bit less though

This is one of the main reasons people have started advocating raising to 3x or 2.5x on the button. Also I think a 4x raise is much more typical of the same type of 19/17 type player as the above steal percentage.

Of course given these parameters we could/would just 3bet 100% of the time.

I don't really think this is a nitty range for a SB to 3-bet TBH, even against a button open.

Isn't this whole example/math ignoring the fact that when he calls us he has our wide 3-betting range crushed in a big pot w/position on us? We lose a lot of money in these spots. EDIT: I see you give us like 48% equity in these situations, OOP against a reg our real EV is much lower imo.

I also hesitate to use the word "solvable" when it comes to poker. Against one type of player in one type of situation you might be able to come up with a rigid starting hand chart that is optimal, but if you change his range 2-3% or change the other players at the table, or game-flow considerations, or he happens to be an actual human being and not a robot with strict parameters it all changes. Not to mention if they are opening to 3x or pot (like a lot do on FT) the math changes pretty drastically.

That said I appreciate the post and I think we can learn a ton from the math of a situation but if you aren't careful in interpreting and applying the results you can really hurt your game. I mean, in this specific example we are talking about 3-betting extremely light out of position against a guy with pretty good ranges for most stuff. Yeah, some guys can't adapt, but there are definitely more than a handful of regs that can and will adapt to it. If they adapt to the way you are exploiting them, and you don't realize it because you are staring at your hud and are thinking "the math says I can 3bet, I raise" and not realizing that they are 4-betting you light or calling and taking it away on the flop a lot, then you have become handcuffed by the math.

Also, if you find yourself in this situation to the left of nit and in the BB against a TAG reg on your button, maybe find a better table.

Honestly Monk, I'm not trying to rip it apart, I know you are aware of most/all of these things, but there are a lot of new guys I'm sure reading your post thinking "ok I'm gonna start 3-betting T8o against a button raise." So my post was for them, please understand what Monk was trying to get across and not just go out and blindly implement this example.

Unless you are at my table.

It seems that we are assuming that both players are in some sense 'equal' postflop, regardless of position, in order to include the extremely simple calculation for when the 3bet is just flatted (9.5% of the time). In order for postflop to correspond exactly to preflop hot and cold equities, when one player makes the other player fold, the complementary situation needs to occur exactly in proportion to the preflop hot and cold equities after taking a weighted average with pot size as the weight. Even if we make a hugely simplifying assumption like this, you have to add some unknown portion between 0-84bb of the remaining stacks into that part of the EV calculation to get the right answer. Right?

0,095*0,485*(16+x)-0,095*0,515*(15+x), 0 < x < 84

1) anyone good isnt stealing with 4BB raise sizes always. it should fluctuate between 2-4BB depending on the blinds.
2) 3betting from BB should be a polarized range of monsters combined with bluffs that have no postflop value. in between hands like KQ or AJ or TT are calls.
3) same thing with 4bets. against a frequent 3better, you are polarizing to monsters and bluffs. you rarely 4bet JJ for example, but might with A4s.
4) lots of the ranges you are using dont make sense. why is the BTN stealing with 56o but not Q7s? high card strength is what matters in steal situations.

to clarify, i hope you mean their BTN steal %, because their 'preflop steal %' is an average from several positions.

what? what happened to postflop play? is this a weird form of poker where you skip to showdown and share your equity of the pot from preflop? BTN has huge positional advantage. the math for 'calling' the 3bet makes no sense.

This is just good advice with any strategy implementation, especially advanced play {i.e. bloating the pot OOP against calling stations or players who can/do adjust}

to add on, i think OP is dangerous for the horde of weak tight uNL TAGs who will interpret this all as 'i can 3bet light against people who steal 40% and auto profit'. thats a very dangerous road for a poor player to take. for one reason, the people who steal 40% are usually the better TAGs, who are most likely to adapt. they will start to 4bet bluff you if they see you repeated 3betting their steals, or they will call and try to steal the pot from you on the flop/turn.

you have to learn what range to 3bet and it better not be 'Ax,22+,KJ+,QJ+,QTs,KTs,J8s+,T8s' like in OP. it should be polarized and change opponent to opponent. then you have to learn what to do when your 3bet gets called and you have 55 on a Q76 board OOP.

unless you are playing the game OP suggests and you can just ask for your 48% equity from the pot when your 3bet gets called and move on to the next hand.

btn opens to 3 to win 1.5 which means he has to win 2:1 66% of the time.

If he is calling 3bets with JJ AQ KQ and add a few **** hands because people spazz out and its just for widening his range a tad like 22. He is 4 bettting QQ+ AKs AKo (pretty tight but whatever)

lets assume for this example you are only 3betting when sb folds

so if you 3 bet 100% this is what can happen

You 3bet button folds : you gain 3.5 bbs each time.

This will happen 35.1% out of 39.7% of the time

you 3bet button calls : you lose 11 bbs each time.

This will happen 2.4% out of 39.7% of the time.

you 3bet button 4bets : you lose11 bbs each time.

This will happen 2.6% out of 39.7% of the time.

