Hello,

Quite a doubt here using GTO+ as in his book Matthew Janda shows that against a half pot cb opponent should defend at least 66.7% of the time to prevent his opponent from being able to profitably cb any two cards (1/(1+p) when p is the cb in % of the pot).
Whereas in that screenshot GTO+ give an overal defence of 63% and the cb is even smaller (47.5% pot).
How to explain this contradiction ? Who'm is mistaken GTO+ or Janda ? Can someone run the simulation in PIO ? Sorry if I'm missing something obvious here

I can't tell whether this is the river and if 63% is calls + raises or just calls but any way...

The results you are referencing are from a river toy betting game where one player has all 100% equity or 0% equity hands and the other player has hands that can only beat the 0% equity hands.

In that very specific toy game scenario that equation holds true. As you play real poker other things will change that calling frequency.

Things such as having mixed ranges with a contiuum of hands that are nuts and air by both players, having other options such as raising, and the equity of your opponent's bluffs.

The reason, I believe, is that there will be more betting on later streets and we are OOP with a range disadvantage. Our opponent raised preflop and basically paid the price for this advantage earlier in the hand - this is why we are not being exploited due defending at less than MDF (the concept Janda is explaining here).

Credit to Upswing blog. You can read the full article here.

Thanks raimbow for taking the time answering, I think I stumbled across that article some months ago but never really took the time to read it, now it's done, I think indeed it's part of the answer even if it's still not that clear

MDF doesnt apply when youre at a range disadvantage

Why is that?

Because of future betting and the fact a lot of your hands won't have showdown value in the future, even vs villain's bluffs.

Actually my understanding is because it’s of past betting.

See the thing is when u complete from the bb getting 6:1 (for example) then u will be justified in continuing with a wide a trashy range. so now when the board comes down AAK if u try and defend with MDF vs an EP open, u are just gonna be bleeding chips like crazy. In this example, there will be 1) plenty of other board that we can continue with more of our range, and 2) we got such a good price on our preflop cal that we don’t need to continue all that often post to make our preflop call +EV.

And that should be our ultimate goal: making our preflop call of 6:1 +EV, not trying to defend with MDF vs every post flop bet.

You have a minimum defense frequency if you don't think your opponent should be able to profitably take his line with any two cards.

For example, if someone raises, you probably don't think he should be able to profitably raise with any two cards. So if you bet $5 into a $10 pot, and your opponent raises to $15, then he is risking $15 to win $15 and you need to defend 50% of the time UNLESS you think your opponent should be able to profitably raise any two cards (spoiler alert: he shouldn't be able to).

This concept does not apply when your range is trash relative to your opponents (taking position + stack depth into consideration as well), because in this case he likely should be able to profitably bet with any two cards. As the poster above me pointed out button vs BB in a single raised pot is probably the best/most common example of this. BB checks and button can profitably bet with ATC on many flops in this spot.

Because when your range is too weak, it is more -EV to call or raise (rather than just fold) with so many hands that your opponent can profitably bet any two cards. So you take the 0 EV line of folding rather than the -EV line of calling or raising so frequently that your opponent can profitably bet any two cards.

Hadn't really thought about it that way but it makes sense.

Just thought I would add that a range imbalance can also occur purely by chance so it doesn't have to be restricted purely to btn vs bb though it should be generally much more rare from chance.

Edit: last sentence was not correct

The quote is about BB defense. I don't believe that is what the OP is talking about. Upswing is SPECIFICALLY saying, "Don't defend at MDF when in the BB because you will lose money."

This is what happens when you invoke the Janda...

I think this is similar in concept to when you call a raise by a player who plays fit or fold after the flop and only c-bets the nuts (similar because, again, you are playing hands that are -EV - against different players). If you call pre planning to take it away from this v, and v c-bets, you fold around 80% of your hands (give or take)....

Not really the same thing but I see what you’re getting at.
You’re talking about taking an exploitive line when our opponent deviates from optimal play. And your exploit is over folding. Now this exploit is itself exploitable... our opponent could switch strategies at any moment to cbet 100, and our strategy would fail.
This thread is about is about GTO play, so the assumption is that we are trying to defend at an unexploitable frequency...

Well a simpler example would illustrate why. Suppose, every hand in CBettor's Range is better than Caller's Range. Then the optimal strategy for the Caller is to check fold his whole range. Basically, MDF applies against opponents bluffs, but if opponent's range is predominantly value bets then we don't have to defend as much. This has nothing to do with this being BB Vs BU. Similar things can happen from other positions when one board favors one player's range. Basically, Cbettor should be betting enough of their range so that you defend MDF, otherwise they are losing EV compared to equilibrium. They are under bluffing. In this case, Cbettor just doesn't have enough bluffs.

Never imagined my simple question would invoke the Janda! i think you'd probably make a killing if you opened up a line for everyone's GTO questions at $2+/minute (and people will never run out of questions bc even when I feel like I understand **** finally, the next day comes and idk anything all over again).

I'll be your first investor as soon as i can figure out this PLO thing

When the BTN cbets the BB, in most boards, he has a big range advantage. This means that we should overfold a bit, to make up for the fact that we are losing more money on the hand. Or for whatever reason like that. this reason is wrong however, and people often don't understand why we overfold.

When we look at BTN worst bluffs, they are not entirely without eq. Hands like unpaired 65s, J8o, K2s, can still make plenty of pairs that beats the bb, hit some backdoor, or even win unimproved at showdown if the bb allows it. In other words, even his worst hands still have some SDV.
What this mean is that whenever BTN bets as a bluff, he is always sacrificing some small showdown value. This makes us to overfold a bit, because even if his worst bluffs are winning a bit more than 0ev, they would be winning a bit more than 0ev by checking too.
It's very similar to what happens when the bettor doesn't have enough bluffs and the defender can overfold, less drastic tough.

A counter example would be if BTN were perfectly polarized and had enough bluffs and value to cbet the flop 99% of the times balanced. This means that despite our range advantage we are getting crushed, only winning 1% of the pot. Can we overfold in that case? No we can't. Because the ev of checking a bluff is 0 for the BTN in that situation, and if we over folded then he would bet range and we never win the pot

I read that twice and I have no idea what it means

If you defend at MDF then villain will be incentivised to start checking back his bluffs to attempt to realize their showdown value. And by over folding we incentivize villain to keep betting with his bluffs.


But what I am wondering is why is it better for villain to continue betting with his bluffs?

If you defend at MDF then villain will be incentivised to start checking back his bluffs to attempt to realize their showdown value. And by over folding we incentivize villain to keep betting with his bluffs.


But what I am wondering is why is it better for villain to continue betting with his bluffs?