hi,

HU sb raises vs bb call. pot is 60.

board is A63

sb bets 70% of range for 25% pot; 15 into 60.


according to the minimum defence frequency formula, the bb should be defending 1/1+0.25 = 80% of hands, yet piosolver folds 27% of hands.

why does it fold 7% more than the MDF?



thanks

MDF assumes checking has 0 EV
On the flop, checking doesn't have 0 EV with any hand

why not? what does that mean sorry?

MDF is trying to make villain indifferent between bluffing and checking

but why does checking have any EV usually?

Even if SB has something like 72s he can check-back and turn a straight draw, or pair which has some showdown value, as well as the chance to further improve to trips/2P.

to have 0 EV is to lose the pot every single time no exception

BB will always over fold the flop because he essentially had a discount preflop leading to a disproportionately wider and weaker range than would otherwise occur. Going to be pretty rare for the BB to defend = or greater than MDF on the flop. MDF will be pretty accurate for most turns/rivers though (unless the turn/river card is disproportionately favorable to one or the other player due to range asymmetries -- which does occur).

So for what it's worth, MDF is the frequency that you need to defend to not be exploited for a given bet size with one street of betting. When we fold more than MDF we let villain auto profit by betting. This is bad, of course, but it may also be optimal.

For instance, suppose you always have aces and I have 44-KK and the board is 33222. I win whenever I have my single combo of 33, and you win whenever I have one of my 54 combos of 44-KK. Pot is $1, stacks are $1. You can bet $1 every time (even though you technically have the condensed range!!) because I can't defend at the MDF. Here the MDF is 1/(1 + 1) = 1/2, but I can only defend 1 out of 55 combos.

So villain's EV is 54/55 - 2*(1/55) = 52/55, so basically pot.

The takeaway here is some boards are so good for one player that the other player cannot defend at MDF.

(and obviously this is an extreme example to clarify the point)

Nice post

Lightbulb af

I think this kind of thinking is where people go wrong about MDF. It really has nothing to do with exploitability. It just tells you the point at which fold equity for villain is 0.

AA should purely check in this example regardless of position. You should never bet into a perfectly polarized range (opponent only has hands with 100% or 0% equity). You already beat KK-44 at showdown so there is no benefit to folding them out. Betting just gives more action to 33.

It is still true that the polar range massively overfolds compared to MDF when AA bets, just want it to be clear that AA should not bet here. Also maybe worth pointing out that AA defends at exactly MDF when the polarized range bets.

You're right, careless choice of words on my part. By 'exploit' I meant 'autoprofit'. Like, a GTO strategy will 'exploit' the fact that you can't call enough, even though GTO is not playing exploitatively. This is one of the problems of repurposing existing words for technical jargon

Again, good point. I was focusing on finding a scenario where a player can auto-profit because the other person can't defend enough and wasn't really thinking about optimal strategies. This was a ridiculous/extreme scenario illustrating why we can't always defend at MDF.

Yeah, thanks for the clarification! And good point about AA defending at correct frequencies.

But at GTO you still must defend at MDF. It's just that in the same way you choose whether to raise/bet/call/check/fold an individual combo based on where it is in your overall range, you also choose whether to play more or play less an individual flop/board "combo" based on where it is in the overall "range" of possible flops/boards.

So if a board favors Villain, you will defend less than MDF dictates. But when if favors you, you will defend more than MDF dictates. So in a GTO/NE strategy, accross all boards, it should average at MDF.

I'm new to theory, just started learning it. But am I wrong? Seems like a quirky and unusual way to think but I think it might be correct.

I don’t think that’s true, but more importantly i don’t think it matters .-.

Constructive reply, solid argument! Keep it up

For what it's worth your reply is not constructive either and is not really worth typing out on an online forum. You're going to get a lot of useless/thoughtless replies when utilizing the internet. At the very least the poster you're referring to has made several contributions to this forum within the last week regardless of that one post. He also is directly replying to your question, "But am I wrong?" with his opinion.

You don't need to defend at MDF because sometimes you simply get a bad board/runout as ranges are not symmetrical this will definitely lead to certain situations in which it simply makes sense to over fold. Attempting to defend at an MDF frequency will just cause you to lose money more money than if you had just folded more in these situations.

MDF is useful in getting a reasonable approximation of what frequencies are likely close to at equilibrium, but it definitely isn't always correct. The most important thing is always simply "what is the most profitable play I can make for my hand/range/this spot--etc" and the answer to that even at equilibrium can and will be to sometimes fold more than MDF.

You're right, my bad - I'm new here & meant no harm.

Right, got it now, thanks.

It also depends on board texture, this happens most frequently in river spots I think where a certain card may strongly favor one player thus the base frequencies can get really thrown off.