I am a small stakes (tournament) player and recently been looking into more GTO stuff as I would like to improve my game. In my current stakes I think exploitative play is superior but I would like to have a solid GTO basic strategy to default to and diverted from based on situation. Also when I move up this becomes more important.

One of the concepts I came across is minimal defence frequency. As far as I understand it, this just means you have to continue/call with a x percentage of your range based on betsize otherwise opponents bluffs show a profit. In practice I kinda struggle with it though.

Suppose we end up on some arbitrary river and opponent bets half pot. We have to call/raise with 2/3 of our range. Say our range consists of like 40 percent missed draws, a lot of ace highs and some pairs. If we have to defend 2/3 this would mean we have to call/raise ALL ace highs and pairs and even bluff raise some air (if we are capped somehow this might be an issue to balance).

I know this is a hypothetical spot, but I am confused if I should include missed draws and things that have zero showdown in my total range or only look at bluffcatchers+value and call 67 percent of that.

I think it is about your entire range so missed draws definitely count, but in our hypothetical spot I feel like we end up calling way to much. I mean what if 50 percent of our range is draws and opponent bet 1/3 pot?

I hope you can help me with this!

EDIT: Generally when explained it is assumed opponents have purely air and value, so that would mean our Ace highs should always be good, in practice this is where I struggle, if 50 percent of our range is missed non ace high draws we have an issue I would think. Or does that mean we are unbalance somewhere else in the hand and is this just a result (and thus kinda hypothetical)?

The simplest way to understand mdf is that you are trying to make villain worst (worst mostly means highest showdown value) bluff indifferent to bluffing. So if any hand you have doesn't beat villain's worst bluff, that hand probably doesn't "count" towards mdf. This means that you only apply mdf to your catcher/value region. But just because a hand is a missed draw it doesn't mean it has no showdown value, if your opponent worst bluff is J hi, then your Q hi is a bluffcatcher in this situation. This even shows up in BTN vs BB cbet flop, where the BB tends to overfold a lot partly due to his worst hands having low equity against the BTN bluffing region.

a good way to study this is by using Equity buckets. for example your facing a flop c-bet. your range Equity bucket is 4% strong hands(75%+) 36% good hands (50 - 75%) 20% weak hands (33- 50%) and the 40% air( less than 33%). if you face a pot sized bet your MDF is 50% and you need 33% equity to call. so if you visualise your range, you have to fold all your air since you haven't got the right price to call then. even though with your weak hands you have the right equity, you will need to fold half of them to keep within MDF. a good way to balance this is maybe fold the weak holdings without a back door and call the ones that do for example. even though you will never be able to know your exact equity vs a bet since you don't know your opponents betting range however if you study with equity calculators you can get a good estimate .

also one more thing. your equity of your hand is way more important than MDF. if you have a hand that has 0% equity you shouldn't call it to try make the MDF. if you look at GTO solvers they overfold quite often on certain flops due to not having enough equity.if your range is 60 air, you should fold 60% of your range to even a tiny bet.

Thankyou Lezaleas and R1zxo for the replys. My apologies for the late response, I had a very busy week. For the flop I can see the importance of equity over MDF, although not fully grasping the situation yet. For me the first step would be to understand river situations, in that case equity is irrelevant and MDF can be applied purely (right?).

I was struggling to find a good hand as an example, but I actually just played one in a 33 dollar tourney, where MDF would be interesting to look at. I opened from LJ to 2.2x (ITM, I had a large stack, some small immediate payjumps). I open like KJo+,K9s+, All suited aces, pairs, A9o+, suited connectors and gappers or something given position and dynamics. I had KJo in this instance.

