• Bronze
Joined: 16.06.2011
Hi everyone,

Boomer and I have a little "conversation" about balancing, and I'd like to continue it here. Its not convenient to write long comments in video posts, and I think its worth to see and get other peoples involved to it, so I'd like to see your opinions and arguments as well.

The starting point is the following thought experiment :

We are on the flop before any bet happens, I (the villain) have the initiative IP and Boomer (the hero) is OOP. The flop is 222 and there are two different cases

case #1:

- Boomer donks out

case #2:

- I c-bet and Boomer x/r-s

In both cases, the pot is 9 bets big, and I have only one bet left,so I can fold, or call and go all-in . And in both cases

- Boomers range after he bet is : 6x AA, 3x KK, and 1 bluff hand which is J7o

- my range before I call is: 6x QQ and 3x JJ

Boomer says, that in case #1 when he donks I have 9:1 for calling so he has to bluff 10% of his range in order to be balanced, and thats why he has 9 value hand ( 6x AA and 3x KK) and one bluff hand (J7o), and because he bets 1 to 8 I should fold around bottom11-12% of my range, hence I fold one of the JJ-s and call with the rest. So in average I loose the 9 bets against his value range ,but in every tenth time I catch his bluff and then I win 10, resulting my EV at 0.

In case #2 he says that he should have the same bluff ratio, since my odds for calling are the same (9:1), however I should fold more,because now he bets 2 to 8.

My question is:

Why should I fold more ? If he makes the x/r with a tighter range thats ok, but compared to case#1, he has the same range, he bluffs the same amount, I have to call the same amount, and my payoff is the same. Nothing changes from my side, I have the same equity and the same risk/reward ratio. If I was able to catch his bluff 1 out of 10 in case#1, I should be able to do this again, and if this is so then my EV should be at least 0 again.

Boomer says that if I do so, Im overcalling him thus walking into his value range, but I dont really see how could I do that regarding the things I mentioned above. Nay I think he is the one who might be overbluffing,as his risk/reward ratio is worse in case#2 compared to case#1 (8:2 vs 8:1).

Im gonna just quote the relevant comments ( I hope boomer doesnt mind it):

Boomer2k10, 28 Mar 13 03:48

You're talking about the EV of one bet, not of the street I gain extra because you've now put 2 bets in with the worst hand on this street and not 1 When we think about the range we should be bet/folding we don't just bet and then suddently make a decision it's based on the mathematics of the hands we want to put 2 bets in with. In the example you've given you're now putting 2 bets in to see showdown and not one where you're a 90% dog. Yes the individal decision you have to make on the river is the same because you're treating is as a 1-bet problem. In your eyes facing a x/r is exactly the same as facing a donk (I'm getting 9-1) when in fact it's a totally different animal because the maths of the street play out very differently.

kavboj84, 28 Mar 13 13:14

Which two bets are these ?
A call costs only one bet and this is the only time when I put money in the pot. So how is this gonna be two ? I dont understand..

Boomer2k10, 29 Mar 13 14:48

So what is your original bet on the river, in order to get x/r'd, if not a cost to you? What you are saying is that your bet/calling range on the river (In a 6BB pot) is the same as the range you'd call a single bet with (In a 9BB pot).

kavboj84, 29 Mar 13 19:00

What river are you talking about ? I go all in on the flop with my last bet. And yeah..I think its a hilarious attempt to take previous bets into consideration to defend your argument. In which article have you seen that previous bets were taken into account when catching a bluff ? Should I add then preflop bets to the costs as well ? Cause without them theres no x/r on the flop ?

