Minimum Defense Frequency (MDF)

Also known as: Minimum Defence Frequency, min defense freq, minimum defending frequency

The share of your range you must continue with so a bettor can't profit by betting any two cards as a pure bluff.

MDF is the minimum fraction of your range you must continue (call or raise) against a bet so that a pure bluff betting any two cards shows zero profit. Let \(b\) be the bet and \(p\) the pot before the bet: \[\text{MDF} = \dfrac{p}{p+b}.\] This is the exact complement of alpha, the bettor's bluff-success threshold: \(\alpha + \text{MDF} = 1\). The intuition: if you fold more than \(\alpha = \dfrac{b}{p+b}\) of the time, a 0% bluff prints money, so you must continue with at least \(\text{MDF}\).

Two critical caveats. (1) MDF is a defensive ceiling on folding, not a target you hit blindly — it ignores your equity when called. Against a polarized bettor who only has nuts or air, you should often defend less than MDF because your continues have no equity against value. MDF matters most against merged ranges and as a guard against overfolding. (2) It assumes one street; on early streets your equity and ability to realise it shift the right defending frequency.

When pool reads say opponents under-bluff, ignore MDF and overfold — that's correct exploitative play.