Renton theorem aka ABCD theorem

In poker, we attempt to make money by playing the best we can, making what we feel is the most profitable play in every scenario, making as few mistakes as possible. Assuming you know the exact hand range of your opponent, there is almost always a clear best play, and if you like money you should make that play every time, right?

Yes, on a basic level this is true. Whenever we have the nuts we should bet/raise/reraise, whenever we have nothing we should fold. If we have nothing and feel like we can make our opponent fold a better hand enough of the time, we should bet as a bluff.

However, theres another level of poker that goes beyond this one hand. Not only does your opponent have a range, but you do as well. Not only do you want to make the best play with THIS hand, THIS time, but you want to make the most money with your range, EVERY time. You want to make the most profitable plays when you are in this spot. You want the average EV of your play with your range in this spot to be as high as possible.

A pretty common example of this was in an infamous Samoleus/EmpireMaker2 thread on 2p2 a while back. Samoleus criticized EM2 for 3-betting QJs in button vs blind scenarios. His reasoning was that "QJs has too much value in calling." He believed that it was more profitable to call QJs than to waste it on a 3-bet.

The other less obvious reason why "QJs has too much value in calling" is that EM2's range consists of subdivided ranges in which he 3-bets/calls/folds, and putting QJs into the 3-bet range reduces the number of profitable plays he makes as a whole.

Renton Theorem:

In any no limit hold'em scenario where there is money left to be bet, hero's range is divided into subranges A, B, C, and D, where:

A = hero's 'nut' range consisting of hands to be aggressively bet/raised for value.

B = the range of hands that aren't as strong as range A and benefit from passive play and/or pot control.

C = the range of hands that have a nominal amount of value, but can stand little or no action.

D = hands with little or no value

The four ranges are determined by the resultant play that is optimal for the range as a whole.



Subranges A, B, C, and D are directly adjacent in terms of playability/strength (i.e. the bottom of 'A' borders with the top of 'B'). All of the hands in a given subrange should be played the same (barring randomizing your play), and this is how the range is defined.

What do I mean by "optimal for the range as a whole?" Is that different from "optimal in a vaccum? Let's start with an example similar to the QJs above.



Example 1:

Thinking opposition opens a wide range (we'll say 30% of holdings) and we are on the button. We have 3 ways of exploiting this player:

1. 3-bet for value
2. 3-bet as a bluff
3. call and exploit postflop

We don't have many reads on this player but we can safely assume that like most players, he is going to fold his open to 3-bets an exploitably large amount.

So as an example within the example, lets say our hand is 98s. What is the optimal play in a vaccum?

Hard to say. Since we think our friend is going to fold a ton to 3-bets, it is highly likely that 3-betting is optimal, due to a high amount of preflop fold equity. However, 98s is a great hand postflop, and can continue on a very high %age of flops, so we are also certain that its profitable to coldcall with. So do we 3-bet or call? Probably 3-bet if we feel that given gameflow he's gonna fold 85% of time.

However, even if he folds a massive amount of the time, the best play for our entire range is to call.

In this situation our ranges are subdivided as follows:

A = {QQ+ AK}. These are hands we'd be glad to stack off with, and should 3-bet for value and get it in.

B = {55-JJ, AJ-AQ, KQ, suited broadways, suited connectors, some 22-44}. These hands aren't comfortable stacking off and are certainly profitable to coldcall.

C = {22-44, gappers, offsuit aces/broadways}. These are hands that are slightly too weak/unplayable to call, and we elect to 3-bet these as bluffs/semibluffs.

D = {the rest}. Have almost no value and we fold.


We can play ranges A, B, and C profitably. So our duty, in order to maximize the amount we exploit our opponent, is to make A + B + C add up to the highest possible percentage. 'A' is a static value range. 'B' consists of all the hands we feel we can profitably call that aren't in range 'A'. 'C' consists of the widest possible percentage of remaining hands that we can 3-bet and get away with it, and are chosen from hands just below 'B' strength due to maximizing value when called.

By 'get away with it' I mean that since we're up against thinking opposition, we want to play as aggressively as we can whilst avoiding exploitation at all costs. If villain wizens up and starts 4-bet bluffing us, thats very bad, and we are no longer exploiting him without readjusting which takes time and causes us to make mistakes in the transition.