Boomer2k10, 30 Mar 13 11:44

I'm using the river as an example becasue it's hyper rare to go all in on the flop so I misspoke Whatever street you are talking about you have to take that entrie street into account in order to balance your range, not just the final bet you're calling otherwise by your logic it doesn't matter how many bets do in on 1 street as long as you balance the final bet. I am not talking about previous streets I am talking about the current one. This is not a 1-bet decision, it's a street decision Your goal is to make me indifferent to bluffing, I need a x/r bluff to suceed 23% of the time to breakeven, so fold 23% of the time, ergo bluff EV neutral. My 10% range also makes you indifferent to calling down becasue you're getting 9-1 and will win 10% of the time with a bluff-catcher. In logical terms, how can a range which calls over twice as much as it "should", by your own fold equity laws, be good against a range which is 90% value? How can a bet/call range in a 6BB pot be the same at a call of a single bet in a 9BB pot? When the "bluffer" is risking more why should we call with the same range as when he's only risking half as much in a bigger pot? After 12 back and forth's however I am not going to go on with this: If you want an explanation as to why we construct ranges based on our opponent's payoff/bluffing odds I recommend reading The Intelligent Poker Player by Phil Newall (Specifically the chapter on Game Theory, Page 390 onwards)

kavboj84, 30 Mar 13 14:31

If I have to take two bets into account by making that call(so the entire street) that means I have to consider this when risking the very first bet before the x/r. This is due to the fact that you cant take back money from the pot, if that bet is in it is lost anyway even if I bet/fold. So as I understand practically my c-bet range (as well as my c-bet/3bet/fold and my c-bet/3bet/call) should not only be balanced against your calling range but all your possible ranges on the entire street up to your x/r/caping range. Now this is the most weird thing I ever heard from you. I haven never seen any calculation following this logic from you in any of your videos that I have seen, and you are not following it even in your previous post, because you say that my odds are 9:1, tho you should say that my odds are 9:2 cause you should count two bets for the bluffcatch. You doesnt even seem to be consequent with yourself. And I have not read P.N-s book,but I would be seriously surprised if he claimed anything like this. Altough everything could be possible until there is a clear proof, so I dont say that it isnt so its just very unlikely based on what I have read about poker.
• 79 replies
• Bronze
Joined: 22.09.2010
Taken from page 390 of PN's book

"This is exactly like the previous mixed strategy equilibrium where players change their strategies when their opponent’s payoff changes."

So I'm afraid you're wrong on what PN says

Pretty much all my combonator calculations in my videos are based on this:

Here are the actions on the river (And I'm calling it the river becasue I'm assuming no cards are going to come to make this as easy as possible):

You: Bet/Fold or Bet/Call
Me: X/R

When you bet I am getting 7-2 on a x/r and offering you 9-1 to call. There is nothing untoward about that.

Assuming the pot is now 2BB bigger so I can donk giving you the same odds, I am now getting 8-1 on my bluffing and giving you 9-1 to call.

So the distribution between value bets and bluffs in my hand doesn't change. You're getting 9-1 to call so I bluff with 10% of my range in both cases.

However my cost of bluffing has gone up considerably.

In the first example I am getting 8-1 on my bluff so you can only fold 11% of your range otherwise I exploit you by default, we both seem to be agreed on that

In the 2nd example I'm getting 7-2 on a bluff so I need you to fold 22% of the time. If you fold more than this the bluff exploits you, if you fold less than this you are paying 2BB on this street in a 10BB pot where you're going to lose 90% of the time.

The problem is you are treating the final street as 2 seperate actions when they aren't:

No you can't get your money back when you have a decision to make on the river when I x/r but that's also called putting good money in chasing bad.

If I have to risk more to bluff, you therefore are able to fold more of your range, that is basic balance play.
• Bronze
Joined: 15.06.2009
Note:I haven't read Boomers post above - or the earlier conversation.

Given the premises, the way you formulate them, the situations are identical.

The pot itself lies there in the middle even if both you and Boomer suffer a blackout and wake up 20 years later wondering how on earth the money got in the middle. All you recall is how to play good poker and that there is one bet to call. The odds against Boomer bluffing is 9:1 even if the pot is donated from the casino.

Well, those were the premises as you gave them. Identical situations.

