Very very good post.

So I have the same criticism as ATsai- I don't really like the semantics separation between value/equity either. It is true that everything in the OP is correct the way it's defined. However, IMO basically everything boils down to this little snippet:

so yea like I said, everything in the OP is correct using the definitions presented, but they aren't the common definitions. Like 90%+ of posts on 2+2, books, videos, training sites, people at the table, etc. still call it a value bet if that happens. So... I feel like the quoted snippet above is kind of like arguing that there aren't any Indian reservations in the US, only Native American reservations. It's just not how most people use the term "value bet".

But yea other than the semantics disagreement I think this is a really well-written post.

I don't have time for a long reply now and I intend to get back to this, but in the meantime, let me just say, I think the crux of the issue with the definitions is this: if you want to eliminate the definition of "equity bet", then you need to re-define value betting and bluffing. How would you do so? (ATsai never actually said.) In post #14 I already discussed one issue with defining value bets and bluffs based on the result we hope to achieve from them, and I would contend (unless you can convince me otherwise) that "how most people use the term 'value bet'" suffers from the same problem, which is why I felt it would be better to make different definitions.

EDIT: This is also why it's taken me such a long time to respond to the posts about betting for information--because coming up with a definition that is consistent and clear while still mostly agreeing with people's intuition is very tough! That's part of the problem here--any definition of value betting or bluffing that agrees with people's intuition too much will be inconsistent or have other similar problems, I think.

Can you explain how combo betting fits into all of this?

Imo, definitions based on intent are much more useful because you must make in-game decisions based on intent. We also talk about hands on these forums based on intent. Your definitions, based on results, don't make sense to me, but I'm willing to concede that it may help others think about the game properly. I do worry, that it will make discussing hands on the forum more difficult because people will be using varying definitions.

Edit: Personally, I find it is more useful to think of the following:

Value Bet: Betting with the intent of being called by a worse hand.

Bluff: Betting with the intent of making your opponent fold a hand that you would like them to fold.

Combo Bet: Betting with the intent of being called by some of the worse hands in your opponents range, while also intending to fold out some hands that you would like them to fold.

Imo, these definitions are much simpler and encompass the vast majority of situations at these stakes.

Again, as I explained above, the problem with these definitions is twofold. First of all, it does not always make sense to evaluate a bet based on whether it did what you intended it to do. It could succeed for a reason you were not intending. Second of all, these definitions: a) do not encompass all situations where it is most +EV to bet (which I think you agree with?), and b) are not mutually exclusive (assuming you mean what I think you mean by a "worse hand"), so that it is possible, by your definitions, to be value betting and bluffing in the same spot against the same hand (not different parts of a range). For instance, by your definitions, you would have to classify every equity bet in my OP as both a value bet and a bluff.

Sorry for the double post, but can't edit. I should not have said "both a value bet and a bluff". Really, by those definitions, every equity bet in my OP should be classified as a bluff, which is inconsistent with what Aesah said earlier that equity bets should usually be classified as value bets. That's the problem with the intent-based definitions--if you actually use them as written, they lead you to conclusions you may not think should be true.

Sure your opponent may respond in a way you don't expect. For example, you make a value bet, but your opponent folds a worse hand. Imo, you can't really incorporate this into your decision making because it is unexpected.

I agree they do not encompass every +EV spot to bet. However, I don't think your definitions do either. However, I think going beyond our definitions is not prudent for 99% of live low stakes players.

My definition of value bet wasn't the best. It would be better to say, "Value Bet: Betting with the intent of being called by hands you want to be called by." This would change the combo bet definition slightly as well.

Betting vs. a range of only draws that have the correct odds to call you is really a semibluff. There are spots where you will never get a fold and are fine with that, but nonetheless you want a fold, which makes it a bluff. The more marginal spots that make this clearer. In these spots your opponent may fold draws that he has the correct odds on because you have redraws and dominating draws in your range. Those are the spots where you successfully semibluff the draw. This comes up much more often in PLO. This really is no different from when we have the OESFD and raise our opponents cbet. Even though we have the best hand, we often want a fold because our opponent has a large amount of equity in the hand. Once again, this would be a semibluff.

However, we must ensure we always think about our decision to bet in terms of ranges. When we make value bets we will Generally speaking we are value betting if we are happy when our opponent calls and we are bluffing if we are happy when our oppent folds.

I welcome discussion of these definitions, because even many top notch players use definitions which aren't entirely accurate, and I would like to refine them as much as possible. However, I stand by my opinion that intent-based definitions are much more useful when making decisions. Your definitions may be more useful in seeing where your EV comes from in a particular spot, but you can't really make in-game decisions based on results.

