Hi Matthew, I finished reading, its a great book.

I would like you to give me an advice for balancing our range.

When a really bad card for our range falls, I have a hard time to construct a balanced range. (not perfectly but as possible as it can be)

For example, in HU match, we are in BB with 16% 3bet range, and V's 3bet call range is 30%. We 3bet to 8bb vs his 2bb open.

Flop comes the T98
my goal here is to jam about 50bb into 100bb pot with a balanced range on the river.

Since we 3bet to 8bb, pot growth rate is 2.32(16R^3=200).
So I am betting each street 0.57 pot size, which means 73% of our river bet has to be for value.
So we are betting on the turn and river with 73% frequency,
then 39% of our flop bets have to be for value. (0.73)^3

On the flop, say we have 192 combos, which means 75 combos of value(192*0.39).
Okay, I can come up with some combos to make it roughly around 75.
I believe thats a good start.

Turn is 3
Here, I can put some combos to have around 73% turn CB%, no problem.

River is J
This is a very bad card for our range although some our bluff combos got there.
This is where I feel uncomfortable to construct a range, I cannot say if shoving a set here is superior play than checking without further analysis, but even if we jam all the sets combos and even 7x, I think our value combo is so small, and now we have a lot of bluff catchers which will be XC or XF.

When the river is really bad, we just have to give up a lot of time, and give our opponent profitable bluffing spot? And is it okay for us to give him +EV bluff chance because he risked a lot of money to get this opportunity on the river?

If I misunderstood any concepts the above, please correct me.
I really appreciate your advice, thank you.

I'm confused about using the different equations for constructing river play. For example in the above post, if using a 57% sizing, in the book the example says to use (1.57)(1-x) - (.57)(x) = 0 where x = .73 ---- meaning 73% of our river bet range must be value.

However, what about using the x/(x+1) equation where betsize x = .57, giving us .57/1.57 = 36% of our range should be bluffs, 64% value.

Apologies if I am missing something easy, but when should I use each and what are the differences?

In a lot of your examples I noticed that you used a 60% defending percentage. Ed Miller from reading your book came up with a betting and calling percentage of 70% to be the usual percentage. I'm trying to find a good avg defending and betting percentage to use in practice. What percentage do you think would be a good avg percentage to use for practice in the average scenerio?

I play low stakes MTTs online. Would this book be of any help for me? Or is it just for cash games?

Its a good book for any nlh player.

The problem is you're trying to model an incredibly complex spot where the terms "value bet" and "bluff" don't really work very well. Kind of like how pre-flop those terms don't work very well.

On this flop, no hand has close to having 100% equity (like a "value bet" on the river would) and even some pretty awesome hands (say 88) are going to be either outdrawn pretty often or get a bad enough turn and/or river that they can't keep value betting even if they remain the best hand. Likewise, most of your "bluffs" are going to have a good chance to improve to the best hand.

It's pretty impossible to "balance" this spot in the sense of having X value bets and Y bluffs because those terms don't even work. Instead, you have to focus on emphasizing betting the right type of hands (hands with reasonably "robust" equity, whether they be strong or weak) and making sure your overall betting range doesn't get too weak or strong in the process.

Honestly the best place to start here is to make sure you can defend your checks reasonably aggressively on this flop. Since you are playing HU you may not 3-bet QJo whereas your opponent should certainly call a 3-bet with those hands. So you may have a very high flop checking % here to begin with.

Where did the X/(X+1) equation (I guess technically an "expression" for the math nits) come from? Is that somewhere in my book or someone else's (just want to know what formula you're using).

I hate guessing on this kind of stuff and it depends way too heavily what the positions and pre-flop action are.

CO vs BTN post-flop frequencies are going to be drastically different than BTN vs BB post-flop frequencies. Someone who defends their BB very aggressively probably will check-fold post-flop a lot more than someone who is folding very slightly +EV hands in the BB that are very hard to play post-flop.

To bet 70% of the time and defend 70% of your checks would require a very strong range relative to the opponent's I think. I don't think that'd be normal.

