nl100 zoom Qao

Hey Sandraardnas,

Calling pf is fine. Squeezing is probably the stronger option and should certainly not be too thin vs late position openers.

Flop is fine as played.

Turn lead is fine. Sizing is already fine imo. BTN is unlikely to be that strong. CO can potentially have a stronger range but he may even still lead sets on the flop due to it being multi-way.

I would put out a small river value bet here for value from worse Qx. Something like $10 should be fine. Plan should be to bet/fold. X/c is not likely to be a decent option here, especially since CO is firing 3way.

Hey, could you tell what is worst Qx that can give us value here on the river?
Also you said CO has stronger range. Why? He was opener and my guess i that he cbets Tx+ super often.

Originally posted by sandraardnas
Hey, could you tell what is worst Qx that can give us value here on the river?
Also you said CO has stronger range. Why? He was opener and my guess i that he cbets Tx+ super often.

Yeah, neither player has a strong range actually, misread the hand somehow. BTN would bet IP and CO would cbet.

Worse Qx can still call. But we acknowledge value is thin hence the smaller sizing.

So you assume that they can have hands like Q8s, Q7s right?
Then we have a valuebet against one oponent.

But if both of them are in the hand with similar range:
(loose and not very possible)

MP3 38.59% 34.89% 3.70% KJs+, QJs, Q9s-Q2s, KJo+, QJo, Q9o-Q8o
CO 38.59% 34.89% 3.70% KJs+, QJs, Q9s-Q2s, KJo+, QJo, Q9o-Q8o
BB 22.83% 22.83% 0.00% AdQs

Not too good of a situation. How is that even possible?

Originally posted by sandraardnas
So you assume that they can have hands like Q8s, Q7s right?
Then we have a valuebet against one oponent.

But if both of them are in the hand with similar range:
(loose and not very possible)

MP3 38.59% 34.89% 3.70% KJs+, QJs, Q9s-Q2s, KJo+, QJo, Q9o-Q8o
CO 38.59% 34.89% 3.70% KJs+, QJs, Q9s-Q2s, KJo+, QJo, Q9o-Q8o
BB 22.83% 22.83% 0.00% AdQs

Not too good of a situation. How is that even possible?

This is incorrect use of equilab.

We need 50% equity against the calling range of either of our opponents. Not 50% equity vs the combined potential calling range of both opponents, this is nonsensical.

Even if we decide betting is too thin (should just about be profitable), the next best option is to x/f not to x/c.

ok, I still dont get this math but whatever.

So when I check and he bets 17$ to 28$, he doesnt have KQ often enough to call? How would you play KhQh in his place?

Originally posted by sandraardnas
ok, I still dont get this math but whatever.

As a rough guide simply put in your hand vs the calling range of one opponent not two.

Originally posted by sandraardnas
So when I check and he bets 17$ to 28$, he doesnt have KQ often enough to call? How would you play KhQh in his place?

I might bet river small. Although it's interesting that you think AQ is too thin for a value bet yet I'm assuming you think villain should always bet KQ =p

However there is still KJ, potentially stuff like Q9. Worse case scenario maybe even some TQ/9T/sets if he's taking a weird line. Plus villain may not always bet river 3 way with KQ.

But yeah, assuming villain has all combos of KJ,KQ and Q9s, we are in pretty bad shape vs his range but can just about argue a close to break-even pot-odds call if we run it through equilab.

We need 50% equity against the calling range of either of our opponents. Not 50% equity vs the combined potential calling range of both opponents, this is nonsensical.

Can you please explain this statement, or even better provide some reference where I can read about this? I was never reading about this, and would like to know it.
I think your statement is just partially correct, which I will try to prove:

We can divide the problem into 4 sub cases:

EV_bet = EV_both_defend + EV_bu_folds_co_defends + EV_bu_defends_co_folds, + EV_both_fold

1) EV_both_defend
Here it is clear that when we bet and both of them defend, we need to win the hand > 33% of time. We can calculate this by 1/number_of_opponents.
You said that it is enough to have >50% equity vs individual defend ranges. Lets say you are ahead exactly 50% of each defend range. Then, the probability that they both have weaker hand when they defend is 0.5*0.5 = 0.25, which means that when they both defend we win the hand 25% which is going to be -EV bet (here is assumed that probabilities are independent, meaning their ranges do not overlap). So your statement is not correct for this sub case. It might be correct for case when their ranges overlap enough, but it doesn't hold for all cases.
This would be even more wrong if you bet vs more opponents, e.g vs 3 opponents you would be ahead in 0.5*0.5*0.5 = 0.125 (12.5%), and you need at least 1/4 = 25% equity vs 3 opponents.