Edit: Now I have read Boomers post. Nothing changes logically if the ranges are intact.

/Johan =
• Bronze
Joined: 22.09.2010
Originally posted by YohanN7
Edit: Now I have read Boomers post. Nothing changes logically if the ranges are intact.

/Johan =
Except you are trying to analyse half a street when you're analysing the x/r'ing hand.

You are saying you will bet/call (i.e. put 2BB in) almost 90% of your betting range on the river in a pot that's 6BB on the river vs someone who has 90% equity vs you.
• Bronze
Joined: 15.06.2009
Originally posted by Boomer2k10
Originally posted by YohanN7
Edit: Now I have read Boomers post. Nothing changes logically if the ranges are intact.

/Johan =
Except you are trying to analyse half a street when you're analysing the x/r'ing hand.

You are saying you will bet/call (i.e. put 2BB in) almost 90% of your betting range on the river in a pot that's 6BB on the river vs someone who has 90% equity vs you.
Question: Are the given premises in kavboys op the same as the ones you use?

/Johan
• Bronze
Joined: 22.09.2010
Originally posted by YohanN7
Originally posted by Boomer2k10
Originally posted by YohanN7
Edit: Now I have read Boomers post. Nothing changes logically if the ranges are intact.

/Johan =
Except you are trying to analyse half a street when you're analysing the x/r'ing hand.

You are saying you will bet/call (i.e. put 2BB in) almost 90% of your betting range on the river in a pot that's 6BB on the river vs someone who has 90% equity vs you.
Question: Are the given premises in kavboys op the same as the ones you use?

/Johan
The problem, I believe, we are having is that kav is looking at this solely from the final decision he has on the river

I'm getting 9-1 so I call w/ my 11% range

Which is fine when facing a donk bet

However when facing a x/r, yes you are still getting 9-1 but the action has been totally different on the river and you don't start analysing river ranges in the middle of a street figuring out how you should balance because you're ignoring the fact you've already put in 1 bet with your range and the x/r'er is getting a worse price to bluff so you can naturally fold more of your range.

In the examply kav has given he is saying he would bet/call the same range in a 6BB pot he would call a donk bet on the river, in a 9BB pot, with because for the final call he has to make he's getting 9-1.

I also believe there's a slight disagreement on why we use the odds our opponent is getting to decide our range tendencies and not the odds we ourselves are getting.

This is a very sticky point about GTO/Nash/Balance style play because it goes contrary to how most people have been taught to play poker and feels very uncomfortable (for 1 you feel like a calling station)

The whole point of balanced play is to make your opponent indifferent to bluffing or calling you.

That means when facing a potential bluff range you work out what % of your range your opponent needs to breakeven on any bluff he makes and fold that and when deciding on a potential bluff range you work out what odds you're giving your opponent and bluff that %-age

In that case you are both playing a mixed balance strategy with no incentive to deviate. If you fold more than is optimal you lose to your opponent's bluffing range and if you call too much you're opponent's value range takes advantage.

This is easy enough for 1 street 1/2 bet capped poker but obviously gets a lot tougher when you go multi-street.

Now obviously there are superior exploitations. In fact in this case if Kav did bet/call 90% of his range here, the correct exploitative line would be to never x/r bluff, of course kav could then counter-react and start bet/folding more than in strictly optimal and you end up in the levelling game.
• Bronze
Joined: 15.06.2009
In the examply kav has given he is saying he would bet/call the same range in a 6BB pot he would call a donk bet on the river, in a 9BB pot, with because for the final call he has to make he's getting 9-1.
No. He says he'd call with the same frequency getting 9:1 beacuse your range is identical in the two cases. You explained that your ranges are, in fact, identical in the two cases. If you suggest he shouldn't value bet in the first place, then that would be another discussion, but as laid out, there is no difference whatsoever. In an EV calculation, the pot odds and the odds that you are bluffing are the only ingredients. These ingredients don't change (according to both you and kavboy) from scenario to scenario.

