extremely abstract isf theorem question

Pretty simple question. Its the river, there are 5 cards on the board, we have two, and our thinking opponent in this headsup pot has two as well. There is moneys in the pot, and we each have a psb left.

Hero is first to act, and his range has >66% equity vs Villains range. Should hero shove his entire range?

I'll bring up some examples in a bit.

I think if you make the right assumptions then the answer is yes, but in the real world it's closer to "yes but."

FWIW I posted something like this a couple of months ago and got ripped on by Lukie.

I'd say yes, as long as we are confident that our opponents' perception of our range is going to be roughly accurate.

I don't see how we can induce our opponent to make a bigger mistake than to call when he is behind our range with the effective stacks so small.


what conditions do you have in mind mcat?

Obviously there isn't enough information.

Suppose villains range consists of 9 high 66% of the time and the nuts 44% of the time. Should hero push in this case? No. Suppose hero holds the 2nd nuts, and 44% of the time villain holds the nuts and 66% of the time, the 3rd nuts. Should hero push? Yes.

Either way, what's the point of the question?

Originally Posted by Vi-Zer0Skill

what conditions do you have in mind mcat?

The conditions are first of all that our range is polarized to really good hands and hands with no showdown value, and second of all like you said, that his perception of our range is accurate and that he'll play correctly according to that perception.

But in the real world people play badly and we have to adjust to exploit their specific mistakes. I.e. if he's a station and is calling more than 50% of the time then obviously we don't want to bluff, even if we know he's making a huge mistake by calling against our range. Likewise if he's a nit and is never calling without the effective nuts then obviously we don't want to make thin value bets, even if he might have a lot of worse hands that in theory are making a huge mistake by folding against our range.

Originally Posted by TheWorstPlayer

Villain is Gogol's Nose, MTBlue from 2+2. He's very tough and a very big winner and he has gotten the best of me most of the time over the past two years or whatever. We haven't played much recently, though, since I took 4 months off from poker, pretty much.



Poker Stars, $5/$10 NL Hold'em Cash Game, 6 Players
SB: $541
BB: $1,288.25
UTG: $3,124.35
TWP (MP): $1,369
CO: $1,302
BTN: $408

Pre-Flop: 8 8 dealt to TWP (MP)
UTG folds, TWP raises to $40, 3 folds, BB raises to $140, TWP calls $100

Flop: ($285) J 7 J (2 Players)
BB bets $180, TWP calls $180

Turn: ($645) Q (2 Players)
BB checks, TWP checks

River: ($645) J (2 Players)
BB bets $968.25 and is All-In, TWP...?

Originally Posted by Renton

Pretty simple question. Its the river, there are 5 cards on the board, we have two, and our thinking opponent in this headsup pot has two as well. There is moneys in the pot, and we each have a psb left.

Hero is first to act, and his range has >66% equity vs Villains range. Should hero shove his entire range?

I'll bring up some examples in a bit.

I guess this all depends on his calling range when we bet and his betting range when we check. There's not enough informtion in there to give a good answer.

Originally Posted by Renton

Pretty simple question. Its the river, there are 5 cards on the board, we have two, and our thinking opponent in this headsup pot has two as well. There is moneys in the pot, and we each have a psb left.

Hero is first to act, and his range has >66% equity vs Villains range. Should hero shove his entire range?

Not necessarily.. Villain could potentially call with the 34% of his range that beats us and fold the 66% that we beat.

Originally Posted by Renton

Originally Posted by TheWorstPlayer

Villain is Gogol's Nose, MTBlue from 2+2. He's very tough and a very big winner and he has gotten the best of me most of the time over the past two years or whatever. We haven't played much recently, though, since I took 4 months off from poker, pretty much.



Poker Stars, $5/$10 NL Hold'em Cash Game, 6 Players
SB: $541
BB: $1,288.25
UTG: $3,124.35
TWP (MP): $1,369
CO: $1,302
BTN: $408

Pre-Flop: 8 8 dealt to TWP (MP)
UTG folds, TWP raises to $40, 3 folds, BB raises to $140, TWP calls $100

Flop: ($285) J 7 J (2 Players)
BB bets $180, TWP calls $180

Turn: ($645) Q (2 Players)
BB checks, TWP checks

River: ($645) J (2 Players)
BB bets $968.25 and is All-In, TWP...?

ez fold imo.

Still thinking about original post.

Answer to question: I'm pretty sure no

Answer to variation of question "Should we set up our ranges in a way that even though we will be bluffing a certain large % (I think the most you are going to have is 33) of the time our opponent will make an unprofitable call if he does?":

I'm pretty sure the answer to this is yes.

Also, one problem with the question is there's no longer equity on the river. A hand is either the winner or the loser. Which brings up an interesting point about ranges and bluffing on the river...

i guess what im kinda getting at:

When you perfectly balance your bluffing frequency, it puts your opponent in "tough spots" but does it really make you any money? Don't you have to bet exploitable ranges to exploit?

Also, re: the op, lets add ranges.

Villain's range here is 3, 4, 5, 6, 7, and 8.