Example 2:

Seat 1: AmPHisbaenA ($414.25 in chips)
Seat 2: gl79 ($402.60 in chips)
Seat 3: Tnx4urMoney ($456.10 in chips)
Seat 4: Kodack ($186 in chips)
Seat 5: 69MadMike69 ($53.70 in chips)
Seat 6: jhndh541 ($106.05 in chips)
Seat 7: Renton555 ($524.60 in chips)
Seat 8: jfager007 ($394 in chips)
Seat 9: whaaatever ($253 in chips)
gl79: posts small blind $2
Tnx4urMoney: posts big blind $4

*** HOLE CARDS ***
Dealt to Renton555 [9d 9c]

Kodack: folds
69MadMike69: folds
jhndh541: folds
Renton555: raises $8 to $12
jfager007: folds
whaaatever: calls $12
AmPHisbaenA: folds
gl79: folds
Tnx4urMoney: folds

*** FLOP *** [Ac 8s Jd]

Renton555: checks
whaaatever: bets $24
Renton555: folds

In this hand, betting the flop is absolutely certainly profitable, as this flop bitchslaps our range and he has to fold the vast majority of his. Betting may even be best. However, checking is profitable with 99, since he likely checks down worse pairs.

Without going too deep into this, let me create the subranges.

A = {AJ, A8, AA, JJ, 88, AK, AQ, T9} Hands we bet and continue to a raise.

B = {A2-AT, QQ-KK, Jx} Hands we check call for pot control and deception.

C = {77, 99, TT, 87ish} Hands we check fold for showdown value.

D = {air} Hands we bet as a bluff.

Even though betting 99 is profitable and maybe best, we prefer to bet all our air and try to check down 99, and hence have a less exploitable cbet.


Extrapolating further:

Say we bet ranges A and D and get raised. Then we have a whole new set of subranges.

A = {AJ, sets} Our nut range, we 3-bet all in or call and get it in on turns, depending on what we feel is most profitable.

B = {AK, AQ, A8, T9} We call and reevaluate.

C = {air like KcQc} We 3-bet as a bluff and shove turns we improve.

D = {rest of air} We fold.

It goes on and on.


The Renton theorem is something I think good players think about a ton. I've never seen anything like this quantified very clearly, and only recently started seeing it this clearly myself. Hopefully this isn't totally redundant info to you guys.

gl

So if I understand this correctly, you're saying that against "thinking" opponents, we should play our garbage hands the same as our monsters in order to gain more value our big hands?

your "subdivided ranges" appear to me to be just the difference between when you are merging and when you are polarizing your range.

i dont care if it was samo, i've said a lot of dumb things in the past, but i am pretty sure of one thing.... by excluding certain hands specifically from my 3betting range it does a number of things:

1. allows villain to get a better read on how i think and how i play
2. makes it easier to put me on a hand postflop, i guess i just said this, but actually the more hands you include in your 3bet range, the more difficult it is for villain to play against u if he decides to play back at all or more specifically call preflop.
3. i dunno, this is all dependent on the range of hands we estimate villain to be flatting 3bets or folding/possibly 4betting us with anyways. to say "never" is a sin in poker, and to never 3bet jqs, especially in a bvsb scenario seems straight retarded to me if you understand anything about your opponent.

the dynamics at the time might have suggested that it was bad timing to 3bet that particular hand and given that it would have been more profitable to call, then u have an arguemtn for a specific situation, but to say always, or never ... its just ignorant.

as far as renton theorem or whatever, i think u r close to getting it, spend some time thinking about why you came to these conclusions ... specifically considering random distribution of cards (we are all dealt roughly the same amount of good and bad hands over the long run). so like, if you can force a fold out of someone where u have like 30% equity and they had 70 to win the pot, like you 5bet bluff someone w/ A5s and they fold TT or whatever.... you are gaining a ton in that sense. this is part of the reason you want your pure bluffs/semi bluffs and your monsters to have similar lines. to blur your opponents perception of your range, and make it as difficult as possible for him to play you correctly.

--my drunken rambling 2 cents.

I don't see why this is so complicated lol.

Originally Posted by spoonitnow

I don't see why this is so complicated lol.

It isn't but a lot of people will not get it to no fault of their own.

Originally Posted by Renton

The four ranges are determined by the resultant play that is optimal for the range as a whole.

Subranges A, B, C, and D are directly adjacent in terms of playability/strength (i.e. the bottom of 'A' borders with the top of 'B'). All of the hands in a given subrange should be played the same (barring randomizing your play), and this is how the range is defined.

Shouldn't you have more subranges, if you link them to playability?

The way it is, you suggest there's only 4 possible plays. But when we're OOP there are a lot more (c/f, c/c, c/r, b/f, b/c)
When we're a bit deeper, theres even more like c/r/f, c/r/c, b/c, b/shove)

Especially the difference between made hands and draws I don't see coming back into the subranges, and would expect to.
Let alone the 'strongness' of the draw. (i.e. a monster draw is still something else as a nut hand, as a real nut hand we should consider slowplaying from time to time). A monster draw is still something else than a weak draw, as a monster draw you sometimes want to c/r, while leading a weak draw. etc.

