It seems like MDF's and even the indifference principal are at best incomplete ways to conceptualize poker situations. The indifference equations of GT and the idea of having a MDF to stop auto profit in post flop spots does not account for range advantage/equity distributions, etc right?

So, yeah, seems pretty obvious that we can't defend the same on AK8r as we would on JcTc8s when UTG opens for 3x off a 200bb stack in a ring game when we flat from the bb or the BU.

So, how should we use MDF?

Should we; try to stick about to them exactly and only when there is not a very clear range advantage for one of the players over the other?

Should we; always try to start with the MDF/indifference as a guide but just sort of modify the way we continue based on the way specific ranges interact with different boards?

Can we really stick more or less to the MDF ideas and expect it to be a more reasonable guide than maybe I'm thinking?

Or Should we just about pitch the ideas all together because they just don't really work with a game as complex as NLH?

Wow awesome thread. I will start by suggesting humans implement mdf best from the river (facing a call) and play the hand backwards into the ranges they assign to each other.

So if the bettor on the river should have a favorable range with lots of seed combos that make sense, then the potential caller has to balance those with the draws that missed and any made hands caller also beats and decide to call or fold, with the odds provided.

The more accurate the estimation will give the correct MDF.

Each runout versus your range and your actual cards would have a theoretical perfect MDF which is then compared to the size of a potential call.


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^^^^^ i cant do this and don't even try, full disclosure, just theorizing...


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I will try to find it but there was a thread where a poster ran simulations and found that most of the time MDF was a pretty good approximation for defending until ranges were completely asymmetrical. The poster was bob_ something. It had a lot of good discussion and he even explained his simulation methodology.

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But facing a river call is just the easiest scenario to implement, theoretically. You know everything about the hand and both ranges.

In theory, MDF can be applied at any point in the hand, inside out, or way back at the opening bet.


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Yes. Bob's simulations simulated non river calling frequencies because that was the point of contention among the posters. It of course made assumptions about ranges as it wasn't a full strategy solution.

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I think MDF is pretty much irrelevant on the early streets, especially when one of the players is in the blinds. The game is already "asymmetrical" if one player paid less money than the other to see the flop.
MDF probably has more relevance when there's a pot between UTG and BTN, for example, as both paid the same price pre-flop, but board texture will usually give one or other player a 5% or greater range equity advantage, so sticking slavishly to MDF numbers is going to be sub-optimal. In addition, position is a thing. The player in position usually wins a greater share of the pot than his raw equity would indicate. i.e. being IP allows you to continue at higher frequencies, being OOP does the opposite. As far as I can tell, MDF only comes into its own (especially on the river) when facing a jam. If there is stack depth behind (or future streets to play), there are options other than call or fold.

Thanks so much.(I really appreciate this)

Please find it man haha... :3

But your saying that pen & paper MDF matt janda type style calcs were basically "exactly" the same to nash equil solutions in crev/piosolver?
Tbh i'd say they are similar/close, but MDF just aims to make villain indifferent to betting or checking (ev of checking = ev of betting) not nec best overall range strat to defend MDF even the solver will show.

Also MDF is pretty negligable if there are massive range advantages/nut combo advantages right?

As I know at equilibrium if player play mix strategy with some hand EV of those two actions must be the same.So if we are on the river V should bet some bluffs and c/f some bluffs so its obv that in order to make him indifferent we must call MDF,so its not that weird that pio and pen and paper give us close to same results.
If V gets to the river only with nut (so he has range advantage) obv he never checks so there is not mix strategy and no need to make him indifferent to anything we should just fold every time.

No I am saying Bob's (bob_f I believe) simulations tended to converge really close to MDF calculations when ranges were symmetrical and diverged by I think +15% when ranges were extremely asymmetrical. These results even held for streets before the river.

I also remember his methodology seeming reasonable at the time as in he made some assumptions and simplifications but nothing to the extent that you could throw out the results based only on his methodology.

I am not quite sure what you are stating here. I agree that MDF aims to make villain indifferent to betting and checking his bluffs. I also agree that MDF is not equivalent to an NE strategy in all situations. Bob's simulations were just surprising in that it should that MDF can be a pretty good approximation in certain situations.

Yes as ranges became more asymmetrical the simulations defense frequency would stray farther from mdf.



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The naive toy game model of MDF is not very useful except for some river situations.

To get a more mature model of MDF you need to take into account
1. Range asymmetry
2. Price paid to see the flop and risk assumed preflop
3. Flop texture
4. Position
5. For the IP player, the value of checking
6. For turns and river, price paid in the previous street to see the current street
7. Probably more stuff I'm forgetting about

As you can see it's way way way more complex than just A-1. You can sort of guesstimate how much these factors will alter the defense % but the only way to know for sure is to use solvers. To give you a relevant example, naive MDF for the BB vs a BU half pot flop bet is 66%, in reality when you take into account all other factors, the optimal number is closer to 50%


If you want a rough guideline, here are some situations where you should definitely fold more than MDF, double so if more than one applies at the same time:
1. You're OOP
2. You have a capped/weak range preflop
3. A turn or river card comes that completes so many draws that it becomes almost impossible for villain to have a pure bluff.

http://forumserver.twoplustwo.com/15...df+limit+games

That's the thread I think was referred upstream.

Tipton Volume 2 basically says that MDF is dangerous to use unless there are no more future streets of betting.
The problem with that book is it is so dense that I can't find the page when I just read this yesterday.

That is the one thanks, Bob.

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MDF on rivers is usually good. You can compare MDF to what piosolver spits out and its usually within 1%. Obviously lots of factors come in to play which deviate from this value and most are mentioned in this thread.

MDF is a good quick and dirty start as you can get an answer in under a minute and it should point you in a good direction.