Seeking ways to implement the MDF concept in real poker, I seem to have found some discrepancies between what minimum defense frequency and pot odds should dictate.

Let's use the AKQ like setup to make the problem clear.

AKQ type game that goes like this: It begins at the river. Board is 22234 rainbow. Effective stacks are 100bb. Both players' starting ranges are AhAs, KhKs and QhQs. Oswald is OOP and always checks, then Ivan, player in position can bet an amount of his choosing or check and see a showdown. Oswald now can only call or fold, not raise.

Ok, now, for a bet size of half pot, the GTO strategy for Ivan is to bet 100% of his aces, check 100% of his kings and bluff 33% of his queens. On the other hand, the gto response for Oswald is to call 100% of his aces, fold 100% of his queens, and call 33% of his kings.

If we observe, the Kings in Oswald's range have 25% equity against the range of the bettor (100% AA, 33%QQ).

Now, let's also note that Oswald is getting 3 to 1 odds on his call, meaning he needs 25% equity to warrant a call, and his kings have it. However, the GTO solution according to MDF and GTO+, is for Oswald to call only 33% of his Kings. How is this possible? If his kings already have the equity that pot odds dictate, why do we have to call only 33% of the time with kings, aka less often that pot odds dictate?

Second scenario. Ivan now bets 75% of the pot, and plays optimal gto. His strategy should be AA 100% bet, KK 100% check and QQ 44% bet.

Against this trategy, according to solver, Oswald's strategy is to call 100% with AA, fold 100% with QQ, and call with KK 13% of the time.

However against Ivan's betting range (AA 100% and QQ 44%), Oswald's kings have 31% equity. Pot odds here dictate we should call with at least 43% of equity, Oswald's kings doesn't doesn't have it, ergo he should fold them.

What to make of this? Or maybe more importantly, what do I seek with this?

I am basically trying to implement MDF in real poker, where hands on the river always have a % of equity against the bettor range, even though individual combos are either beat or beating.

Calling with KK more often probably makes you exploitable for calling too much.
So the bettor could start betting less often with KK and/or QQ to exploit you.

The purpose of GTO is not to make as much money as possible, it's to play unexploitable.

Pot odds don't dictate how often KK should call, MDF does.

KK has exactly the equity required to call. This leads to a call having the same EV as folding, 0, so it doesn't really matter whether he calls or folds vs. this strategy. We say that KK is indifferent here.

When KK calls 33% of the time, he is causing IP's QQ to become indifferent between bluffing and checking. You can check the math to show that the EV of betting QQ here is also 0.

At these frequencies neither player is offering the other an incentive to deviate, because there is no other strategy which can achieve higher EV.



You must have miscalculated the equity requirement, because it is 30% for KK to call. Our equity required is (amount to call)/(final pot size).

.75/(.75*2+1) = .3

31% != 30% because of rounding I suppose.

Then, what is the difference between calling according to MDF and just calling with the percentage of equity dictated by pot odds? MDF is for the whole range (of hands that beat a bluff) and pot odds are for a single hand?

So all the hands in MDF range have at least the minimum equity dictated by pot odds?

Yes.

Quick question on OP's topic.

If villain bets 50% on the river, he's getting 2-1 on bluffs getting through, therefore we should call with 66% of our range. (MDF)

We're also getting 3-1 on the call, and need to be good 25% of the time with pot odds.

Therefore, is it correct to estimate 66% of our range will win 25% of the time?

@Tuma. No because some hands will be 0ev calls while others are pure calls because of blockers so they win >25% of the time.

α = 0.5/(1+0.5) = 1/3
For the caller that is the optimal folding frequency that means he should fold 1/3 of bluffcatchers and since he has 2 of them (AA, KK) he should fold KK 2/3.

You should follow that frequency in order to make his bluffs indifferent.

Zenith poker has tutorial on this topic and a lot much more and it is all free.

1-α = mdf
ω = 0.5/(1+2*0.5) = 1/4 = pod odds