Originally Posted by IowaSkinsFan

Originally Posted by spoonitnow

I don't see why this is so complicated lol.

It isn't but a lot of people will not get it to no fault of their own.

This is probably true.

I think my comment was born more out of the AIM convo we had before he posted this here. He explained it and I was still waiting for him to tell me the idea because all of it was leading up to something else hehe.

bump

Forgive the ignorance, this is all something I've been trying to wrap my head around.

Is the general idea here to have as wide and balanced a range as possible for each of our actions? i.e. we bet a flop with our A/D hands and check with our B/C hands. This gives us a very wide range for each action (we're betting with garbage or nutty hands) and checking hands both fairly strong and fairly weak.

However, don't you have to sometimes check your As and Bet your Bs to balance your lines?

good post renton.

No longer a sticky? Wat?

Originally Posted by donnybaker

Forgive the ignorance, this is all something I've been trying to wrap my head around.

<snip>

However, don't you have to sometimes check your As and Bet your Bs to balance your lines?

If you're below 100NL you don't need to worry about balance. You make money off the lose passives who don't pay attention, let alone adjust. The "regs" are probably all tight and don't really adjust either.

Originally Posted by Marshall28

your "subdivided ranges" appear to me to be just the difference between when you are merging and when you are polarizing your range.

i dont care if it was samo, i've said a lot of dumb things in the past, but i am pretty sure of one thing.... by excluding certain hands specifically from my 3betting range it does a number of things:

1. allows villain to get a better read on how i think and how i play
2. makes it easier to put me on a hand postflop, i guess i just said this, but actually the more hands you include in your 3bet range, the more difficult it is for villain to play against u if he decides to play back at all or more specifically call preflop.
3. i dunno, this is all dependent on the range of hands we estimate villain to be flatting 3bets or folding/possibly 4betting us with anyways. to say "never" is a sin in poker, and to never 3bet jqs, especially in a bvsb scenario seems straight retarded to me if you understand anything about your opponent.

the dynamics at the time might have suggested that it was bad timing to 3bet that particular hand and given that it would have been more profitable to call, then u have an arguemtn for a specific situation, but to say always, or never ... its just ignorant.

as far as renton theorem or whatever, i think u r close to getting it, spend some time thinking about why you came to these conclusions ... specifically considering random distribution of cards (we are all dealt roughly the same amount of good and bad hands over the long run). so like, if you can force a fold out of someone where u have like 30% equity and they had 70 to win the pot, like you 5bet bluff someone w/ A5s and they fold TT or whatever.... you are gaining a ton in that sense. this is part of the reason you want your pure bluffs/semi bluffs and your monsters to have similar lines. to blur your opponents perception of your range, and make it as difficult as possible for him to play you correctly.

--my drunken rambling 2 cents.

Playing polar ranges doesn't necessarily make you easy to read postflop at all. It might allow them to weight out some nut combinations from your range, but if you have a bluff frequency that is in reasonable ratio with your value frequency, they are in just as tough of a spot as if you had a linear range.

Also everyone seems to take issue with the ABCD concept, saying that "you should not play all hands the same blahblablah." The theorem defines optimality. It doesn't say this is always how u have to play the hands. I threw in a (barring randomizing your play) in there somewhere. You can and should 3-bet TT/JJ a percentage of the time in position, but it should be a low one.

Originally Posted by minSim

Originally Posted by Renton

The four ranges are determined by the resultant play that is optimal for the range as a whole.

Subranges A, B, C, and D are directly adjacent in terms of playability/strength (i.e. the bottom of 'A' borders with the top of 'B'). All of the hands in a given subrange should be played the same (barring randomizing your play), and this is how the range is defined.

Shouldn't you have more subranges, if you link them to playability?

The way it is, you suggest there's only 4 possible plays. But when we're OOP there are a lot more (c/f, c/c, c/r, b/f, b/c)
When we're a bit deeper, theres even more like c/r/f, c/r/c, b/c, b/shove)

Especially the difference between made hands and draws I don't see coming back into the subranges, and would expect to.
Let alone the 'strongness' of the draw. (i.e. a monster draw is still something else as a nut hand, as a real nut hand we should consider slowplaying from time to time). A monster draw is still something else than a weak draw, as a monster draw you sometimes want to c/r, while leading a weak draw. etc.