2) EV_bu_folds_co_defends
In this case, we need to be ahead 1/number_of_opponents = 50% (one opponent).
So in this case, your approach is correct.

3) the same as 2) but we calculate equity vs CO defend range

4) EV_both_fold
We can approximate EV_both_fold = 0, but in reality it is not zero, because sometimes they fold better hands, so this ev is better than EV_check.

So I think I shown that it is not enough to look to have >50% vs both individual defend ranges.
If it would be the case that both opponents defend super rare, then we could approximate the EV_bet as you did, but otherwise it is wrong.
Do you agree?

I will look at the maths later when I get time.

Notice I said "as a rough guide", I'm not expecting the statement to be 100% mathematically correct, but inputting the calling range of 2 players is way off imo.

The reason it should serve us a rough guide is that the most likely outcome is that 1 player calls or both players fold. Both players occasionally calling should not affect this too much. But no, I've never read about it, and can't refer you to anywhere at this stage.

I think it's unecessary to consider the possibility of opponent folding a better hand - we don't typically consider this when value-betting against one opponent so no reason it should suddenly become necessary against two.

Notice I said "as a rough guide", I'm not expecting the statement to be 100% mathematically correct, but inputting the calling range of 2 players is way off imo.

Sure, inputing the calling range of 2 players is way off, and approach you said is more close to the real solution. I think if we want to be closer to real solution and approximate, we should use threshold 55% equity vs each individual defend range, instead of 50%.

I asked this because I wanted to see mathematically correct answer.

The reason it should serve us a rough guide is that the most likely outcome is that 1 player calls or both players fold. Both players occasionally calling should not affect this too much.

I think it is not soo rare that both players defend vs our bet. If we bet 1/2 pot, and lets say realistically each of them defends 40% of time (folds 60%), then the probability that they both fold is:
p_both_fold = 0.6*06 = 0.36 (36%)

This means that at least one of them defends 64% of time. The probability that both of them defend at the same time, is
p_both_defend = 0.4*0.4 = 0.16 (16%).
This means that the probability that one of them folds, one defends is
p_one_defends = 1 - 0.36 - 0.16 = 48%.

So we can see that the scenario where they both defend is 33% of time when non of them fold, which means we can not really just ingore the case, it can lead to -EV bets for borderline equities
50%-55% equity vs both individual ranges.

Gingerkid,

Couple of questions for you....

Where are you getting 40% defend frequency from?

In the scenario where both players decide to call, we win more money when good right? We win twice as much as our investment right? So do you think we need 50% equity vs our opponents combined calling range or 33%? Because if the latter the impact on both players occasionally calling will still be negligible. I.e we may have way less equity when called by both guys, but we are also getting better odds.

Originally posted by w34z3l
Gingerkid,

Couple of questions for you....

Where are you getting 40% defend frequency from?

I just gave example, lest say each of them fold 40% vs our bet, to be easier to understand what I meant.

Originally posted by w34z3l
In the scenario where both players decide to call, we win more money when good right? We win twice as much as our investment right? So do you think we need 50% equity vs our opponents combined calling range or 33%? Because if the latter the impact on both players occasionally calling will still be negligible. I.e we may have way less equity when called by both guys, but we are also getting better odds.

Ok, I see it is correct 100% what you are saying, and mathematically correct.

I thought, that equilab is combining
2 ranges (making one range from 2 ranges) and then calculating equity of our hand vs that single range. That would be incorrect (example when one opponent have e.g. 10 combos and all are better than our hand so 0% equity, and other opponent have 90 combos all weaker than our hand, so our equity vs that combined range would be 90%, but in reallity we always lose because the player with better hands always calls and wins).

But equilab is actually calculating as I explained above, taking into consideration both ranges independently. So, I guess I missunderstood the concept of "combined range".

Yup I completely get it.

For example -

Board: AdKhJsTs8s

Equity Win Tie
MP2 100.00% 100.00% 0.00% { AA }
MP3 0.00% 0.00% 0.00% { KK }
CO 0.00% 0.00% 0.00% { TT }

KK has 0% equity overall despite having 100 equity vs TT