Supposing now that you are not allowed tweak the numbers (i.e. the ranges) 9:1, and 1 for a call, can you quantify your reasoning?

How much should he call when faced with a check-raise given that the odds against you bluffing is 9:1 and it costs 1 bet to call?

How much should he call when faced with a donk bet given that the odds against you bluffing is 9:1 and it costs 1 bet to call?

/Johan =
• Bronze
Joined: 22.09.2010
Originally posted by YohanN7
No. He says he'd call with the same frequency getting 9:1 beacuse your range is identical in the two cases. You explained that your ranges are, in fact, identical in the two cases. If you suggest he shouldn't value bet in the first place, then that would be another discussion, but as laid out, there is no difference whatsoever. In an EV calculation, the pot odds and the odds that you are bluffing are the only ingredients. These ingredients don't change (according to both you and kavboy) from scenario to scenario.
If it's his range that he has facing a x/r it MUST be his river betting range as well unless somehow online sites are allowed to delete hands from your betting range because your opponent has Check-Raised.

My ranges are identical becasue I'm presenting him 9-1.

His ranges need to change becasue my odds (i.e. my payoff) are different

You are both just completely ignoring the fact that you are betting and calling on the same street, and think that somehow you only have to put 1 bet in to call my 2 bet investment on the river, YOU ARE BET/CALLING this street, not just calling!

How much should he call when faced with a check-raise given that the odds against you bluffing is 9:1 and it costs 1 bet to call?
78%

I'm getting 7-2 on a x/r bluff so I need it to work 22% of the time in order to break even (0.22*7BB) - (0.78*2BB) = 0 ish

Ergo in order to make me indifferent to bluffing he should fold 22% of his river betting range

How much should he call when faced with a donk bet given that the odds against you bluffing is 9:1 and it costs 1 bet to call?
89%

I'm getting 8-1 on a donk bet bluff so I need to work 11% of the time in order to break even (0.11*8)-(0.89*1) = 0 ish

Ergo in order to make me indifferent to bluffing he should fold 11% of the tiem when facing a donk bet
• Bronze
Joined: 15.06.2009
I get it!

From an EV perspective, it doesn't matter whether kav calls 0%, 11%, 22% or 100% of the time (as long as you don't start exploiting by bluffing more or less frequently).

But to keep you indifferent to bluffing, then he needs to call with the frequencies you give.

I have learnt something valuable here. Thank you.

/Johan = (10.5BB/100 last 10k at the micros where I belong)
• Black
Joined: 30.07.2008
Hi!

Ive been reading this and I dont really get what you are talking about....if I should watch vid then I should do it I guess else Im prolly just stupid and pls try to help me.

First... Player names you mention(kav being vilain and Boomer being oponent) are I guess not relavant.I assume two players dont have history...problem I have is that if it really is Boomer I doubt he often donks on 222 flop

....so I assume its just player1 and player2,unknwon to each other with no reads...

second...you say that in both cases pot is the same size?!? how is that?!? isnt it exactly 1SB bigger when he c/r

third... so whatever he does you are in 9SB?!? pot with just 1 SB left? how can that ever be a fold?!?

so pls...expain
• Bronze
Joined: 28.04.2010
owned by the Dawn muhahaha
• Bronze
Joined: 17.06.2010
The game theory section of my book The Math of Hold'em covers this, too. In the first example on page 206, you get check-raised by a player who would have been almost all-in by calling, and you get 41:1 odds. In that example, it was safe to fold the bottom 27% of your range because the raise was expensive to your opponent, even though the call is cheap to you.
• Bronze
Joined: 13.04.2010
I think I get it! its not about playing exploitive, pretty much the opposite. Cause there isnt a he knows i know-thinking in the hand when doing it this way. Cause if you knew he knew that you were gonna raise 1 of 10 hands cause hes getting 9-1 to call it then hes beating one hand out of ten of the hands you raise with then he should call in an ev kind of way. But the thinking here is, if i bet 1 and if he raises hes paying 2 in a pot of 7 and so he needs to be good 22% so i should fold 22%, cause theres no leveling...