I think having strong draws in group A and weak draws in group B works in most scenarios. Its really about thinking on step ahead. Once you are thinking two or more, then things become more complicated and that goes outside the scope of this.

Originally Posted by Renton

Hopefully this isn't totally redundant info to you guys.

Originally Posted by IowaSkinsFan

Originally Posted by spoonitnow

I don't see why this is so complicated lol.

It isn't but a lot of people will not get it to no fault of their own.

for me this has been very useful. Not too difficult to grasp once read carefully, but something i had never before seen clearly described.
Thanks.

Originally Posted by donnybaker

Forgive the ignorance, this is all something I've been trying to wrap my head around.

Is the general idea here to have as wide and balanced a range as possible for each of our actions? i.e. we bet a flop with our A/D hands and check with our B/C hands. This gives us a very wide range for each action (we're betting with garbage or nutty hands) and checking hands both fairly strong and fairly weak.

However, don't you have to sometimes check your As and Bet your Bs to balance your lines?

Yes to the last part, as i just mentioned in my last post.

The general idea is to make the maximum amount of money vs their range with your range, to avoid being bluffed off of medium strength hands, to get maximum value out of our value range, while retaining the maximum fold equity out of our bluff range.

Originally Posted by Renton

Originally Posted by Marshall28

your "subdivided ranges" appear to me to be just the difference between when you are merging and when you are polarizing your range.

i dont care if it was samo, i've said a lot of dumb things in the past, but i am pretty sure of one thing.... by excluding certain hands specifically from my 3betting range it does a number of things:

1. allows villain to get a better read on how i think and how i play
2. makes it easier to put me on a hand postflop, i guess i just said this, but actually the more hands you include in your 3bet range, the more difficult it is for villain to play against u if he decides to play back at all or more specifically call preflop.
3. i dunno, this is all dependent on the range of hands we estimate villain to be flatting 3bets or folding/possibly 4betting us with anyways. to say "never" is a sin in poker, and to never 3bet jqs, especially in a bvsb scenario seems straight retarded to me if you understand anything about your opponent.

the dynamics at the time might have suggested that it was bad timing to 3bet that particular hand and given that it would have been more profitable to call, then u have an arguemtn for a specific situation, but to say always, or never ... its just ignorant.

as far as renton theorem or whatever, i think u r close to getting it, spend some time thinking about why you came to these conclusions ... specifically considering random distribution of cards (we are all dealt roughly the same amount of good and bad hands over the long run). so like, if you can force a fold out of someone where u have like 30% equity and they had 70 to win the pot, like you 5bet bluff someone w/ A5s and they fold TT or whatever.... you are gaining a ton in that sense. this is part of the reason you want your pure bluffs/semi bluffs and your monsters to have similar lines. to blur your opponents perception of your range, and make it as difficult as possible for him to play you correctly.

--my drunken rambling 2 cents.

Playing polar ranges doesn't necessarily make you easy to read postflop at all. It might allow them to weight out some nut combinations from your range, but if you have a bluff frequency that is in reasonable ratio with your value frequency, they are in just as tough of a spot as if you had a linear range.

Also everyone seems to take issue with the ABCD concept, saying that "you should not play all hands the same blahblablah." The theorem defines optimality. It doesn't say this is always how u have to play the hands. I threw in a (barring randomizing your play) in there somewhere. You can and should 3-bet TT/JJ a percentage of the time in position, but it should be a low one.

its all just opponent dependent ... i think i responded too quickly and didnt sort out my thoughts clearly enough. obviously just having a polar range vs thinking opponents isnt going to always be good ... its probably going to be bad vs players better than you. its really best against weak imperceptive opponents who won't try to put you on a hand and just assume that what they are holding is no good when you jam all in repping a strong hand.

i 3bet TT and JJ 95% of the time in position ... it'd be silly for me not to .. ive sat at a table w/ you before, you play like 14/12 so yeah of course you should be 3betting these hands at a lower rate because you are missing postflop value or getting stacked if you decide to go w/ them preflop.

u asked for my comments im just telling you what i think. but i think the part i said about random card distribution is real important.

if TT and JJ are part of your nut range, then of course its good to 3-bet them.

I run 22/18ish at six max in general, in there are some players that i can for sure stack off pre with JJ/TT, and against them I do 3-bet those hands. Three betting JJ/TT in position without history is generally a weak play though.

Originally Posted by swiggidy

Originally Posted by donnybaker

Forgive the ignorance, this is all something I've been trying to wrap my head around.

<snip>

However, don't you have to sometimes check your As and Bet your Bs to balance your lines?

