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Comment by waprin | Hacker News Reader

> What's interesting about this is the minimum defense frequency is based on what the strongest hands you can possibly have in that situation are and the opponents possible hands do not even factor into it.

This is actually not quite true. MDF is purely a formula based on pot size and the bet size (pot size / pot size + bet size). The fact that it doesn't consider various ranges is why it's not really useful - it was a simplified formula used to try to understand the game before solvers existed.

There are situations where your opponent can bet any two cards profitably and you do have to fold - imagine they bet the size of the pot, but have the better hand 99% of the time, you're simply forced to let them bluff the 1% of the time they're bluffing. MDF is a pre-solver concept and not an especially useful concept in the modern game.

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I'm pretty sure mdf applies to rivers when you are last to act. I'd be interested in being proven wrong however if you have solver output that shows it. I remember studying solver output and seeing it in action.

I know that before the river there are range advantages that make defending mdf a losing play.

What's true is that equilibrium strategies typically converge to solutions where the better makes the caller indifferent between calling and folding. In the toy example I've given where the betters range is so strong, the caller should always fold, the better now has an incentive to add more bluffs to the range to take advantage of the folds. Then the caller will want to call more. This might converge to the MDF which might be what you're suggesting, assuming we started with ranges that could have enough bluffs given the runouts.

If you open up the solver, and give one player only Ace-Ace as their starting range, and the other player a pair of twos, and the board Ace-Ace-Three-Three-Three, then the pair of twos will fold 100% on river and will not call at MDF.

You are absolutely right! Haha damn back to the drawing board

I think another way to say this is that MDF works only if you're in a spot where you have hands that are strong enough to call. If you play every hand, and you see every river in that 100into100 situation, you shouldn't call with 50% of your hands because your hand range is too wide for that to be profitable.

So you can't make a ton of mistakes say "MDF" and call off, you have to have done the right things in previous streets to end up with a range that can call at MDF. That range (and those street actions) require an understanding of GTO (and the adjustments needed when someone isn't playing GTO).

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