When you bluff with A9, you'll often make a hand you beat fold (like A3s) since ace high with a nine kicker is often the best made hand. When you bluff with a hand like 98s when it's just 9 high, just about every hand you make fold would have beat you at showdown. Since you are often bluffing with A9 only to make worse hands fold, you're often "wasting" some of it's equity (or at least not utilizing it very effectively).

Thanks, Matt.

Is the concept here regarding the flop and turn, or would you say this also applies to the river?

It can apply to the river too. Like if you have to turn a made hand into a bluff I guess you could say you're wasting it's equity, because you're now no longer using the showdown value of the hand (so it really doesn't matter if your hand has 15% equity or 0% equity versus your opponent's checking range since you're going to bluff with it).

I guess that's what's throwing me for a loop with the idea. It seems to me you're saying this concept is a reason to prefer 89s. However, I'm not seeing that. I agree decisions may be more clear cut with 89s, but I'd rather have A9.

When the opponent has worse hands, the relative ev between checking and bluffing is reduced. The decision is less critical; the choice normally more difficult.

When we have the nut-low, the relative ev between checking and bluffing is larger. We can make a large mistake; the choice is simpler.

Having said that, I see each hand with these options (just with checking vs. bluffing):

A9: EV of checking - decent; EV of bluffing - good

89s: EV of checking - 0; EV of bluffing - good

Choosing to bluff with A9, I don't see that as wasting (or poorly using) the showdown equity. Albeit a small improvement, bluffing is simply the better choice (assuming it is). I'd say A9 is the better hand of the two.

Hoping this isn't nitpicking. Just want to make sure I'm not missing an important concept as I'd not heard of wasted equity before.

when you check with A9, villain will sometimes bluff, pushing you off the best hand. when that happens, the equity is wasted (the same is not true with the nut low). presumably you choose to turn it into bluff when you believe that will happen often enough, and when you believe villain's range is weak enough that a bluff will be profitable. so the the situation of having to throw away your showdown equity and bluff is a result of the alternative in which your equity is wasted because villain can bluff when you check. i'm not sure if that's what matthew meant, but it's one way to think about.

True. However, position isn't the concern (afaik). In the example, we're on the button.

good point. let me try one more time.

it's checked to you on the river holding A9 UI, and you think you are usually beat are sometimes are good, and that your opponent's range contains many hands that can't stand a large bet, but some that will call. now, what you would like in ideal world is for an angel to tell you "now is a time to check back," and you check back those times, and then bluff the others. but this is exactly what the case would be when you hold the nut low. except in that case the angel always tells you, "don't check back this time, you'll lose."

let's do some numbers and see if this reasoning holds up. let's say he has 10% hands you beat (which fold to any bet), 70% better hands that fold to your pot size bet of P, and 20% hands that call and win.

when you have your angel and check back the 10% of the time to win, then what's left over the other times is a 70:20 ratio of hands you beat to hands that beat you. so your bluff will be effective 7/9 of the time.

EV = .1*P + .9*((7/9)*P - (2/9)*P) = .6P

In the case with no angel where you always bluff we have:

EV = .8*P - .2P = .6P

so it looks like there is no difference. but since we're talking about GTO, your opponent will rebluff some % of the time, and when that happens with him holding those 10% of hands you beat, you would have rather checked back, since that locks up your win right there, whereas if he rebluffs and you fold it's "wasted equity." this argument would only apply when your pot size was not an allin bet, and when he holds some value c/raise hands ofc. if those assumptions don't hold then the two cases really do look the same.

i'm curious to hear matthew's thoughts on this. because that's a fairly subtle distinction which isn't worth a lot of money. but of course as he says in the book the hand is much more effective on the flop and turn, and this point only addresses its river advantage.

Hello,

I have encountered a problem on page 61 and would really like to clear this up. The book states: "we assume the SB 3bets 16% and calls 8% and the BB 3bets 14% and calls 20% of the time. Blind are 3betting the BTN open 27,8%.