If you're below 100NL you don't need to worry about balance. You make money off the lose passives who don't pay attention, let alone adjust. The "regs" are probably all tight and don't really adjust either.

Poker is a game based deep down on optimal strategy, the sooner you can start optimizing your play against a wide variety of styles the better. A balanced 100nl player who acts on reads is lot stronger than a player who only exploits loose passives. The mathematically balanced player will be stronger by far by all metrics if he/she can adjust even slightly to opponent tendencies.

Originally Posted by daven

Originally Posted by Renton

Hopefully this isn't totally redundant info to you guys.

Originally Posted by IowaSkinsFan

Originally Posted by spoonitnow

I don't see why this is so complicated lol.

It isn't but a lot of people will not get it to no fault of their own.

for me this has been very useful. Not too difficult to grasp once read carefully, but something i had never before seen clearly described.
Thanks.

Same for me. Thanks.

Good post, should be saved in a digest/sticky for the future.

Originally Posted by vegascoop

Originally Posted by daven

for me this has been very useful. Not too difficult to grasp once read carefully, but something i had never before seen clearly described.
Thanks.

Same for me. Thanks.

+2

I was following most of your theorom - but lost the plot a bit here. Can you elaborate and explain this part please.

Extrapolating further:

Say we bet ranges A and D and get raised. Then we have a whole new set of subranges.

A = {AJ, sets} Our nut range, we 3-bet all in or call and get it in on turns, depending on what we feel is most profitable.

B = {AK, AQ, A8, T9} We call and reevaluate.

C = {air like KcQc} We 3-bet as a bluff and shove turns we improve.

D = {rest of air} We fold.

It goes on and on.

Also does this only apply to limit games?

Thank you.

Originally Posted by LuckySlevin

Also does this only apply to limit games?

The hand history in the original post was a NL hand, and the post is in the NL FR forum. I believe the post was intended for NLHE specifically. I don't play enough limit to know what cross-applications it has.

Originally Posted by LuckySlevin

I was following most of your theorom - but lost the plot a bit here. Can you elaborate and explain this part please.

Extrapolating further:

Say we bet ranges A and D and get raised. Then we have a whole new set of subranges.

A = {AJ, sets} Our nut range, we 3-bet all in or call and get it in on turns, depending on what we feel is most profitable.

B = {AK, AQ, A8, T9} We call and reevaluate.

C = {air like KcQc} We 3-bet as a bluff and shove turns we improve.

D = {rest of air} We fold.

It goes on and on.

Also does this only apply to limit games?

Thank you.

uhhh no limit.


What that means is that since we decided to bet ranges A and D (namely our strong one pair hands, our two pair and better, and our air), and our continuation bet gets raised, well then we have to re-evaluate the situation with a whole new set of subdivided ranges. We take original A and D ranges and re-subdivide them into a new A, B, C, and D.

Any chance we can get a few more hand histories analyzed in here? I hesitate to post any of my own hand histories, as I don't think I play many hands well enough to be used as a teaching instrument. I don't want to post up a hand that is screwed up on the flop or whatever and then we could only analyze the flop.

damn i dont get it, what is the principle your trying to show by breaking our range up?

I would've thought it would make more sense to break up our range for each action we take (bet/call/raise) in order to maximise EV?

In eg 1, what your trying to say is you can adjust your range for C depending on how often your opponent will fold basically?
And eg 2, your saying check 99 to balance the air range that you check on the flop?

I swear i read it twice and a half

Originally Posted by wakeup

damn i dont get it, what is the principle your trying to show by breaking our range up?

If we play our A range aggressively and our C/D range passively, even micro-donks will notice and exploit us. Renton's showing how to think about mixing up our play, keeping some poor hands in our check-raise the flop range, for example, to benefit from the strong line by (1) having opponents fold better hands and (2) by having opponents "look us up" more often when we check-raise with big hands.

I really find this theorem great!


Of course, i need to know more.

1) How does this apply to the turn and river? How do the subranges change depending on opponents actions and history on the later streets?

2) I noticed that this hand history is probably simpler to explain because of the fairly dry flop. What happens when you apply this to a very lubricated and coordinated flop (ie. sheets, 3-to-FD, 3-to-SD etc)?

3) In general, what stats do you absolutely need in your HUD to incorperate this theorem to its max value?

4) Lastly, what are the anti-theorems to this one?


Thanks Renton!

Originally Posted by Im_new

I really find this theorem great!


Of course, i need to know more.

1) How does this apply to the turn and river? How do the subranges change depending on opponents actions and history on the later streets?

2) I noticed that this hand history is probably simpler to explain because of the fairly dry flop. What happens when you apply this to a very lubricated and coordinated flop (ie. sheets, 3-to-FD, 3-to-SD etc)?