BB defends, flop A44, 33 percent c-bet. I c-bet with nearly my whole range in these situations, because people overfold against (small c-bets), at least that is my read in these playerpools. Lets for argument sake assume I c-bet my entire range. Opponent calls, turn is a J bringing BD FD. Check-check. River offsuit 5. Opponent leads for 75 percent pot, making MDF 57 percent. Say I bet AJ and better on turn and checkback rest. As I am currently still playing I can't use Equilab so I just counted combo's of Q high and better. So all suited aces below AJs that aren't top2/full house (3*8=24 combo's), ATo, A9o (2*12=24 combo's). KJo (12 combo's), QJs, JTs (2*3=6 combo's), King/Queen highs like KQo, QTs, KTs, K9s I counted partial as I might bet some broadway draws (18 combo's). Giving me a total of 84 combo's. Meaning I have to call like 48, making KJo the exact cut off and a fold (all aces are 48 combo's).

Apart from possible math mistakes, forgetting combo's and just my possible play bad etc. , is this the right way to think about it? I completely disregard all other suited connectors etc as they have no 'showdown value'. To me that is kinda weird as they are still in my range, I dont see why it has to be part of my value/bluffcatch range and not my total range. Although it somewhat makes sense that my opponent bluffing with a hand that I already don't beat doesn't make sense to defend.

In game I ended up calling the KJo as I got like around 2 to 1 and I felt like my opponent was bluffing 1 in 3 times or more for that sizing and folding my best jack felt like folding to much. But I tanked for a bit because it seemed close.

What do you guys think about this hand? And more importantly, how I apply MDF? Do I do it 'right' now?

EDIT: I just realize I also have a lot of pocket pairs still in my range, that changes things. I also might bet more aces on turn given my small sizing on flop. Still, I hope it is a reasonable example to look at. I might also look into this hand in Equilab/HRC the coming few days if I am off table and update it.

If you have low suited connectors they probably don't "count" towards mdf in that situation. You should answer question like these with toy games and it's easier to see.

River and we face a pot bet,
villain's range is A(2)/Q(1), hero's range is K/J.

The solution is we defend MDF of our K region and we always fold J. The J don't count towards MDF here. This tends to work this way in real poker a lot, you can even see it in the flop against a cbet (so in your example your opponents are actually right to overfold because they have plenty of total airballs)

Thanks for your response. Your suggestion about toy games helps quite a bit. In your example it is clear that it makes zero sense to call with a J. In essence that is the same with our suited connectors in my hand.

I therefore see more of the reasoning to defend hands so that he doesn't win by overbluffing. My mistake was that I thought about him bluffing with hands that already have the weaker part of my range beat. I thought that would make sense because it generates so many folds while otherwise I might bet and he has to fold. But essentially that is a different question (for him), if he starts bluffing with combo's that already beat a large part of my range, that is ineffective for villain although me not being able to bet is beneficial (in some sense it is kinda a blockbet then). Also he not necessarily has to fold, because all of a sudden these combo's are part of his MDF range.

I still have one question though, if villain adds only one combo that I beat with a large part of my range, all of a sudden a lot more of my ranges becomes relevant from a MDF standpoint. I feel you still get counterintuitive and wrong results, let me demonstrate by changing your toy game a bit.

Suppose villains full pot betrange is equal distributions of A, K, 9. Our range is equal distributions Q, J, T, 8, 7, 6, 5, 4, 3, 2 (10 combos for easy math and I disregarded chops). In this case only Q-T are relevant in our range for MDF, meaning we fold T, call half of J and all Q right?

However, suppose we edit one thing, above his 9 was essentially his bluff range, A and K his value. Suppose we add a 1 in his range. All of a sudden our entire 10 combo range becomes active. We should call 7+ given MDF, him bluffing with one extra combo all of a sudden results in us calling way more often and him getting a lot more value. So I feel in this case still not all combo's count. How do we solve this/what do I do wrong?

EDIT: I actually realized that in the latter case we actually are +EV in calling so much as far as I understand it, because if he has equal distributions we always win when he has a 1, that is 25 percent of the time. We win 3/5 if he has a 9 (as our Q, J, T beats it but 7, 8 not), that is an additional 3/5*0.25 is 15 percent. In total we win the pot 40 percent of the time instead of the needed 33 percent. I think this has to do with the non balancedness of his range/not completely pure value and bluffs.

