Every poker player basically knows how to react to bets.
When you have a weak hand, you fold. When you have a good hand, you continue by calling or raising…
…but that doesn’t help you with the close hands that fall on the borderline of call and fold. We need a more advanced process for that.
In this article, we’ll discover how and when to use two concepts to determine the exact optimal continue range in a given spot:
- Minimum defense frequency
- Pot odds
Both are useful and both have their place in a strong poker player’s arsenal.
Let’s dive in, starting with minimum defense frequency.
How to Use Minimum Defense Frequencies
Minimum defense frequency (MDF) describes the portion of your range that you must continue with when facing a bet to remain unexploitable.
In other words, the minimum percentage of the time you can call (or raise) to prevent yourself from being exploitatively bluffed by your opponent.
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 a simple one:
pot size / (pot size + bet size)
Multiply the answer by 100 to express it as a percentage. For instance:
$1/$2 Cash Game on the River
Hero has J♥ T♥ in position
River ($100) T♠ 9♥ 3♠ 6♦ A♥
Villain bets $50
In this spot, Villain is risking $50 to win a pot of $100. Let’s plug that in to the MDF formula:
$100 / ($100 + $50) = .67
…which comes out to a minimum defense frequency of 67% in this spot.
In other words, if he 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.
Here is a table with the MDF for the most common bet sizes:
|Bet Size as % of Pot||MDF|
When to Use Minimum Defense Frequencies
Calculating minimum defense frequencies is most useful against tough opponents with well-balanced ranges, or for just playing around with to elevate your default strategy…
…but when we have reads, it is not as useful, especially against weak players.
MDF is a great way to guarantee profit against opponents whom you know nothing about – especially when playing heads up – but it will not always be the most effective strategy. Keep in mind the following:
- Using MDF is not optimal against exploitable opponents.
- Disregard MDF when your opponent is unlikely to have bluffs in their range given the runout.
Here is an example that demonstrates both of these points:
25NL 6-Max Cash Game, 100BB Effective Stacks
Hero is in MP with
Hero raises to 3BB, Only CO calls
Flop (7.5BB) T♦ 7♥ 4♠
Hero bets 5BB, CO calls.
Turn (17BB) 6♣
Hero bets 12.5BB, CO calls
Pretty standard stuff so far. Hero opens ATs and bets twice with top pair on a coordinated board.
Let’s see a river.
River (42BB) J♦
Hero checks, CO bets 31.5BB
Hero checks and CO bets 75% pot on the river which comes out to a minimum defense frequency of 57%. Let’s take a look at the range of made hands (not including give-up bluffs) we would expect Hero to open, bet flop and turn, and check the river with:
(Overpairs are close, but against weak players I prefer betting those on the river rather than checking.)
If we were to abide by the MDF in this spot, ATs would be a clear call as it is in the top 57% of hands in your range here…
…but what could our opponent be bluffing with? Every two card straight draw completed, so CO would have to turn a hand like 87s or 65s into a bluff for our top pair to be good (if they even call those hands pre-flop).
At lower stakes, players are more hesitant to use made hands as bluffs, which makes it even less likely this river bet is a bluff.
This is definitely a spot to completely disregard MDF.
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How and When to Use Pot Odds Against a Bet
Unlike minimum defense frequency 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.
But you can skip those steps by using this formula:
(bet size) / (pot size + bet size + call size)
Multiply by 100 to express the result as a percentage.
Obviously pot odds have a number of uses from pre-flop to post-flop. When determining the optimal call range against a bet, pot odds are usually a more practical solution than the minimum defense frequency.
When facing a bet on the river, we can calculate our pot odds to work out how frequently we must be correct when calling. Below is a chart displaying pot odds with bet sizes commonly used:
|Bet Size as % of Pot||Pot Odds|
As the chart shows, there is a noticeable difference between MDF percentages and pot odds percentages.
Let’s go back to that hand with ATs. This time we’ll use pot odds to make our river decision.
River (42BB) T♦ 7♥ 4♠ 6♣ J♦
Hero checks, CO bets 31.5BB
CO bet 75% pot on the river. In order for a call to profit, Hero has to have the best hand at least 30% of the time.
Let’s plug in the ranges and see if Hero has the equity needed:
Once again, Hero’s top pair falls short of a profitable call on this river.
Always Consider Your Opponent
When thinking about MDFs and pot odds, you should always consider the style and range of your opponent before reaching a decision.
As the earlier example showed, if you are up against a player who simply does not have many bluffs, then you’d be best to exploitatively fold often, particularly against weak opponents.
Both concepts can help you out at the table when necessary, but always consider the tendencies of the player that you are faced with when coming to a decision.
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