3) In general, what stats do you absolutely need in your HUD to incorperate this theorem to its max value?

4) Lastly, what are the anti-theorems to this one?


Thanks Renton!

wow, get a coach. no one is going to touch this with a 10 foot pole.

lol, im_new,

i wudnt even kno where to begin lol prob wudnt even kno how to finish

Originally Posted by nutsinho

Originally Posted by Im_new

I really find this theorem great!


Of course, i need to know more.

1) How does this apply to the turn and river? How do the subranges change depending on opponents actions and history on the later streets?

2) I noticed that this hand history is probably simpler to explain because of the fairly dry flop. What happens when you apply this to a very lubricated and coordinated flop (ie. sheets, 3-to-FD, 3-to-SD etc)?

3) In general, what stats do you absolutely need in your HUD to incorperate this theorem to its max value?

4) Lastly, what are the anti-theorems to this one?


Thanks Renton!

wow, get a coach. no one is going to touch this with a 10 foot pole.

haha, figured it was a bit out there. But hell, I asked anyway. If you don't have answers (which I wouldn't expect you to) can you at least start with your thoughts about it?


And who needs a coach when the answers are on the net somewhere?

Well, I always thought the original post was a bad explanation. Here's how I understand it:
Our range is as follows
|----check/fold-----|-----fold/bluff-----|------call------|----bet for value---|

you can swap the bluffing parts with the check/fold parts depending on the situation
for example, if it's limped to you in the big blind you'd rather raise 92o as a bluff than 45s because 45s is good enough to check and play post-flop

but if someone raised in front of you, a better hand to 3b with would be 45s than 92o because we'll flop a draw more often that we can semi-bluff with

Originally Posted by Im_new

I really find this theorem great!


Of course, i need to know more.

1) How does this apply to the turn and river? How do the subranges change depending on opponents actions and history on the later streets?

2) I noticed that this hand history is probably simpler to explain because of the fairly dry flop. What happens when you apply this to a very lubricated and coordinated flop (ie. sheets, 3-to-FD, 3-to-SD etc)?

3) In general, what stats do you absolutely need in your HUD to incorperate this theorem to its max value?

4) Lastly, what are the anti-theorems to this one?


Thanks Renton!

meh i will do my best but i've also been lubricated (wow this sounds wrong, i mean alcohols).

Turn and river, I don't really see the problem with this question. You just break down into new subranges. For instance, on an Axx 2 tone flop your A range (as a random not well thought out example) is Ax, two pairs and sets.

The turn completes the flush and does not pair the board.

Our new A range - Strong Ax (obv this is soooo villain depnendant this is just an example), two pairs, sets flushes (idk if this should be included because I'm extracting from the A range on the flop but it is certainly in our A range on the turn...)

B range - Some Ax maybe strong As depnding on villain and his nittiness/ aggressiveness. A player who bluffs a lot but will alos make nitty fold would make our B range wider here.

C range - weak Ax

D range - I can't really think of anything. I guess it's quite rare from a hand from A on the flop to go to D on the turn but I guess it could happen (4 to a flush / straight comes to mind.) Then do this for every single range (A-D) from the flop.

2 - Coordinated flops are obviously more tricky to deal with. The weighting of the ranges is again extremely difficult to work out. For example, a player who will raisea balanced range including a lot of draws is more tough to play than a player will call their draws. Against a player who will always call draws we can widen our A range since we are obviously getting value from worse.

A player who is going to raise with a good frequency is harder to play, since bet/fold will become a less profitable line. This forces us to widen our stacking off range (i guess this is the top of our A range) but our B range becomes a lot trickier since we're going to get raised a lot with worse, as well as the fact that it is often very tough to accurately analyse ranges in these spots. It's obviously very tough to give any sort of detailed theory about this without exaples but the opponent is obviously crucial in how we form the ranges.

3 - Oh god. ummmm, it's so hard to work this out using a hud since a lot of the info will either come from standard stats and your own reads. Fold to cbet, fold to 3bet, aggression factor, cbet, 3bet, etc. etc. are all useful but i think getting actual reads from hands played is much better, perfect information i think is the phrase dogishead used...(?) ie. huds give imperfect info since it is a collection of statistics over a given sample whereas when you see what they had at showdown you know exactly what they had and how they played.

4 - The beauty of this theorem is there is no obvious counter. It is just a simple way of thinking about your own range and your opponents range, and maximising profitability be it in the form of value, fold equity or whatever, as a result of that info, which (I think) is the way to play optimally.