0,278 = 0,16 + (0,84) (0,14)

Also BTN will be called 21,7% of the time. I do no understand this equation provided to calculate the frequency of BTN gettin called. It says:

0,217 = (0,08) (0,86) + (0,20) (0,74)

how do you get 0,86 and 0,74?
I know im missing something very obv, but I really want to understand the concepts.

Cheers

Someone already pointed it out earlier, and rather than 0.86 it should read 0.84. Let me know if that clarifies everything, and if it doesn't I'll try to help explain in more detail.

I know people are waiting for additional updates but there's been a slight delay for two reasons:

#1) I took an unexpected trip to Vegas.

#2) B3lly was doing an incredibly good job of finding little errors/typos so I traded him some coaching to make a list of all the mistakes he found. He did an amazing job with this and just sent me the list a few days ago. So it's going to take me a bit longer than expected to look over them all, but when I do I should have a much more extensive list.

If the opponent never bluffs, then whether you bet and make your opponent fold a worse hand or check and win at showdown doesn't matter. You showed this in your equations. But once your opponent starts check-raise bluffing, then now you win at a lower frequency (since you're bet-folding so you'll "effectively lose" to his bluffs) so the EV of the bet decreases. So yeah, as your opponent starts check-raise bluffing the EV of your checks decreases and that will cause your equations to change.

Though in your example I'd just say you're "turning a made hand into a bluff." (most people won't technically call ace high a made hand, but since it has showdown value and is a +EV check it pretty much is). Either way, you should still bluff it if EV to bet is greater than the EV to check since that's all that matters. It just showcases why A9 (with 10% equity if it checks back) is no different than two blank cards on the river since both will be bluffs which function exactly the same way, so it's reasonable to say the equity of A9 is wasted on the river in this spot since you're never utilizing it's showdown value.

Do you know whether there some kind of Adobe update process that will allow us to patch the ePUB file that we've already downloaded, or will we just have to download a new correction sheet?

Unfortunately I doubt there will be a patch that automatically updates anything. Hopefully most of the mistakes are pretty minor and it should be easy to look at the sheet if you get confused with anything.

Thanks for quick response Matt, I really like it how you help people in this thread
So now, 0,2192 = (0,08) (0,84) + (0,20) (0,76)

I get why 84% of the time we get called by the SB because he 3bets us 16% (ty for pointing out its 0,84 instead of 0,86 because if you want to learn concepts that you do not know I think every number matters). Out of the 76% of the time BB calls 20%. Did you get the 76% from the 16%(SB 3bets) + 8% (SB calls) = 24% and 1-0,24= 0,76 ?
The book says 0,74 but you said it is supposed to be 0,76 in your first post in this thread. Did I get that right?

Great book!

I really liked the sample hands at the end of the book. Would have been interesting to know how you view situations were we are not an oop pfr or an ip cold caller.

I guess you would suggest that we cbet a little bit more value hands on the flop since its so easy to just show down at the river? Are you usually trying to stay close to a 60% defend range if you are cold calling oop or do you call less since it is obviously harder to float oop?

Pg 302 Following a flop c/c by c/r the turn.

In this section you give the example of c/c flop with 88 on A84 mono board and c/r turn cards that make a lot of draws. Then you follow that up with saying we can balance that by c/r bluffs on turn such as flush draws, straight draws, and pairs with 5 outs. But that means we would have to c/c flop oop as pfr with no pair and no draw to be able to pick up those draws on the turn. Can you give me an example of hands w/ no pair no draw that would be profitable to play this way on this board? This is a spot that is difficult for me to figure out how to have a balanced range on the turn since I would have to c/c with np/nd hands to have a bluffing range on turn to balance out my value range. Also what would you do with said hands if you don't pick up any draws etc on the turn?

I'm pretty sure a mono board = all of one suit, so like 9h 6h 3h. Someone can correct me on this if I'm wrong, but I believe what you meant is a rainbow board.