Our range is 10, 9, 8, 7, 1, and 0.

Whats an optimal range for us to bet? One that puts 5 in a tough spot? 3? 8?

Ok.

If you only bet T987 it would be unprofitable to call with anything and even money to call with an 8. If you bet T9871 it would be unprofitable to call with anything but an 8 still, but an 8 would become profitable. If you bet your entire range he should call with everything, but only 7 and 8 would be profitable and the rest would be even money.


The hole in this question is that poker isn't all about balancing ranges, vaccums, and theoretical situations, because what you do in the situation above all depends on what your opponent is going to do. If he's going to snap call his entire range then of course you should never bet 0 or 1. If he's only going to call with 8, than you should always bet 0 or 1, and never bet 7. Betting 8 would depend on what you want to accomplish in later hands.

So the optimal range for us to bet isn't going to be found in this theoretical situation, it's going to be found in the read of the opponent.

Originally Posted by Renton

When you perfectly balance your bluffing frequency, it puts your opponent in "tough spots" but does it really make you any money? Don't you have to bet exploitable ranges to exploit?

If there is money in the pot, and you force your opponent to fold, you make money.

Game theory is really hard to understand, I struggle with it the same way you do. I've asked the same questions you are asking, and the truth is I still don't know the answers. Which is why my response to that post was that sentence; your statement is wrong, but I can only explain it to you that much. I have no idea why its the case, and what it has to do with poker, but I am pretty sure it has to do a lot with poker.

Originally Posted by IowaSkinsFan

Originally Posted by Renton

When you perfectly balance your bluffing frequency, it puts your opponent in "tough spots" but does it really make you any money? Don't you have to bet exploitable ranges to exploit?

If there is money in the pot, and you force your opponent to fold, you make money.

Game theory is really hard to understand, I struggle with it the same way you do. I've asked the same questions you are asking, and the truth is I still don't know the answers. Which is why my response to that post was that sentence; your statement is wrong, but I can only explain it to you that much. I have no idea why its the case, and what it has to do with poker, but I am pretty sure it has to do a lot with poker.

Simplifying my above range, lets say that villain always has 5, 6, and 7. We have 8, 9, and 0, and theres a pot size bet left, we'll pretend pot is 100 dollars.

If we shove our whole range he has a 2:1 call and is exactly a 2:1 dog to win.

ev(call) = (.33 * 300) - 100 = 0
ev(fold) = 0

ev(ourbet[always calls]) = (.66 * 300) - 100 = +100
ev(ourbet[always folds]) = (1 * 200) - 100 = +100

ergo,

ev(ourbet[nomatterwhat] = +100 (the pot size)

So basically the idea is that we always win the pot, nothing more nothing less. But more importantly, while we were entitled to only 66% of the 100 pot to begin with (our range being 66% vs his range), when we bet this range we always win that plus 33 more dollars.

So i guess the answer is, when we feel that the ev of only betting our nuts and always checkfolding our busted hands is > $33, then it becomes better to bet everything.

(i don't know if i got any of this right)

Originally Posted by mcatdog

I think if you make the right assumptions then the answer is yes, but in the real world it's closer to "yes but."

FWIW I posted something like this a couple of months ago and got ripped on by Lukie.

I'm now 2 posts into this thread and this makes me very happy.

well, not really, but in the poker sense, yes.

Hero (most likely) should NOT be shoving his entire range. Why would we do that, barring generally unlikely circumstances?

Shoving the entire range would be +EV but in almost all circumstances would not be MAXIMIZING expectation, which is what we are trying to accomplish. Some ideas to maximize expectation might be to bet less than pot sometimes, check some hands, only shove the top x% of hands, bet your very worst and most of your good hands, checking some hands with SD value, min-betting to induce a bluff shove, who knows.

Originally Posted by dsaxton

Obviously there isn't enough information.

Suppose villains range consists of 9 high 66% of the time and the nuts 44% of the time. Should hero push in this case? No. Suppose hero holds the 2nd nuts, and 44% of the time villain holds the nuts and 66% of the time, the 3rd nuts. Should hero push? Yes.

Either way, what's the point of the question?

this guy is giving it 110%, are you???

Originally Posted by Renton

Originally Posted by TheWorstPlayer

Villain is Gogol's Nose, MTBlue from 2+2. He's very tough and a very big winner and he has gotten the best of me most of the time over the past two years or whatever. We haven't played much recently, though, since I took 4 months off from poker, pretty much.



Poker Stars, $5/$10 NL Hold'em Cash Game, 6 Players
SB: $541
BB: $1,288.25
UTG: $3,124.35
TWP (MP): $1,369
CO: $1,302
BTN: $408

Pre-Flop: 8 8 dealt to TWP (MP)
UTG folds, TWP raises to $40, 3 folds, BB raises to $140, TWP calls $100

Flop: ($285) J 7 J (2 Players)
BB bets $180, TWP calls $180

Turn: ($645) Q (2 Players)
BB checks, TWP checks

River: ($645) J (2 Players)
BB bets $968.25 and is All-In, TWP...?