This strategy is not one like " I always 3bet AA and never anything else" which is obviously easy to adjust to. It's dynamic and considers our opponents, so all you have to do now is work out your opponenets range to the best of your ability and then work out how to play perfectly against their range taking into account their perception of your range. easy.

im going to throw this out there: im drunk. also disregard all of iopq's posts on ftr.

Originally Posted by nutsinho

im going to throw this out there: im drunk. also disregard all of iopq's posts on ftr.

I am also drunk. And I am the new moderator of this here forum. Off to a good start imo

i mean ive pretty much disagreed with every piece of content iopq has ever supplied until the last sentence of his post in this thread which is pretty obvious. lol at dissing the ABCD theorem and explaining it horribly and also lol at 92o being better to raise up vs a bunch of limpers than 45s.

he has more posts than you, so obv iopq>nutsinho

using this theory, however, would mean rilla pwns everyone but Fnord

I read this originally the week Renton first posted it and was clueless. But now that I have been around FTR, studied, and learned and its like a slap in the face on its clarity and brilliance.

Your explanation of how to play C hands is something I was just recently starting to figure out from watching Spenda, Massimo, ISK's videos.. and here it is in black and white.

Thanks again, man for giving us this gem.

O

Originally Posted by Outlaw

I read this originally the week Renton first posted it and was clueless. But now that I have been around FTR, studied, and learned and its like a slap in the face on its clarity and brilliance.

Your explanation of how to play C hands is something I was just recently starting to figure out from watching Spenda, Massimo, ISK's videos.. and here it is in black and white.

Thanks again, man for giving us this gem.

O

Haha this. I just decided to crack open the FR forum and I remember seeing this post before when I first started spamming on this site. I also remember thinking, "lol wat are ranges?" I read some, learned some, donked some, came back, and understand this a WHOLE lot more.

This theorem deserves to be bumped for all to read.

As was said before, it makes a lot of sense now that I have more experience and have re-read it.

I suggest all who have not read this post to read it. It has literally given me a better understanding of poker as a whole (even though I still suck).

Ok, there's something about this that's been bothering me for a while. While I think the practical conclusions of this idea are good, some of the theory doesn't really make sense to me. Since this has been bumped anyway I'll take this opportunity to be controversial and get massively yelled at by everyone:

Originally Posted by Renton

Not only do you want to make the best play with THIS hand, THIS time, but you want to make the most money with your range, EVERY time

So what you seem to be saying is that you should make a certain play with a certain hand in order to be able to make more money with a different hand in the same spot. What I'm going to ask is: When do you make this money?

You obviously don't make it at that moment with that hand, that's kind of the whole point.

You don't make it in some parallel universe where you have a different hand because:
A. I don't really care how much money parallel-universe me has.
B. What I do in this universe doesn't effect what hand range my parallel-universe opponent puts parallel-universe me on.

Therefore the only time I can make this money is in future hands.

So lets assume for the sake of argument that you do the unbalanced thing and cbet 99 and somehow your opponent gets the idea that you're c-betting your entire range. He adjusts accordingly. Surely it's now possible for you to readjust to this? If your opponent thinks you are c-betting everything then surely the way he chooses to play as a result of this will also be exploitable.

I guess what I'm saying is that if you do something once that is profitable this time but would be exploitable if you kept doing it then that's probably not a bad thing. Your opponent will adjust and you can go back to doing the "balanced" thing and make more money from him.

The c-betting example is a pretty complicated one that is quite hard to analyse because of multiple streets of subsequent action, so I'm going to look at a couple of simpler ones where what I see as this same misconception about doing things "for your range" is bandied around.

Firstly, light 3-betting. People will often say things along the lines of "yeah, light 3betting's great because it means you get paid off on your big hands" ie. another way of saying that it's good for your range.

Again I'll hypothesise that 3betting 76s can't increase the amount of money you would have won if you'd had aces. So if we make the assumption that you're not 3betting 76s because it's profitable in isolation, you must be doing it to force your opponent to adjust such that you make more money in future on your big hands. The question I would ask though, is why would he want to adjust? If you're losing money 3-betting 76s without him adjusting and since he hasn't adjusted you're making the same amount from the rest of your range, he's now making more money than he had been without having to do anything. Of course in reality it probably is profitable to 3bet 76s in isolation, but you should understand that the reason you're doing this is to make money NOW. In all likelihood your opponent will adjust in such a way that he is actually less exploitable. It is possible that he'll over-adjust and start paying off your monsters with nothing, but in general, your exploitation is not going to make him more exploitable.