I actually like check-calling hands like KQs and KJs quite a bit on an Ah 8s 4c. This allows us to have some hands which function well as bluffs on later streets. Also, if we check-call with KQ we keep our opponent's KJ, KT, and QJ type hands in his range, and these hands are unlikely to outdraw us (and if we both turn a pair and we have him outkicked, we can probably get additional value).

There's too many different turn or river cards to say what I'd do on each one, but hopefully that gives you an idea. All of the above hands can of course turn a pair, gutshot, or flush draw and can be used as bluffs when needed.

I'm probably going to do a lot more work on this in CardRunners videos this year, as it's something I've only recently (last year or so) gotten a lot better at. The problem is a lot of the coolest and most important spots (say button vs BB) involve very wide ranges which wouldn't have fit well into the book. In fact, I even did like 10 hand examples of button vs big blind spots, but they were such a mess that we ultimately decided not to include them. I think these spots I think are much easier to analyze with computer software in videos than they are in books.

I don't try to defend 60%+ when I cold call in the BB vs the button, but sometimes it happens. I believe the button should usually be able to profitably bet any two cards since he has the stronger range and position, so if he bets 50% of the pot you won't see me try to defend 67%+ on most board textures usually (but again, sometimes I will).

Sounds like you have it right. All I'm trying to do is figure out how often the button open is called by one or both positions, so I'm figuring out how often the SB folds (whether it be 74% or 76%) and multiplying that by how often the button calls.

Oops yes I ment rainbow board. I was also thinking about hands like KQ, KJ hands but once we c/c the flop and our opponent bets after checking to him on the turn, then he is going to have the more polorized range (as hes likely to check back marginal hands) and we'll have the condensed range. Vs a polorized range wouldn't it be better to c/c KQ, KJ hands as we could likely still have the best hand? Plus if we bink our draw on river is one of those hidden draws u talked about. Thats why im having a hard time coming up with a range to c/r bluff with. C/c a hand with no SD value seems like a hand we would just bet flop and barrel with or c/f flop with? Maybe im way off though.

You're not way off. It's hard to tell, but sometimes you have to really go out of your way to bluff in a spot even if another line is good too (if you're trying to stay balanced).

An easier example might just be turning a made hand into a bluff on the river. Checking will be +EV (often quite ++EV in certain spots), but sometimes you need to bluff with it anyways since you don't have other hands to bluff with.

In reality the turn situation you're talking about likely uses a pretty mixed strategy with a lot of the draws and pairs you're mentioning. So it's not something I'm very passionate about either way.

Understood. Thanks for the help.

Hi Matthew, loving the book! On my second read now.

On page 331 you write:
I was reading this passage and I was like, yes Matthew I know I know but how can the advanced players know that? How could they possibly have obtained such knowledge? How? I need to know!

But then thank God I saw a footnote, and in the footnote it explains that it was David Sklansky that taught the advanced players the concept, and he did so 35 years ago, and he explained it in detail.

Good job on also including footnotes explaining that David Sklansky coined the terms semi-bluff and implied odds. It would have been a shame to leave that information out.

hi
can someone explain to me this for the preflop unexploitation.
we open 15% utg and a player 3bet us from CO,so we 4bet bluffs+values,il shove and we call with our value range.
but if we are in the first round at the table and the vilain is in fact a nit only 3betting AA but folding everything else (no calls)but we dont know that, arent we crushed here.thanks

The pre-flop ranges aren't unexploitable and no one knows what the actual game theoretically optimal ranges are.

Also, if you play game theoretically optimally and your opponent does not, every hand in your optimal range will not be +EV against the opponent. Rather, you will overall with money in the long run with your range against his range. For example, if your opponent never folds you'll lose money with your bulffs, but overall win money as he'll be calling with too weak of hands when you're value betting.

I have no idea what level you're on here, but I laughed anyway.