Theory: Bluffing

[spoonitnow]

Recently I've given thought to what my bluffing ranges should look like in various spots. One of the distinctions I've been considering is what that characteristics that range has with cards left to come as opposed to not having cards left to come, and more specifically in position.

Consider a simple spot on the river where we are last to act heads-up and we're facing a bet that will put us all-in. Clearly we call with the top of our range (whatever portion is necessary) and fold the rest, so it looks like:

<---fold---|---call--->

So now consider the same case except we're not all-in. Then above our calling range, we have hands that we would raise for value with:

<---fold---|---call---|---raise--->

But if we have a range where we would bluff raise with, it would come from the top portion of our folding range like this:

<---fold---|---bluff raise---|---call---|---value raise--->

Now let's back up a street. Suppose we're on the turn instead, and again someone puts us all-in. Our range looks the same as before:

<---fold---|---call--->

Now if the bet doesn't put us all-in and we don't have a bluffing range, it looks the same as before:

<---fold---|---call---|---raise--->

But when we add a bluffing range here, I run into a problem. Should the bluffing range typically include hands that would be +EV to call, or should that range mostly come from the top end of the folding portion of our range?

I'd like to see what people think about this question before I go any further.

[jyms]

I typically try to use a range with some EV. I am not sure if it's what you are thinking, but I don't seem to bluff anything that is EV to call. I like to have a suckout factor included in my turn nut shoving range.

Not sure if anything can be part of the bluffing range if it's ev to call? Or are you referring to your shoving range

[Vrax]

But when we add a bluffing range here, I run into a problem. Should the bluffing range typically include hands that would be +EV to call, or should that range mostly come from the top end of the folding portion of our range?

Mathematically speaking, it's good to choose the best of "usually fold" range, that has maximum equity vs villain's _calling_ range. It's slightly different, than having absolute top of "folding range".

Like:
100bb deep, we raise pf 4bb, BB (which is bad player, who sometimes donks in random spots) calls.

flop: 655

BB leads 6 (let's say he has 77-jj, 6x, and some nuts hands)

If BB calls us with 77-JJ, 6x , when we make it $15, then it's better to do it with KQ, than 33.

<---fold-------+--bluffraise-+--fold--|---call--|---valueraise--->

"+bluffraise+" moves across "fold" field, and changes its width according to:
-villain's overall folding frequency
-our equity in spots, when villain just calls the raise.

[spoonitnow]

Right, and that's kind of an LDO but I'm having a hard time articulating the type of spot I'm talking about.

Basically there is a shared interval of the folding range and calling range that can see a gain in EV by raising as a bluff (or semibluff). An example that comes to mind is we're starting to see more river plays where people decide a call is +EV but a raise is more +EV because of the hands it gets to fold, and so on. A more typical example is something like betting a flush draw when we're OOP on the flop when we could also check/call profitably.

The big picture is that we would like to maximize the value for our entire range, which doesn't always mean maximizing the value for each individual hand, but it's the bottom end of our "usually call" range that's making me scratch my head.

without getting into it too much I'd say that if a hand is profitable to call OR bluff, and it's close, then you should randomize. Balances our range while still getting near-optimal value.

[nutsinho]

It Depends.

[BankItDrew]

When faced with a situation where two of our options include: +EV call or a +EV raise, I prefer the raising option.

You need a decent enough read on villain to make the most profitable move ldo, but I think you have it here. Your hand has merit.

[spoonitnow]

DoGGz.

[Robb]

Now if the bet doesn't put us all-in and we don't have a bluffing range, it looks the same as before:

<---fold---|---call---|---raise--->

But when we add a bluffing range here, I run into a problem. Should the bluffing range typically include hands that would be +EV to call, or should that range mostly come from the top end of the folding portion of our range?

I'd like to see what people think about this question before I go any further.

I'm not sure what you're looking for, here. In terms of game theory mathematics, the inclusion of "bluff raises" is going to decrease the number of folds to our raises, so some bets where we were getting better hands to fold now get called. What I think happens here (regardless of where the "bluff" range sits) is that the Value Raise range shrinks a bit. That, in turn, nudges his equity DOWN in the case where we raise and he calls.

For the Bluff Raise range, I think it has to come from the bottom end of the calling range. Let see if I can explain what I'm thinking.

Hands in the top end of our calling range are not going to improve overall expected value much if we bluff them - they're getting less value than they "should" based on equity, but they're balancing the bottom portion of our calling range. But if we take hands that were part "fold" and part "bottom call" as bluffs, each of them improves dramatically in expected value vs. equity thanks to the bluff. And the other expected values remain more stable.

This is just a rough guess at the mathematics based on experience analyzing game theoretic situations and the equilibrium of mixed strategy solutions. But without concrete analysis, it's hard to tell how the interchange of expected values will behave.

[Fnord]

It Depends.

This, because you need to consider the range of hands you'll get to the river with and if the river completed any draws. Hence, it is sometimes more profitable (or a reasonable mix-up) to turn a pretty goodish hand into a bluff because pretty betterish hands fold. Also, you may be able to make a big value bet/raise expecting a worse hand to try to pick you off.

[Vrax]

This, because you need to consider the range of hands you'll get to the river with and if the river completed any draws. Hence, it is sometimes more profitable (or a reasonable mix-up) to turn a pretty goodish hand into a bluff because pretty betterish hands fold. Also, you may be able to make a big value bet/raise expecting a worse hand to try to pick you off.

That's pretty Fnordish reply imo