Introduction to minimum defense frequency.

Introduction to minimum defense frequency

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There is a lot of interesting math in poker, and we use it to determine profitability, to judge balance and other relevant factors throughout a hand. When somebody makes a bet, they give their opponents certain pot odds to call, and there is math to determine how often the bet needs to work to be profitable. For example, if your opponent bets 100% of the pot, then that bet needs to work at least 50% of the time to be profitable.

Minimum defense frequency (MDF) is far from the most common concept, yet a very useful and important idea to decide how large of a portion of your range you need to continue with against a bet of varying size. Your minimum defense frequency is the inverse of your opponents profitability percentage, so in the case of a pot bet, your opponent’s bet needs to work 50%, which means that you need to continue (call or raise) at least 50%.

For example, if your opponent bets 100% of the pot, then that bet needs to work at least 50% of the time to be profitable.

The MDF formula is: pot size / (pot size + bet size).

This table outlines your MDF versus standard bet sizes:

Practically, what this means is that when you face a half pot sized bet, getting 3:1 pot odds, around 67% of your range needs to have at least 25% equity. You can defer from GTO, and proper use of MDF in a structured manner by recognizing situations when your opponent’s range is likely to be disproportionately skewed towards value. You may find yourself in a river situation with a board runout that does not facilitate a lot of natural bluffs like busted draws or otherwise, and in such instances, it would be prudent to under defend your range. At least against weaker opposition that can be assumed to lack balance in their range.

Let me give you an example:

The board: 

 

The river:

So called natural bluffs often consist of busted draws, but when you think about this river, a lot of those natural bluffs do not exist, because the busted draws almost all turned into actual value hands. The flush draws made a flush, and the straight draws made a straight. The idea of natural bluffs is important, because the weakest players are quite poor at bluffing. This often results in under bluffing, as in not bluffing enough. 

When your opponent lacks natural bluffs, you can often assume that they may find themselves under-bluffing. As mentioned previously, when this happens, you can deviate from your MDF in good conscience. To meet the required amount of bluffs in scenarios where natural bluffs are lacking, you need unnatural bluffs. Unnatural bluffs are often when you turn something like a pair, or two-pair into a bluff. This is generally rare for people to do, as they prefer to just check these hands down instead. 

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