I read this thread and I'm about 99% sure I know the exact comment from gogol (MTBlue) that sparked this thread. Something along the lines of "i know know, my range is ahead of your range, easier to just go allin"

that is a very good post--- for image purposes only. gogol doesn't think that way and he doesn't play 'that' aggro. Given action and board though, TT is almost always good here though, and TWP never folds. good shove IMO.

Originally Posted by minSim

Originally Posted by Renton

Pretty simple question. Its the river, there are 5 cards on the board, we have two, and our thinking opponent in this headsup pot has two as well. There is moneys in the pot, and we each have a psb left.

Hero is first to act, and his range has >66% equity vs Villains range. Should hero shove his entire range?

I'll bring up some examples in a bit.

I guess this all depends on his calling range when we bet and his betting range when we check. There's not enough informtion in there to give a good answer.

yes this is very important information

Let me quantify Renton's hypothetical with some possible betting ranges for hero and some possible calling ranges for villain.

I assumed pot size of 36 and remaining stacks of 36 to make the numbers even out, since there are 36 possibilities for our hand and villain's hand. The number is the average amount of chips won by us given our strategy and villain's strategy.

The ranges for hero are the "shove any two range," a thin value betting range, a nitty range, and a bluffy range. Just for fun I added a couple more ranges where hero bluffs half the time. Villain's ranges are calling station, nit, and somewhere in the middle.

The green box in each column is hero's best play given villain's play, and the red box in each row is villain's best play given hero's play. Anyway here's the chart.



Discuss the best strategy for this game and how it applies to actual poker situations. I have a lot of comments, I'll post them in a few minutes.

No matter what we do, we're kicking villain's ass in the long run, it's just a question of how badly his ass is being kicked. This is what happens when we get into good spots where our range is way ahead of his range.

In a static world where villain always makes the same play, then shoving our entire range is bad. He's either going to call or he's not. If so, then we should value bet thin and never bluff. If not, then we should bluff a lot and only value bet really good hands. Balance isn't important against crappy players who don't adjust. The only strategies that are optimal in a vacuum are the two most un-balanced ranges we can have.

As soon as villain is capable of adjusting to our range, then the un-balanced ranges suck. Thin value bets are designed to exploit donkeys, but this range results in the worst outcome on the entire chart if villain plays well against it. Likewise, the bluffy range sucks against good players, but not quite as bad as the thin value betting range.

The Minimax Theorem from game theory says that a good strategy for games is to optimize our worst possible outcome. In other words, against good players we should do whatever maximizes our overall EV assuming that villain is going play optimally against us. According to the Minimax Theorem our best play is to shove our entire range because then our EV will always be at least 30.

This is sort of a variant of the Prisoner's Dilemma. We can guarantee an EV of 30. If we try and get greedy by bluffing too much or not enough, we might win more than this in the short run if we stay one step ahead of villain, but that's really hard to do against good players. If we can't do it then we're better off doing what Gogol's Nose did and saying fuck it I'm shoving my whole range.

no

guys- game theory is not very applicable to poker

anyway here is what im sorta getting at:

There are certain spots in poker where we have the initiative, and we can actually profitably bet 100% of the air in our range, because our range is so strong. An example would be an AK3 flop after raising under the gun and getting called from blinds, or betting a Q33 flop and then the turn is an ace.

In the AK3 scenario, we're on a range thats like 65% vs villains range. That, plus the fact that theres the threat of future bets, makes it profitable to bet all of our air.

What i was wondering, is what of those factors have to be emulated to be able to bet 100% with air in other poker scenarios? I imagine having money behind and a later street to bet is pretty important, but is there a magical % equity number where we can make no mistake by bluffing?

Originally Posted by Renton

In the AK3 scenario, we're on a range thats like 65% vs villains range. That, plus the fact that theres the threat of future bets, makes it profitable to bet all of our air.

Isn't this conclusion based on the faulty premise that the donk across the table gives a shit about what happened pre-flop?

Read: he's taking his threes to the river.

Renton,

The problem (which is also a problem with my other posts in this thread) is that you are assuming a dichotomy between betting and checking but we can actually bet any amount we want to bet.

Let's say we get to the river against a really predictable villain and our range looks like this
top 80% of our range >>> his entire range >>> bottom 20% of our range. If we make a PSB on the river then it's technically +EV with our entire range but it's still a mistake because there are other options that are even more +EV, for example a half-pot bet would likely be better.

questions for renton:

1. how is this extremely abstract?

2. how did you come to the conclusion that shoving all of these hands is the best option?

Originally Posted by Lukie

questions for renton:

1. how is this extremely abstract?

2. how did you come to the conclusion that shoving all of these hands is the best option?

1. http://dictionary.reference.com/browse/abstract

i'll go with definition one

2. I never did.

Originally Posted by Lukie

questions for renton:

1. how is this extremely abstract?

2. how did you come to the conclusion that shoving all of these hands is the best option?

wow quality post

you gotta have an idea of his range and your image (as well as how much he is paying attention to you)