How to Make Profitable Decisions Against Any Bet Size (Minimum Defense Frequency vs Pot Odds)
Faced with a bet, you can react in one of three ways: call, fold, or raise.
It’s usually pretty apparent when raising is the correct decision–with super strong hands that want to extract value and with bluffs that want to steal the pot. Whether to call or fold, on the other hand, is often not so clear.
In this article, I will explain two concepts the best poker players in the world use when deciding what to do versus a bet––namely, minimum defense frequency and pot odds.
Let’s get started!
This article has been updated to help you better understand minimum defense frequency and pot odds, originally published on 4/4/2017 by Ryan Fee.
How to use minimum defense frequency
Minimum defense frequency (MDF) describes the portion of your range that you must continue with when facing a bet in order to remain unexploitable by bluffs.
In other words, MDF is the minimum percentage of time you must call (or raise) to prevent your opponent from profiting by always bluffing you. If you fold more often than the MDF indicates, your opponent can exploit you by over-bluffing when they bet.
The formula to calculate MDF is simple:
pot size / (pot size + bet size)
Then, multiply the answer by 100 to express it as a percentage.
Let’s consider an example:
Online $1/$2. 6-Handed. Effective Stacks $200.
Hero is dealt J♥ T♥ on the button
utg folds. MP raises to $5. co folds. Hero calls. 2 folds
Flop ($13): T♠ 9♥ 3♠
MP bets $8.5. Hero calls
Turn ($30): 6♦
MP bets $22.5. Hero calls
River ($75): A♥
MP bets $37.5. Hero…?
In this spot, Villain is risking $37.5 to win a pot of $75. Let’s plug that into the MDF formula:
$75 / ($75 + $37.5) = .67
The minimum defense frequency is 67% in this spot. So, if Villian were bluffing, this bet would have to force a fold at least 33% of the time to make a profit––Hero has to call more often than that to prevent Villain from exploitatively over-bluffing.
For your reference, here is a table with the MDF for the most common bet sizes:
When to use minimum defense frequencies
You should use this concept when you are doing off-table work in order to get familiar with the hands you should be calling with against strong opposition. Doing so will serve your intuition well as you move up through the stakes, where you will be playing against better and better players who will know how to put pressure on your ranges.
However, you will rarely use this concept in practice. This will be especially evident at the lower stakes, where players have very unbalanced strategies.
The only situations in which using MDF would be superior to using the pot odds, which we’ll discuss momentarily, is when playing against unknown players, or in an unknown environment without population reads.
For example, suppose you are visiting Guatemala for the first time and decide to play a session at a $500 ($2/$5) buy-in game in a casino.
It’s your first hand, and you are in the big blind (BB) holding J♠ T♥. It folds to the cutoff (CO), who looks to be a young and possibly experienced player. He opens to $15. The button and small blind fold. You call.
The flop comes J♥ 8♠ 5♦. You check and the CO fires a $20 c-bet, which you call.
The turn is the Q♠. You check and the CO bets $45, which you call.
The river is the 4♦. You check, and the CO bets $110.
You are now forced to make a decision with a marginal hand, with no relevant or reliable information about this opponent’s strategy.
This is a situation to use the MDF concept. So, let’s work through the thought process in this scenario. For this, we will use PioSolver. (Flopzilla would work as well.)
Editor’s note: As always, we’ve used red boxes to highlight the relevant information in each PioSolver calculation for those of you unfamiliar with solvers.
Here is the BB vs CO defending range (for live games) recommended in the Upswing Lab:
And here is the Upswing Lab-approved CO open-raise range:
Now, I’ll input these ranges and the details of the hand into PioSolver to see what it suggests:
As you can see (unless the text is too small), the solver suggests a mixed strategy with JTo–folding 78% of the time, calling 20% of the time, and bluff-raising 2% of the time. Complex mixed strategies like this are nearly impossible to execute as humans, however, so we should simplify the solver’s suggestions to make it more practical.
In this case, I would humanize the solution by folding JT every time, which I’d compensate for by calling with AJ every time (the solver suggested calling with AJ just 54% of the time).
Playing this way means never making a huge mistake. This is what MDF is best for––protection from making hugely -EV plays.