Game 1.
2 players have 20$ starting stack, each get one card with number from 1-100 (1 beats 2). Player 1=(SB) posts 0.5$ Player 2=(BB) posts 1$
SB can only raise to 2$ total or fold.
BB can only fold or go all in for 20$ total.
SB can only fold or call 18$.
What’s GTO strategy for both players?
BB should go all in with 1-50. SB risks 1.5$ to win 1.5$. Formula bet/(bet+pot) = 1.5/3 = 50%
SB should call with 1-27. SB should call with all numbers that have 45% equity (18:22 pot odds) and 27 is the last number that has 45% chances of winning against 1-50 shove.
SB should call after he opens 14% of time. SB can’t allow BB to bluff with anything. BB can bluff with anything if SB folds more than 86%.(fold equity formula (amount to steal) x Y + (Total pot when called x equity when called - amount at risk)(1-Y)).
SB should open raise to 2$ 100%. 14% = 27 100% = 193 SB has only cards with numbers from 1-100 so he opens all of them.

So, GTO strategies:
SB opens with 1-100 and calls with 1-27.
BB shoves with 1-50

Am I right???

If the turn is a blank, would you still use a descending betting structure?

Smaller relative to the size of the pot, right?

Forgive me as I am still not completely through your book, albeit making my way.

The X/(X+1) is coming from your book, pg 99, as well as (and I admit I am probably wrong here) other sources from my memory.

On pg 99 at the bottom it reads, "For example, suppose our opponent bets 50 percent of the pot. This means bluff rate should be 33.3 percent of the time." ---I took this to mean that our betting range should consist of 33.3 percent bluffs---

After reading your response and the page again, I am thinking that it means that the minimum bluff success rate should be 33.3% to make an "any two" bluff profitable for betsize = 0.5? (with the important part being villain folds > 66.7? , or basically just finding the reciprocal of the min. defending freq 1/(X+1)?)

I know this should be quite simple, but just for clarity, for a betsize X on the river, what should the correct ratio of value:bluffs be for our river betting range? I was under the impression that it should be 1:3 bluff:value for betsize X = 0.5 (using 0.5/1.5), and 1:2 for bluff:value for betsize X = 1, but now I am confused.

Thanks in advance for the explanation, really enjoying the book Matthew

> Cero dinero

I think the last example you gave is correct.

The game has reached a GTO point when no player can improve his results by changing strategy.

Its the pot odds you give the caller that dictates you Vbet / bluff ratio when you are the bettor.

So if you bet potsize, your offering the caller odds where he needs to beat you 33 % of the time to break even. Hence to be indiferent to wheter the caller he calls or fold when you are the bettor and bet potsize you should have 2/3 Vbet and 1/3 Bluff. ( Asuming his only option is to call or fold vs your bet )

On page 114 the equation,

(0.8)(x)+(0.2)(1-x)=0.389

which basically calculates what % of flop raising hands should be able to value bet the river.

Just out of curiosity we tried plugging in the equity of out bluffs as 0.4 and the equation gives the result of x as -0.0275

(0.8)(x)+(0.4)(1-x)=0.389
x=-0.0275

How is this figure negative, cause we still have value hands in out bluff raising range. I understand that raising 40% equity hands as bluffs is silly but why does the result still come negative?

I have had this same doubt for sometime but I finally figured it out thanks to someone playing much higher explaining the math to me.

So we are basically dealing with 2 equations pretty much and these help answer a lot of questions.

Example: CO bets $50 into $100 pot and BU calls.

2 equations.

1. The first one is the FE equation, I call this the CO equation. This is when CO tries to figure out before he bets how often he needs BU to fold so he can bluff ATC.

x(100)-(1-x)50=0
x=50/150
x=33.33%

Notice x=x/(x+1) is the same thing as 50/150 also the same as FE=B/(B+P) where P is pot before the CO bet and B is CO's bet size.

so then we also figure out that BU needs to defend 66.67%(100-33.33) of his range after the CO bets to prevent him from bluffing ATC which is same as 1/(1+x) in this case, 1/1.5=66.67%

So the CO equation tells us primarily what the BU needs to defend.