But if he knew you were gonna raise 1 out of 10 hands in this spot cause he gets 9-1 for a call, then he should call with all hands except one, and if you knew that, then you shouldnt raise your bluff hand cause you need to be good 22% of the time, but he would only fold 10%, so you would only raise value hands... in an exploitive way

but imho he should check!

but... did I get it?
• Bronze
Joined: 15.06.2009
Do you notice how brittle the equilibrium is?

If Boomer check-raise bluffs just a tad too much, then the EV takes the upper hand and kav should be calling the check-raise more, not less. Balancing calling can only be the best choice when the bluffer already is balanced.

Back to where the bluffing on Boomers part is balanced. If kav wants to rock the boat he should call more (for free, EV is 0) expecting to see less bluffs later on - or call less (still for free, EV is 0) expecting to see more bluffs later on. The meta game is on. Right?

• Priority 1: Go with EV. If Boomers bluffing frequency is slightly off, take immediate advantage of that
• Priority 2: If EV is independent of calling frequency, keep unexploitable by calling with the right frequencies (which differ according to Boomer last post when he donks and when he check-raises)
• Priority 3: If you actually want a levelling war, call more or less. It is initially free.

Mathematically we are looking at an unstable equilibrium. If either player deviates, the other could deviate too to gain a profit.

@Boomer: Wishlist. Please make something on rebluffing, math + Combonator example (or live) with balancing in mind all the way.

/Johan =
• Black
Joined: 30.07.2008
Originally posted by pzhon
The game theory section of my book The Math of Hold'em covers this, too. In the first example on page 206, you get check-raised by a player who would have been almost all-in by calling, and you get 41:1 odds. In that example, it was safe to fold the bottom 27% of your range because the raise was expensive to your opponent, even though the call is cheap to you.
Woooot?!?!?

how can 41:1 ever be a fold on the flop. Almost any card any combo will have that 2,5% on the flop.Or... other words...if you fold 27% of your range for 1 SB getting 1:41 that is extremly exploitable and now Im prolly playing 100% of my hands vs u like a maniac and be a huge winner.
• Bronze
Joined: 16.06.2011
Originally posted by Dawnfall26
Originally posted by pzhon
The game theory section of my book The Math of Hold'em covers this, too. In the first example on page 206, you get check-raised by a player who would have been almost all-in by calling, and you get 41:1 odds. In that example, it was safe to fold the bottom 27% of your range because the raise was expensive to your opponent, even though the call is cheap to you.
Woooot?!?!?

how can 41:1 ever be a fold on the flop. Almost any card any combo will have that 2,5% on the flop.Or... other words...if you fold 27% of your range for 1 SB getting 1:41 that is extremly exploitable and now Im prolly playing 100% of my hands vs u like a maniac and be a huge winner.
Be careful, youre gonna walk into his valuerange Anyway...joking aside, there is only one thing I dont understand. If Boomer takes my c-bet into account when calculating my costs, why doesnt he consider it when calculating his bluff frequency. He says the whole street counts, hence he pairs my bet/call range with his check/raise range, but when he calculates his bluffing ratio he takes only one bet (so half the steet) into consideration. If the my cbet matters as well, the he should count 9:2 instead of 9:1, otherwise my costs should be 1 bet instead of 2 IMO. If this is so, then he should bluff less.

The reason why Im adhering so stubbornly to this is that my picture about the GTO is conflicting with Boomers thoughts. What I think is that to a state of equilibrium at a given potsize belongs only exactly one pair of bluff-bluffcatcher frequency (HU ofc). What boomer says that implies that there is at least one bluff-frequency at a given potsize to which you can assing two different bluffcatcher frequencies.

