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What does "defend with x% of your range" mean?

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  • What does "defend with x% of your range" mean?

    Hi guys, new here. Wanted to pose a quick question. I can't remember what lesson in one of the master classes was, but I have notes from it that mention MDF. It says "If villain bets, use MDF to determine how often you should defend. MDF = 1 - bet/bet+pot."

    So if my MDF is 30% I have to defend with "30% of my range"

    What does that even mean? Do I take my range, guesstimate the top 30% of it, and defend with those hands? Later on in that same topic Jonathan says "You should be defending with 30% of your range even up to maybe 60%" which has me all kinds of confused. Can someone ELI5 this MDF/range defense topic for me?

  • #2
    MDF=Minimum Defense Frequency, how often we have to defend against an opponent's bet to prevent their bluffs from being immediately profitable.

    To determine how often a bluff has to make our opponent fold in order to be immediately profitable we do bet/(pot+bet). If we make a half pot bet .5/(.5+1)=.33. When we bluff half pot, we win 1 when they fold, and if we assume we always lose when they call, we lose .5 when they call. So if they call 2/3 of the time we will break even (.33*1)-(.67*.5)=0. So if our opponent folds more than 33% of the time, our bluffs are automatically showing a profit. On the flop and turn bluffs can even work less than this and profit because our bluffs will usually have some amount of equity on flop and turn.

    The reverse is true when our opponents bluff against us, if we fold too frequently their bluffs will immediately profit. So MDF determines how often we have to call, and it's the inverse (I think that's the mathematical term) of the formula for how often a bluff has to work to immediately profit. 1-(bet/(pot+bet)). If our opponents bet has to be successful 33% of the time, our MDF is 67%.

    If we have to defend X% of our range, we need to look at our whole range and see what hands we are calling/folding/raising with. We do this study off table and eventually it becomes easier to implement in game .

    For example say LJ opens and we call on the B, Flop comes Qs7h6h, LJ c-bets 1/2 pot. We know MDF against a 1/2 pot bet is 67%. So we might defend our range like below:

    Click image for larger version

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    We're raising or calling the opponents bet ~72% of the time, MDF is 67%, so Villain's bluffs are not immediately profiting. This all goes out the window if the opponent is playing an unbalanced strategy, the more weighted towards value an opponent is the more we should fold, the more they bluff the more we should call.

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