In essence my point stands though in case he has 10 combos A, 10 combos K, 10 combos 9 and adds one single combo of 1. If our entire range becomes active due to that single combo, we are calling way to much, if you take the limit we end up winning 3/5*0.25 is 15 percent against his 9, a little more due to beating the one combo of 1. But that clearly is way less then the needed 33 percent.

EDIT2: In our toygame we have 14 different cards in a deck, adding the 1 made sense to avoid chops haha.

You still wouldn't call 2-8 because you are way behind his bluffing region, just beating 1 combo out of 11 wouldn't make you want to defend. Yes, villain's getting more than his fair share of the pot this way, and no you are not getting exploited because there's nothing you can do to solve it. Kinda explains why small range cbets are strong on the flop with a range advantage

Pot Odds >> MDF when it comes to calling river bets.

When facing a river bet, you can only call with hands that have correct pot odds to call. You don't knowingly make unprofitable calls just to remain exploitable; that's like shooting yourself in the foot to prevent someone from stealing your shoe.

The way to solve your toy game is straightforward. Facing a pot sized bet, EVERY hand you call with needs at least 33.3% equity to call (pot odds). In this case, you would fold all of your 2-8 because they only have 25% equity, and are therefor a losing call. Even solvers behave this way.

Thanks for the responses! But in that case when is MDF really relevant? In spots before the river equity, position and range (dis)advantage change it a lot if I understand correctly. On the river it gives you suboptimal results. Does that mean it is just a flawed concept?

@tombos21, this makes a lot of sense. It is kinda what I do now, if a spot is unclear to me on the river I usually try to estimate bluffing combo's versus value combos and see if I beat enough bluffing ones to profitably call with my specific hand.

I think there is nothing wrong with this and almost always superior (I am definitely dropping the MDF concept for in game situations). I am just trying to understand the GTO side of things. Because I think to check if your specific hand is profitable to call is not always correct either. Suppose we are on a river where we only have J, opponents has A, K, Q in his full pot betting range. We clearly fold. Now our opponent starts bluffing 9 in equal amounts to the A, K, Q. We win 25 percent of the time, we need 33 percent so we fold based on pot odds. His 9 has 100 percent fold equity and is crazy profitable. Aren't we getting exploited here and shouldn't we call partials of J here to counter that?

I am not at all sure about it, it might have to do with his range being unbalanced and value heavy (he clearly has to little bluffs right? For a potsized bet he needs 1 bluff for every 2 value, not 1 for every 3 right?)

In this example, we would end up folding 100%. Yes you are getting exploited. No, there's nothing you can do about it. In this hypothetical your just gonna get run over.

Let's use the same example but change the size of the bet to half pot. This changes your pot odds to 25%. So it's a break-even call. This is the scenario where you would use MDF in theory. You would call with your break-even bluff catchers just enough to stop villain from exploiting you.

Hmm okay. I still find it very confusing. Because now it seems MDF is a much more niche thing then I assumed it would be. I am gonna read up on it some more in the future, but for now I will definitely use pot odds. Thanks for the help fellow 2+2'ers! If anyone has a good suggestion about GTO study material (preferable a good book/video series), let me know. I would like to get some more acquainted with it.

The problem with only thinking about pot odds in a spot where villain bets with a polarized range OTR is that you are basically calling every single one of your bluffcatchers when you figure out you beat say 33% of villains betting range, which would be your potodds vs a pot size bet.

Thinking in terms of MDF is a bit better because you make sure you don't call all your bluffcatchers and look to call with the the best ones that blocks value or unblocks bluffs.

Obviously blockers/unblockers will affect how much of villains range you beat but it's harder to figure out in-game. It's easier to know why some combos are better bluffcatchers than others and pick the best ones.

What do you use to study with equity buckets?

The book modern poker theory , explains it all there

Thank you all for the replies. MDF is still a bit confusing to me but the general idea is clear to me now, thanks! If I have some further questions/examples I will post them (possibly in a new thread).