For example if my line was bet/3bet instead of bet/call, and the pot would be 9 bets with his cap, he would have to bluff cap with the same frequency, cause my odds for calling is 9:1 again. On top of that, I should fold more since he invested now 4 bets. So it seems like he had the more fold equity against a balanced bet/3bet range than against a balanced bet/call range (tho a b/3b range is stronger, so I would think he has less fold equity in reality ), yet he can bluff with the same ratio. But to me this sounds extremely weird.
• Bronze
Joined: 16.06.2011
Originally posted by Dawnfall26
Hi!

Ive been reading this and I dont really get what you are talking about....if I should watch vid then I should do it I guess else Im prolly just stupid and pls try to help me.

First... Player names you mention(kav being vilain and Boomer being oponent) are I guess not relavant.I assume two players dont have history...problem I have is that if it really is Boomer I doubt he often donks on 222 flop

....so I assume its just player1 and player2,unknwon to each other with no reads...

second...you say that in both cases pot is the same size?!? how is that?!? isnt it exactly 1SB bigger when he c/r

third... so whatever he does you are in 9SB?!? pot with just 1 SB left? how can that ever be a fold?!?

so pls...expain
This is a thought experiment for understanding the rules of balancing, and has nothing to do with IRL situations, so the circumstances are thereby artificially set. You probably spent too much time on hand judging . You could say that Charlie Brown plays against Yogi Bear, there is more dead money in the pot in the firs case, and Charlie Brown has spent some part of his stack on a lollipop,so he started shortstacked and has only one bet left. The who-s and how-s are just irrelevant, what matters is the situation given.
• Black
Joined: 30.07.2008
problem 1 is the least important actually...

the biggest one is how can you fold getting 1:9 or 1:8 with anything on the flop and ending the hand?!? O.k. if you really have the shittiest possible combo I get it but I guess we are in this spot when 3betting preflop so we are mostly looking at decent hands which will always be at least 1overcard or some backdoor stuff...

...all Im saying is that I think its a really bad example of talking about balancing and I dont get kavbojs initial post at all no offense
• Bronze
Joined: 15.06.2009
I think it can be viewed this way. Your primary goal is to win money. Now, since Boomer has a well-tuned bluffing frequency, you can call or you can fold with the same EV. From that perspective it doesn't matter what you do. He has made you indifferent to calling (with bluff catchers) by bluffing with the right frequency.

Now, since the EV for any play is zero, there is a secondary goal to achieve. That goal is to keep Boomer indifferent to bluffing. He must not succeed with a donk bluff more than 1:8. Also, he must not succeed with a check-raise bluff more than 2:7.

To ward off both bluff types you need to be calling with frequencies 8 calls and 1 fold (donking) and 7 calls and 2 folds (check-raising) respectively. Then Boomer will break even on both types of bluffs in the long run. In other words, he will be indifferent to bluffing, meaning he has no incentive to bluff either more or less with any of the bluff types.

If you, on the other hand, respond to the check-raise with 8 calls and 1 fold, then Boomer can reduce his bluffing of this type (to, say, having 11 value hands and 1 bluff when check-raising instead of 9:1) and thereby exploit you.

But if you call with the 7:2 ratio in the check-raising scenario, there is no way Boomer can adjust to make money by bluffing more or less by check-raising.

But EV must go first, and EV is rarely exactly zero in practice as it is here.

/Johan =
• Bronze
Joined: 22.09.2010
Originally posted by Dawnfall26
problem 1 is the least important actually...

the biggest one is how can you fold getting 1:9 or 1:8 with anything on the flop and ending the hand?!? O.k. if you really have the shittiest possible combo I get it but I guess we are in this spot when 3betting preflop so we are mostly looking at decent hands which will always be at least 1overcard or some backdoor stuff...

...all Im saying is that I think its a really bad example of talking about balancing and I dont get kavbojs initial post at all no offense
Dawnfall

Assume he means all in on the river it makes things a lot easier