When to avoid using MDF
As mentioned in the previous section, you’ll rarely use MDF.
In this section, we’ll discuss the rest of the situations, in which you should definitely not use MDF. There are three in particular:
1. When defending against flop c-bets OOP
It’s a common misconception that you should use MDF against c-bets after defending from the big blind. This is false, and it has been proven by the solvers. Trying to defend at MDF in these spots requires making -EV plays with a portion of your range.
The fact is when you see the flop from the BB when defending against an open-raise, you will almost always be at a range and positional disadvantage. This gives the opener the opportunity to play aggressively, and to bluff a lot, but he paid for that opportunity preflop when he took the risk of opening the pot.
2. When your opponent cannot have natural bluffs
If your opponent’s range is exclusively made hands, it’s foolish to use MDF. Why try to remain unexploitable by bluffs when your opponent doesn’t have any obvious hands to bluff with?
For example:
Online $2/$4. 6-Handed. Effective Stacks $420.
Hero is in MP with A♥ 3♥
utg folds. Hero raises to $9. CO folds. BU calls. 2 folds
Flop ($22): A♠ Q♦ T♠
Hero checks. BU bets $11.5. Hero calls
Turn ($45): 9♥
Hero checks. BU bets $30. Hero calls
River ($105.50): K♠
Hero checks. BU bets $50. Hero…?
In this type of spot your opponent will not have any missed draws––everything in his range is either a pair or better. Here it doesn’t make sense to call down at MDF, since the range he’ll take to the river is incredibly strong, and he is unlikely to turn any made hand into a bluff.
(Note: There is an argument to be made for folding this hand on the turn, since most players will not be bluffing enough in this situation.)
3. When you are playing against weak opposition
Against weaker players who don’t have well-balanced ranges (which happens often), you’ll need to play an exploitative strategy in order to maximize your winnings.
This doesn’t always mean bluffing aggressively or calling down light. It can also mean folding more than usual when your opponent doesn’t bluff enough in certain spots.
So, be aware of who you are playing against, and don’t play like a robot. Take into account all the information available and remember that you are playing against people, not machines.
How and when to use pot odds against a bet
Unlike MDF calculations, pot odds should be kept in mind virtually every hand.
Pot odds are expressed as a ratio, such as 2-to-1, which can be converted into a percentage––33% in this instance.
Here is the formula for calculating pot odds:
(bet size) / (pot size + bet size + call size)
Multiply by 100 to express the result as a percentage.
Let’s reconsider the first hand example and calculate our pot odds on the river:
Online $1/$2. 6-Handed. Effective Stacks $200.
Hero is dealt J♥ T♥ on the button
utg folds. MP raises to $5. co folds. Hero calls. 2 folds
Flop ($13): T♠ 9♥ 3♠
MP bets $8.5. Hero calls
Turn ($30): 6♦
MP bets $22.5. Hero calls
River ($75): A♥
MP bets $37.5. Hero…?
The pot is $75.00, and we need to call $37.50. This is how our formula should look:
37.50 / ( 75 + 37.50 + 37.50) = 37.50 / 150 = 0.25
Multiplying the result by 100 gives us the percentage of the time that we need to win when we call in order to break even: 25%.
In other words, if we have more than 25% equity against Villain’s betting range, we should call every single time, regardless of where the hand falls in our range.
Pot odds have a number of uses from preflop to postflop. When determining the optimal call range against a bet, pot odds are usually a more practical solution than the MDF.
When facing a bet on the river, you can calculate pot odds to work out how frequently you must be correct when calling. (It’s more complicated on earlier streets because the runout may impact who wins the hand.)
For your reference, here is a chart displaying pot odds with commonly used bet sizes:
Conclusion
When thinking about MDF and pot odds, you should always consider the style and range of your opponent before making a decision.
As the examples showed, against a player who simply does not have many bluffs–either because of the nature of the spot or because of their playing style–it’s best to toss MDF aside and exploitatively fold often. Pay attention to tendencies like these in order to apply MDF and pot odds properly.
That’s all for today! As usual, if you have any questions or feedback, don’t hesitate to use the comment box below.
Good luck, grinders!
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