2. The second one I call BU equation( for lack of a better name), this is the one where after the CO has thrown in the bet, BU is trying to figure out what% of times he needs to win to make a call.

x(150)-(1-x)50=0
x=50/200
x=25%

So BU needs to win 25% of the times to make the call. This basically tells us what % of the hands in CO's betting range can be bluffs. So CO should have a 75/25 or 3:1 Value:Bluff ratio when betting half pot.

I made a shortcut for this too
=B/(P+2B)

So once again, CO's equation or FE equation tells us what % of BU's range BU needs to defend and BU's equation tells us what% of hands CO should have as bluffs in his overall betting range.

Hope this clears it all up. Use the appropriate equation depending on what you're trying to calculate, whether its what % of hands BU needs to defend or what % of hands CO needs to bluff.

Basically by plugging in 0.4% as bluffing hand's equity I expected the number of hands bluffed per value hand to go up and overall % of value hands as total hands being raised to go low(as you mention in that section). Just didn't expect it to become negative.

Thank you klondi and maheep for clearing things up a bit!

I just finished reading Ed Miller's book, "Pokers 1%" and I read most of "APPLICATIONS of NLHE". I'm confused though because Miller recommends c-betting the flop at about 70% of the time and in the examples from Matthew Janda's book, Janda is c-betting the flop an average of about 42% of the time. Which one is correct? I don't see how they both could be correct.

Thanks to everyone who helped out other people in the thread.

I have no idea. This is not the kind of stuff I'm particularly good at or have spent much time doing.

No one knows what the optimal frequencies are and how often you continuation bet will be depend a ton on each player's range and position.

Continuation betting 70% of the time may be fine in some button vs BB spots where you're in position or some spots where button opens and you 3-bet from the blinds. But in a CO vs BTN spot where you're CO I am guessing 70% CB is significantly too high.

If I had to guess if the CB frequencies from my book are too high or too low, I'd actually guess even 42% is too high for these spots.

Matt, I think you missed my question.

Matthew,

Could you take a look at my older post (#942) when you have some time?

Thanks

Could you explain this a little more? In the "example of balancing a range out of position on the flop" we are open checking 60% on a K hi flop. Why exactly do we need these 4 open checking ranges in practice? (instead of having a wider and easier to play betting range). And where do these ranges come from? E.g. how do we determine that TT is a value bet on the flop but KQ is a c/c?

I´ll keep this a short as possible, but it´s not gonna be easy…
First of all, I love the book. It really makes sense to me to view poker in this way.

Now to my actual question: How do we, in practice, go about creating ranges?

Let´s say UTG opens and BTN calls. I would go about it something like this:

BTN defense range vs. a bet
1. Figure out how many hands we need to defend (“easy”, since it is based on bet size).
2. Pick the “best” hands to defend with (equity right now, stable equity and all that good stuff…, no problem here)
3. Decide which hands we want to raise. Here I would start with looking at which hands I want “bluff” with (backdoors, gutshots…) and balance them with the proper amount of value hands. Since I know the ratio, this is also “easy”. Important here not to “empty” the calling range of all really strong hands.
4. Double check that the value raise and calling ranges have reasonable strength.

UTG´s bet- and check/call-ranges
Here is where it gets hard, but this is what I would like to do.
1. Choose value hands (Yes, I now value is a dirty word. I mean “fat equity”, or what ever…).
2. Balance the value hands with proper amount of bluffs (“easy”)
3. Select hands with which to check/call (the proper amount depends on bet size, “easy”)
4. Double check that I can defend enough of my checks (we can estimate what “enough” means). Adjust with moving hands from value range if necessary (also remove bluffs to keep balanced).

Now for my actual questions:
- Does this seem like a good way to approach this?
- How do we pick our value hands as the UTG? Do we look at how much equity our hand has vs. Villains defense range, and if so, how much equity do we need (guessing a bit under 50%)? Or do we just do what I do now: “Errrm, second pair is probably a value hand in this situation. Probably…”?

I think that you should decide your "value" hands first and then balance it with weaker hands - it should be faster at least. Otherwise you might decide your bluffs, than realize you dont have enough value hands...