Edit: Typed this before seeing your latest response, so yea, I think we agree.

I also agree with Aesah as far as how the terms are commonly used, but it stems from definitions that aren't entirely accurate imo. That said, I don't think it leads to much in the way of confusion. Good players understand that you should bet vs a draw heavy range in a lot of spots. They also understand the mathematical reasons. Calling it something different doesn't change their understanding imo.

Here is where the OP's 4 reasons for betting get live NLHE players into a bunch of trouble...

2/5 NL: Hero opens $15 BTN with QQ, and mediocre reg in BB calls. Flop: A72r. BB checks. What should Hero do?

Well, a rookie live NLHE player who learned CallMeVernon's flawed definitions would bet $10 and say that he is betting to "Set Up Future Profits" where he might be able to triple barrel bluff Villain off weak Ax and also be "betting for equity" against 7x and gutshots. Puke...

Alternatively, a rookie live NLHE player who learned the value/bluff framework would recognize that QQ IN POSITION as PFR on A72r flop is a bad spot for value betting against worse hands and a bad spot for bluffing hands that we want to fold. So, he would quickly learn the concept of WA/WB with the fundentals of value/bluff reasons for betting as a foundation while the rookie who learned CallMeVernon's flawed definitions would keep spewing with QQ HU IN POSITION cbets on A72r.

This was literally laugh-inducing. In no way does this follow from the 4-definition framework. A player who learned the 4 definitions and misapplies them this way would misapply any framework because he is just bad.

For a similar example of what a "rookie" can do wrong when you follow a 2-definition framework, see parts of earlier posts that you ignored.

Everything I have to say to you in this thread, I already said in earlier posts.

To conceptualize this idea and to also distinguish between a pure value bet vs protection bet, I've found it useful to consider very specific situations and then mathematically compare the EV of a check through, a bet we make that causes a fold, and a bet we make that gets called.

CMV and others, please correct me if I'm using faulty logic in the following examples. One tricky aspect in which I think I may differ with your examples is whether to assume villain sees two cards or only one card after calling our flop bet. Obviously it makes a big difference mathematically whether we consider a low flush draw 35% equity or 17% equity. Some of us may have a much greater tendency to check back the turn in position for pot control with top pair on boards like K 5 4 8 than others, so perhaps different assumptions need to be made for players with differing levels of turn aggression.

Anyway, the first thing I did was compare EVs of the three scenarios I mentioned. One hand I looked at (found in replayer) was when I raised AA in CO, got called by BB holding 75, flop comes T72, he checks, I bet 2/3 pot, he folds. Kind of annoying that he folds a pair in a HU pot with such low equity. The first thing I wanted to figure out was how much I prefer that he call than prefer that he fold. So I compared the three scenarios (x will represent the pot going to the flop):

1. Check through: EV = x (0.83) = 0.83x
2. Bet causes a fold: EV = x (1) = x
3. Bet gets called: EV = 0.83 (x + 2/3x) - 0.17 (2/3x) = 0.83x + 0.56x - 0.11x = 1.28x

So given a 2/3 pot bet, my preference for a call is represented by winning an additional 28% of the pot. I do best when I make a bet and get called, but both of these are better than a check through. Scenario 3 > Scenario 2 > Scenario 1.

The next thing I wanted to figure out was the cutoff point in equity between a pure value bet and protection bet for situations in which I bet 2/3 pot on the flop. I decided to put y in place of the 0.83 I had previously had and then set it up so that the EVs of scenarios 2 and 3 would be equal.

EV = x = y (x + 2/3x) - (1-y)(2/3x)
x = yx +2/3yx - 2/3x + 2/3yx
5/3x = 7/3yx
5/3=7/3y
(5/3) * (3/7) = y
y = 15/21 = 0.714

So this tells me that for any event in which I bet 2/3 pot on the flop, I am betting for pure value when I have greater than 71.4% equity, betting for protection when I have between 50% and 71.4% equity, and semi-bluffing/bluffing/value cutting myself when I have less than 50% equity. So when I have top pair vs middle pair or top pair vs pocket pairs lower than TP I'm pure value betting, but when villain has a flush draw with two low cards I do not have enough equity to desire a call with my roughly 65% equity (under the assumption that I cannot automatically expect to be able to bet the turn).

Let's say that villain had 6 5 instead of 7 5 in the previous hand. How do the scenarios look then?

