eq.fest

Second - and here I guess you might be on the wrong track - once you bluff, it makes essentially no difference if you bluff with a 25% hand or a 0% hand. 25% equity with no cards to come means Villain has 75% better hands in his range. That said, essentially any bluffcatcher has 100% equity vs. your bluffs - regardless if it was a hand that had 0% or 25% to begin with, against Villain´s calling-range any bluff-hand has 0% equity.

It makes a difference to OOP's calling freq. If OOP called vs a PSB 50% of the time, then IP would just check back the 25% hand rather than bet it, and then OOP would stop calling 50% of the time because he then always loses. This would go back and forth till it settled somewhere.

Nick, solve for this toy game.

One street of betting left with Pot size = 1 and a PSB left. OOP's range is Q,J,T,9,7. IP range is A,K,8. OOP will always check while IP can either bet, check or do a mix of both. 

I'll start it off for you. IP has 100% equity with A or K, and 20% equity ( he beats 1/5 of OOP's range) with 8. OOP will call at freq X to keep IP EV of a bet with 8 = EV of a check with 8 

(x)(-1) + (1-x)(1) = 0.20 

x = 0.4

I can't imagine any hands really that UTG plays in this way, even if UTG is playing wierd. I mean, check raising JJ on the flop and then checking the turn is wierd, while check raising JT is just probably bad and we dont think UTG is playing bad :) 

I'm discounting 33 and 44 combos from UTG's range cause if they were not just open folded pre they would prob fold to a 3bet. Once UTG checks the turn his hand actually looks like AsKs or AsQs as those hands make the most sense to c/r flop with. But given the action for the rest of the hand I think we have to discount those because AsQs doesnt want to bet river and AsKs likely bets the turn. The funny thing here is that your range should be so narrow but its still hard pinpointing exactly what it is! In order of likelihood in this unlikely scenario I would say you have JJ,AsKs,44 for value. PFA has played the hand well up until now, unless he believes that AsQs or AsKs is a large part of your checking range on the turn in which case he could bet. On the river he just needs to beat like 1 or 2 combos of a bluff to be able to call against that range so I guess he should call.

I'd prefer checking this river with all of my range. That way, we can induce some bets out of busted draws and weak made hands the villain would otherwise fold to our river bet.

Ugur, I think this is somewhat optimistic. After polarizing our range by check raising the flop and betting the turn, villain will be very happy to check back any weak made hands on the river. And how many draws is he really going to have compared to how many made hands that just want to see a showdown.

Ben, your argument for flop x/r seems sound and there are not many hands in our range that get to accomplish this! However, if range protection is an argument for check calling there already many hands that will accomplish this for us: AsKx, AxKs, 9Txx, As9s,KsQs,QhKh,AsQs ,AJxx should alone give us good coverage on many run outs.

I hope you guys dont mind if I join the discussion!

Ben I modeled your first toy game in CREV. Betting seems to be better than checking because when we check we let IP bet with a balanced range and are faced with a 0ev call the roughly 60% of the time he bets(the rest of the time we win our equity share of the pot vs his draws that he checks back). If we bet though we force villain to call with his entire range. So we'd rather have 46% equity all of the time then 34% equity(vs his draws) some of the time.

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Nick, 87ss would give villain a gutter, and not a med pair. Calling the flop with the gutter to bet the turn when checked to would be a much more common stratgey.

Nick, I gave you a 1:1 ratio of over cards:mid-pairs,sets that calls the turn, and still then you are folding the turn 80% of the time to a bet. If I give you anymore overcards you just end up folding the river too much even though I have you calling pretty much all your mid pairs on any blank. I think check/folding the turn 80% when you are betting the flop with such a merged range is a mistake. I think we should be aiming to keep a hand like 78ss indifferent from betting or checking when facing a check on the turn, and to do that we need to be calling more frequently.

Hey Nick

@ 22mins with the 97ss on J39r, could you explain what your checking range might look like on say a 2s turn?

Thanks in advance

So what you have learnt is that 6bb/100 is a world-class winrate at 500nl zoom.

@lumens, try and work out if we should value bet or not with any hand that isn't that nuts with out making assumptions on what villains starting range is on that street.

@Jonas, I read your response as somewhat defensive of a GTO approach. I use the same method of study for my work away from the table. I'm just wary of your method of analysis using CREV for THIS spot and your confidence on the results of a very simplified model for a very complex hand.

Jonas, our requirements for value betting a hand rely on the range that villain continues against that bet with. How did you structure your sym for the TT bet and not take into account villains range?