So 5.1% / 39.7% = 12.8% of the time you lose 11 bb. equity = -1.4 bb


35.1 % / 39.7% = 88% of the time you gain 3.5 bb. equity = + 3.1 bb

So in a vacuum you can raise 100% of the time. with a net equity of 1.7 bbs.

Even if your cards have no showdown value ever. Which means postflop doesn't matter becuase you are just c/fing 3 streets. Obv he cant know this and obv he will adjust but...3bets are profitable.

The original post was less about 3-betting pre out of the blinds (which was simply his example) and more about taking a mathematical approach to the game that will always be a winning strategy because the numbers don't lie.

I really appreciate the time OP took to write this post. I believe that math should be a facet of our overall strategy, that is to say, you cannot master the game by math alone.

Consider the theoretical situation of a computer playing against a human player, where the computer represents playing poker purely mathematically (because that's all it can do). They play thousands upon thousands of hands and the computer obtains a large sample size to which it can accurately predict how often the human player will do x when y, assign a range to the human player based on past hands, etc. etc. Over a large sample size, the computer would begin to build an edge over even the best human player (assuming the programming of the computer was good) because it won't lose focus, tilt, etc. However, the mathematical edge of the computer will only become apparent if it has a large enough sample size to use to make decisions.

It won't take long for the computer to build up a history of your preflop range because you will have to call/raise/fold every hand, so given maybe 1000 hands the computer can have a pretty reliable idea of your preflop range in any given situation (including 3-betting and other such things). This is simply because you have to make a decision preflop every hand, its the nature of the game. EV calcs aren't actually that hard preflop, its postflop where they become more suspect because postflop situations are much more unique and varied and player dependent.

Now imagine a more complex and weird scenario. Where the human player takes a deceptive line with a set, works donking into his flop lines, starts 5-bet bluffing, etc. None of these things occur often enough for the computer to have a reliable history on to make +EV decisions, so it simply has to guess. Maybe it assigns percentages at random to the EV calc it does every time it makes a decision, maybe its programmed to just fold until it builds up a history, or maybe it takes a random action in turn, who knows.

The point of this illustration was to show that making a +EV decision against a particular player in a particular situation that is purely mathematically based would theoretically be a winning strategy, but you would need an extremely large sample size that you could reference instantaneously in order to have all the information necessary to plug in to the EV calculation. For a computer with good programming this is possible. For a human player with a HUD this is not even close to doable.

Over time a good poker player will build up a 'large sample size' similar to what the computer does, but it won't be explicit information with every little detail recorded. It will be in the form of subconscious memory, the same memory that tells you to stop when you see a red octagon or jerks your hand away from a hot surface. Subconscious memory cannot provide you with raw numbers to feed into EV calcs. Over time you will learn what the optimal line in a given situation is, and maybe later away from the table you can sit down and try to toy around with some percentages and an EV calc, but you would need to be some kind of super-human with an eidetic memory to hope to be able to store every hand you've ever played with a villain in your memory, recall every hand where you were in some unique situation (like when he c/r you on the river) and then plug a % into an EV calculation.

I'm not saying that mathematics isn't important to a sound poker strategy. I'm also not saying that a computer couldn't theoretically play perfect poker. I'm simply saying that math is only a component of the game. The reason I typed out this whole tl;dr post was because I feel that at times the math becomes way to big a part of our decision-making, where we are trying to make decisions based entirely on HUD stats, and sometimes when we have these horribly small sample sizes. uNL is populated with thousands of unknowns that we have zero hands on, when you sit down in a 25NL game you will rarely sit down with reliable stats on more than 1 or 2 players (if you do you are probably at a table of regs and should move). We have to be able to make decisions without large sample sizes all the time, which in turn means we need to make decisions based on other things to.

Sorry if this seemed like thread hi-jack. /soapbox.

at a higher level, poker is more about changing gears, like rock paper scissors. the skill isnt identifying how someone plays every specific situation and putting it in some giant EV calculation, but instead what gear they currently in. are they playing draws fast on the flop right now? are they stealing 30% or 80%? its a constant game of adapting. a computer therefore would need to be good at identifying changes in gear quickly. all the 'random' things you suggested a person could do against the computer, the computer could do back too, in the same type of ways.

also, its not necessarily true that a computer poker player would have to be doing a lot of math. it could be using 'rules', or do random things, or maybe have a large look up table of similar situations from a top player to copy, etc..

like you said the main edge a top computer would have is being able to play its A game constantly.

Eh the 'computer player' thing got a little out of hand it was just an illustration. I think fundamentally we agree though... the details of what approach a programmed poker strategy would take is another subject entirely.

I sort of grunched.

One thing I don't think really makes sense is us choosing a range to make sure villain doesn't make a profit on his steals (or plays in general). I mean, obviously this is just an illustration of how to use EV calcs to determine exploitative plays, but in the case of otb vs blinds, we shouldn't have the expectation that we can find a strategy that makes otb's steals 0EV. The structure of the game is such that otb has an advantage and the blinds a disadvantage.

I'm sure monkover gets this, I just want to make it clear that under realistic assumptions and good button play, we are unlikely to find a strategy that makes the button's steals -EV. Rather, we look for a strategy to minimise the disadvantage of being in the blinds.