1. Check through: EV = x(.66) = 0.66x
2. Bet causes a fold: EV = x(1) = x
3. Bet gets a call: EV = 0.66 (x + 2/3x) - 0.34 (2/3x) = 0.66x + 0.44x - 0.23x = 0.87x

So this example shows that even though we prefer villain to fold his flush draw, we do better when we bet and get a call than we do when we check back the flop. I think this illustrates the point of betting for equity. Scenario 2 > Scenario 3 > Scenario 1.

As far as the argument regarding terminology goes, I find it useful to distinguish between value bets and protection bets so that I can determine how much EV my betting can generate against different portions of villain's range. As a general rule of thumb, when I bet the flop I want villain to have at least a few combos in his x/c range that allow me to get pure value rather than simply protection. If I have something like middle pair good kicker and I expect villain to x/c several top pair combos, pocket pairs higher than middle pair, and high equity draws (i.e. higher than 50% against my hand) while folding bottom pair and weak equity draws, then the EV I generate from folding out his weak draws does not allow me to make up for the EV I lose when I value cut myself against most of the other hands in his range. While I do agree that thinking strictly in terms of value vs bluff can be a useful way to start out, ultimately I do find utility in breaking things down a bit further to consider the different amounts of EV generated against different plausible combos.

Essentially, I want to use a process similar to the river value bet's question of whether there are more combos in the x/c range that I beat, but here I am focused on trying to determine overall EV against villain's flop x/c range. It does become awfully complicated when we start to think about implied odds for certain combos in villain's range, how often we are able to fire turn barrels, and exactly how wide villain is calling to give us opportunities for pure value. Guessing that advanced HUDs might do pretty well at figuring out those sort of details.

nice cotms, read through some interesting subject titles.. anxious to go back and read through thread.. watching paycheck w ben aflek and sum dime piece.. betting for information that is a nice pure open raise tool

Very nice post, Axel. Good illustration that's easy to follow. I will admit that I'm just trusting you on the math, because I'm too lazy to check it myself, but the concept and how to get there is pure gold.

Axel, great contribution. I think that you are misconstruing the definitions in the OP, but you appear to have gotten all the math right, and your example is a good segue to point something out that I missed in the OP.

Exactly. So in this case, when you size your bet this way, you are putting your opponent in a spot where he can fold his equity or he can make a -EV call. In other words, when he folds, your bet is a protection bet and your EV is the pot. But when he calls, your bet is a value bet and your EV is more than the pot. That to me should be the defining characteristic of a successful value bet--that you make more when your opponent calls it than when he folds to it.

I think that some people, such as Aesah in his post, do not agree with this and think that the defining characteristic of a value bet should be that you make more when your opponent calls your bet than you make by checking--which is not the same thing. I think this is just a difference of opinion and that neither of us is objectively right or wrong.

Again, the math is right (though there was a simpler way to do it, but that's not a big deal), but here I think you're misconstruing the definitions. By my definitions, your bet is for pure value when it is called by a hand with 0% equity. It is for value (but not pure value) when your bet is called by a hand that has between 0 and 28.6% equity; it is for protection when such a hand folds to your bet. It is for equity when your bet is called by a hand that has between 28.6% and 50% equity. I would call it a bad bet, or failed bet, when you get called by a hand with greater than 50% equity (because in that case your EV from betting is less than your EV from checking). Anytime a hand with greater than 28.6% equity folds to your bet, you have successfully bluffed! The reason is because 28.6% is the cutoff point where a hand facing your bet should call. So if any hand with that amount of equity or higher folds, he is making an incorrect decision by folding, which makes your bet a bluff. More on this below.

This is exactly right also and highlights some of the disagreements going on in this thread. This is a situation where clearly betting is more +EV than checking, but we make more when our opponent folds to our bet than we do when he calls it. That to me should be the defining characteristic of a bluff.

However, because we have majority equity, we don't need our bluff to succeed for the bet to be better than a check. So obviously Scenario 2 represents a successful bluff, but what about Scenario 3? What do we call that? A failed bluff? I personally am of the opinion that it is very counterintuitive to refer to a bet as "failed" when it makes more than checking. That's why I want to have the definition of an equity bet--because this bet isn't a successful value bet (for reasons I pointed out above and that people are free to disagree with), and it's not a successful bluff if it gets called, but it succeeds at something--namely, at building a pot that we have majority equity in. So that's why I used the term "equity bet".