As a second example I'm going to consider a river situation in which there are two players, each with a pot-sized bet behind on the river. Player A's range is the nuts 50% of the time and air the other 50%. Player B's range is entirely bluff catchers. Both players know this.

So what is the most balanced thing for player A to do? Assuming that if he bets he shoves, then he should obviously push with all his nut hands. To balance this he should push with half his bluffs so that it makes no difference to him how often B calls. (Think about this for a few minutes, it does add up.) So if A does this then there is nothing B can do to exploit him.

Similarly B's most balanced play is to call 50% of the time. If he does this it doesn't matter how much A bluffs, he always makes the same amount. If both players are doing this then the system is dynamically stable, since neither player can make more money by changing how much they bet.

However, just because these would be the most balanced plays to make, doesn't mean they'd be the best ones. In fact doing this makes it impossible to exploit any mistakes of your opponent. Playing with perfect balance means that no matter how exploitable your opponent's decisions are, you only make as much money as you would if he were also playing perfectly balanced poker.

If player B is calling less than 50% of the time then the most profitable course of action is actually to bluff always. At least until he readjusts. Then when he starts calling more than 50% you should never bluff. If two players are constantly trying to readjust and exploit one another, and they are both fairly competent, then over a period it will appear as if they are playing in a balanced way, when in fact they are always trying to make the most profitable decision for that particular hand.

So I guess the main points I'm trying to make are:

1. Being "balanced" shouldn't be a goal in itself, but rather an inevitable conclusion of trying to make +EV plays (and i mean NowEV) on a hand by hand basis against competent players.

2. When you do something "for the sake of your range" you are actually doing it for one of two reasons:

2a Because making the less balanced play would actually be less profitable in this particular hand with these particular cards (often because it would turn your hand face-up.)

2b In order to make your opponent more exploitable in future.

3. For 2.b to be the case your decision has to be either a case of:
3a. Not exploiting a mistake he makes regularly for a small edge, when it will give you a bigger edge if he keeps making it.

(As an eg. think of a player who could be 3-bet with atc profitably. You don't want him to adjust so you don't 3bet him with atc, but only the ones with most EV vs his calling range and you call some hands that can also be played profitably in this way)

3.b Doing something that will tilt your opponent into adjusting badly (even though he doesn't need to) and make him more exploitable.

4. You should always know why you are really doing something (ie. 2a or 2b, profit now or profit later) and not just use the get-out "good for my range".

5. You shouldn't hunt me down and string me up for appearing to diss ABCD theorem, which I do mostly agree with.

@knap - let me just address the light 3b w/ 87s example.

We 3bet someone to exploit them when they don't call/reraise enough. Mostly when we 3b w/ 87s, everyone folds and we take down a nice pot. It pays for itself against someone who plays narrow calling/raising ranges against a 3b. And we play 87s to profit against QQ/JJ type hands on 265 boards or against AK on A87 boards.

We're not balancing, we're adding in "bluffs" to take advantage of all the times opponents will fold to what looks like an obvious show of strength. And we get massive "deception" profit on flops that look impossible for us to hit.

So the bluffs pay for themselves, if we do it correctly. It's only when opponents adjust that the bluffing, semi-bluffing or "light" 3b's become less profitable, possibly unprofitable. So we expand our bluff range until we're no longer "getting away with it," then counter the adjustment(s) when and if they occur. We stay profitable whenever we're an adjustment ahead.

All of the above assumes we're expecting profit in the present time, in this very universe, on these very tables we're playing right now.

@Rob
Yeah I know that:

Originally Posted by knaplek

Of course in reality it probably is profitable to 3bet 76s in isolation, but you should understand that the reason you're doing this is to make money NOW

The point I was trying to make was that a lot of people explain light 3-betting by saying that it makes more money out of your good hands/balancing your range when actually as you say it's about making profit immediately

Originally Posted by knaplek

@Rob
Yeah I know that:

Originally Posted by knaplek

Of course in reality it probably is profitable to 3bet 76s in isolation, but you should understand that the reason you're doing this is to make money NOW

The point I was trying to make was that a lot of people explain light 3-betting by saying that it makes more money out of your good hands/balancing your range when actually as you say it's about making profit immediately

They're both true - we profit now, and we profit later after they adjust.

Only if they adjust incorrectly. If they adjust reasonably well then the extra amount we win with our big hands is less than the lost opportunity to 3bet them light

this thread is excellent. most articles or books which talk of ranges speak exclusively of determining villians range and determining the appropriate line. taking the approach of determining our ranges and optimal lines for each THEN seeing into which range our actual hand fits has helped make both mine and villians ranges, and the better play seem far clearer on all streets. thanks renton!