I know I worded the question in a very qualitative way, but I still think it has it's merits. Put differently: surely allowing our opponent to find him self frequently in a situation where he is able to make well balanced bluffs against us is not optimal?

Chael, ask your self these questions. Against a range of give up's and monsters, what range of hands do you want to bet? What is the size that maximizes the EV of a bet with those hands? 

Maybe someone can comment on my reasoning for not wanting to bet the turn : I feel I dont want to put money in the pot and then be forced to check and turn my hand into a bluff catcher on any river that is a diamond, club, 2, 4, 7, A, K, Q, 6 (pretty much the whole deck). Villain can also raise this turn a bit more frequently, than if it was a Q or a K.

Don't mind the river call. I'm temped to check the turn and call a bet.

Your bet size should be all in with your entire range here.

Thanks, Ben. I did a CREV model of the K2ss with what looks like some fair ratios and frequency's: Our opponent can actually get to the river with a fair amount of air that he could bluff with on the river. 

Didn't want to spam the discussion so I put the CREV textblock here http://pastebin.com/Za1feH0v

With you having said that you think villain doesnt have any bluffs by the river, are you never check calling?

Hi Ben

05.20 with AsJh, are you calling the SB's lead (readless) without the spade in your hand when he bets into 3 players?

06.40 with K2ss, you bet the river. Do you not check a hand stronger than 6x that you use for your check calls here? Villain can rep something like K7-K10 and some bluffs if he bets, and K2ss seems like one of the stronger bluff catchers we can check with here. If we are betting everything stronger than 6x, then villain can bet this river with a hand as weak as 7's, which doesn't seem right here to me.

Thanks in advance :)

I really enjoy that camera!

you have to be calling stupidly wide vs 3bets if you are going to be opening that much on the button.

At ~24:20 you say you want to add K7 to your check calling range on the river. Your range should be really air heavy when you check as you bet the turn with a polarized range so I'm confused why in general you would want to be defending your checks. Is it just that you thought this particular hand plays better as a bet turn/check call river hand or are you actively trying to develop a river check calling range?

Hi Ben! 

At 11:41, you cbet AQ6tt for half pot with TPWK. Assuming you use this cbet size for you entire range, why do you chose to bet 1/2pot? Our cbet range should be quite polarized and his bluff catching range vs any reasonably sized bet should be some pretty strong pairs so why do we not bet bigger with our entire range? 

Thanks in advance.

Ahh don't go, I'm going to miss all of your valuable contributions to RIO.

I thought we just discussed this?

Yes I think this is what is mostly going on.

Well how is this different to one player betting the turn and another playing calling the bet at the appropriate frequency and seeing the river. The bettor put chips into the pot, but his expectation was close to zero if he was bluffing. We can't go ahead and fold the river now with all our bluff catchers because he put chips in the pot.

It seems like you guys have differing definitions "risk", "cost", "pay" etc... BigFiszh is just looking at everything from an expectation point of view which already takes into account what one player has "risked". 

Anyway, I wrote to Janda and he got back to me. Janda assumes that the 3bet caller is defending at a high enough freq that will make most of the 3bettors bluffs preflop slightly losing. He then assumes that the 3bettor should then make that money back by being able to get a lot of fold equity with his cbets on boards that are good for his range overall, or just by flopping a strong hand.

Actually, I was right initially.  

"How that? Say, we have 100% bluffcatchers and our opponent is polarized between nuts and air. That´s the perfect spot where (1-a) comes into play."

Consider the situation where villain gets to the river with a range that consists of 70% nuts and 30% air and hero's range consists entirely of bluff catches. Villain can either shove for a PSB or check fold. Hero can now call or fold vs a shove or if villain checks hero will always check back. Hero needs villain to be bluffing 33% of the time to call vs a PSB, but villain is only bluffing 30%. So hero will always fold and villain will always bluff. This case might seem unrealistic to you, but it will be similar to where a card rolls off that is just way better for one player than it is the other.

In this case villains range is just too strong to satisfy the indifference principle. So both players equity distributions and bet sizes as well as the board texture will dictate whether one player should try and keep the other indifferent with his bluffs or not.

Very surprised to hear this especially considering Sauce gave such a positive foreword to the book. 

I was just referring to the 3bettor here as OOP and not so much about what is expected from different positions. 

BigFiszh, your argument seems valid to me, but have you read Janda's book? He seems decently confident that OOP should be able to profitably cbet of most board textures with any two cards and show a small profit.

Luciaetta, are you referring to Matt Jandas book? I've struggled to see how our opponents bluffs preflop really "cost" him anything since our opponents' expectations with his bluffs preflop should be close to zero.