This is my biggest problem with these results-oriented definitions. When we bet, we have no idea what type of bet we are making. It can be any of the four depending on what part of their range the villain actually has and how they respond. This isn't useful to me. I want to know the point of what I am trying to accomplish. I cannot figure out how you might actually use these definitions in-game without putting your opponent on an unrealistically narrow range.

This to me is the easiest issue. I don't have to have my definitions be intent-based to have my decisions at the table be intent-based. In other words, I can use these definitions but when I'm actually in a hand I can think, "OK, this bet is intended as a value bet against [range X]". I don't need the intentions behind a bet to be hard-wired into the definitions to have clear intentions at the table. I skipped this previously because I thought it would be obvious.

On the same note, thinking about all the different definitions helps with sizing too. For example, I might think to myself, "OK, if I size my bet this way, I'm looking for value against [range X], will probably protect against [range Y], and I'm giving [range Z] a correct call so I'll at least collect equity. Could I do better by sizing bigger or smaller?" I usually don't think about this at the table because it's too complex to answer in 4 seconds, but it really helps when I'm analyzing a hand after my session.

Ok, this makes things much clearer to me. It appeared to me as if this was the thought structure you were advocating for while playing. I kept thinking to myself, "These definitions work for later analysis, but just don't work in-game." So now I get where your coming from.

Personally, I want to be using the same definitions in my post-game analysis, as I do in-game. This is because, I really view my post-game anlaysis as practice for my in-game decisions. My main goal in studying, is to improve upon my in-game thought process. Hopefully that makes sense.

Reasons for Betting that can be effectively used during a real-time decision are 1000x more important than reasons for betting that could only be effectively used to analyze past hands played.

The majority of 2plus2ers are decent/good at dissecting a HH after the fact. What most of them struggle with is a good fundamental thought process towards in-game reasons for betting.

Cliffs: Reasons for Betting that are not practical for determining optimal real-time decision-making are reasons for betting that aren't really relevant/helpful to beating live NLHE games.

Huh? How come you get to redefine Sklansky's definition of a semi-bluff?

How can a person be bluffing when they have the best hand & more than 50% equity? If I have 51% equity, I am suppose to be a long term winner, all things being equal.

These bets [when your equity is 50%+] have varying degrees of value, defined as bet-equity. It's betting for equity.

If, on the turn, the only draw out there is a flush draw & I'm laying him 5-1 on his money, I am still going to win the bulk of the money long term.

Pot $100 - I bet $25 with an overpair & no card to the flush.
He calls with nuttin' but a flush draw.
I win $125 * .7955 = $99.43

V wins $125 * .2045 = $25.57

Neither one of us lose money long term, however, V's +Ev is chump change, unless he makes a bet on the river that I choose to call.

Can I play in your poker game where no one loses money long term and we all get rich?

I think it's customary to call a bet a bluff whenever you're hoping they fold, but if they saw your cards they'd raise or call.

If you make a pot-sized shove pre-flop with TT versus AK (or AK versus TT) you're hoping the other person folds, but of course they wouldn't if they could see your cards.

If you have 51% equity usually it's far more profitable if the other person folds, not calls.

Lol. This whole discussion is about how we choose to define words. I defined it in the way that it makes sense to me. Don't act like I don't understand a trivial concept just cause you don't like my definition.

Edit: Also I hope you realize that you are indeed losing money by not betting larger in your example.

Bluffing is generally used to refer to when you expect to lose if called.

great post CMV
need to re-read it again - but nicely organized

Bluff is one of those terms that simply overgeneralizes situations.

To layman, bluff simply means that you made someone fold a hand that is currently best. In other words, if you have 21 outs and made someone fold a pair on the flop, you are bluffing.

To a slightly more advance player, bluff could mean that you, without currently holding the best hand, made someone fold a hand with SD value prior to river.

To an even more advance player, bluff could mean that you are making someone abandon their equity when a call is +EV.

Equity is only part of the context, but not the whole thing.

Scenario: in a HU situation, you have exactly 51% equity in a pot with at least few blinds, anything you put out there would make it an +EV call for your opponent, so it would be a mistake for him to fold.

IMO, you are bluffing when you can convince your opponent that he does not have 49% equity in the pot, and a call is -EV.

So, if I go all-in with 65 vs. QQ on a flop of
764 and QQ's call will be 40% of the money in the pot.

It is not a bluff, because, although QQ is currently the best hand he only has a 34.4% chance of having the best hand on the river.

If QQ has to put $40 into a $60 pot, he'll win $60*.344 = $20.64
He'll lose $40*.656 = $26.24

So sometimes, a bet with what is currently NOT the best hand, is not even a semi-bluff. It is a bet for equity.