equity denial

How Equity Denial Influences (Almost) Every Decision & Your Results

Equity denial underlies almost all of your decisions at the poker table, even if you don’t realize it.

When understood and considered correctly, it can increase your edge in every spot and thus improve your win-rate.

In this article, I will explain exactly what equity denial is and how it ought to shape your strategy. I’ll also break down an interesting but commonly misplayed type of board, on which equity denial is a determinant factor.

Let’s get started!

What is equity denial?

Equity denial is when you prevent a player from realizing his equity by forcing him to fold before showdown. So, if you fold a hand that had 40% equity to win the pot versus a flop bet, you were denied 40% equity.

This concept becomes less and less applicable the deeper you are in the game-tree (visualized below).

PREFLOP > FLOP > TURN > RIVER

Equity denial is most important preflop, which is the main reason why preflop limping should be avoided–you have no chance to take down the pot and prevent your opponents from realizing their equity. 

Although this concept sounds similar and even overlaps with the concept of bluffing, make no mistake–they are not the same.

To help you better understand this distinction, I’ve prepared a couple of hand examples. Here’s the first one:

Online $0.50/$1. 6-Handed. Effective Stacks $100.00.

Hero is in MP with J T
utg folds. Hero raises to $2.2. 3 folds. Villain calls from the BB.

Flop ($4.7): 5♣ 5 3
Villain checks. Hero bets $2. Villain folds K 8

In this hand, Hero’s flop bet should be considered a bluff because he made the Villain fold a hand with much better equity, as you can see from the Flopzilla calculation below (Flopzilla is an advanced poker range analysis tool–like PokerStove or Equilab on steroids):

Editor’s note: We’ve highlighted the relevant information in red boxes throughout this article for those of you unfamiliar with Flopzilla and Piosolver calculations.

equity denial flopzilla calculation 1

JTs has 24.39% equity versus K8s on 553 (as pictured in the red box on the right)

Let’s take a look at the second hand:

Online $0.50/$1. 6-Handed. Effective Stacks $100.00.

Hero is in MP with 4 4♠
utg folds. Hero raises to $2.2. 3 folds. Villain calls from the BB.

Flop ($4.7): 5♣ 5 3
Villain checks. Hero bets $2. Villain folds K 8

Let’s run this one through Flopzilla as well:

equity denial flopzilla calculation 2

44 has 72.42% equity versus K8s on 553 (pictured in the red box on the right)

In this case, we cannot say Hero bluffed because he didn’t force a better hand–one with higher equity–to fold. What Hero’s bet did do, though, was prevent the Villain from realizing his equity.

This is important for his specific hand because on many turns–any diamond (except the 4) or broadway card–he will be forced to fold versus a bet. Unless, of course, he had a solid read that the Villain probes and barrels with too many bluffs.

So, Hero’s decision to c-bet this hand prevented 3 bad outcomes:

  1. Villain hitting a King or 8, which happens on 12% of turn cards.
  2. Villain bluffing Hero out of the pot on a scary turn card (any non-4 diamond or broadway card).
  3. Even if Hero calls on the turn, Villain can double barrel bluff and Hero will likely fold on most run outs.

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How should equity denial influence your strategy?

Equity denial influences two major aspects of your strategy:

  1. The bet size you should use on a certain board
  2. The frequency with which you should c-bet on a certain board

With this in mind, let’s look at a hand example and solver solution to see equity denial’s influence in action.

Online $0.50/$1. 6-Handed. Effective Stacks $100.00.

Hero is dealt two cards on the button
3 folds. Hero raises to $2.5. SB folds. Villain calls from the BB.

Flop ($5.5): 8♣ 8 2
Villain checks. Hero…?

Let’s plug the details of this hand into the solver to see what it suggests:

equity denial solver calculation

The solver chooses to c-bet every hand at a 100% or near-100% frequency, using mainly a 33% pot sized bet (it uses a larger size ~7% of the time).

This is a somewhat shocking solution. Let’s evaluate the inner workings of it to better understand it.

Why does the solver choose to c-bet 33% of the pot in this case?

We’re about to get deep into the weeds. If you have trouble following any of this section, bear with me until the last paragraph for a plain explanation.

To answer this question, let’s first look at the optimal defense frequencies (according to Piosolver) for the Villain facing the 3 different bet sizes.

For Hero’s bluff to breakeven, it needs to work a certain percentage of the time according to this formula:

Required fold equity (RFE) = Bet size / Bet size + Pot size 

Now, I’ll plug each of the solver’s three bet sizes into this formula and compare it to the Piosolver-suggested defense frequency:

1. Against a pot sized bet, Piosolver suggests that the Villain needs to fold 62% of her hands.

Required fold equity = 55 / 55+55 = 0.5 -> 50% of the time

So, at this price point, the Villain is overfolding by 12% (62% – 50%).

2. Against a 66% pot sized bet, Piosolver suggests that the Villain needs to fold 53.6% of her hands

Required fold equity = 36 / 36 + 55 = 0.395 -> 39.5% of the time

At this price point, the Villain if overfolding 14% (53.6% – 39.5%).

3. Against a one-third pot sized bet, Piosolver suggests that the Villain needs to fold 41.5% of her hands

Required fold equity = 18 / 18 + 55 = 0.246 -> 24.6% of the time

So, at this price point, the Villain is overfolding by 17% (41.5% – 24.6%).

Based on these numbers, we can postulate that the solver chooses the 33% pot sized bet because it forces Villain to fold the most amount of equity for the least amount of chips invested, and since most of Villain’s range has missed this flop, it makes sense to take advantage of this ripe bluffing opportunity.

Why does the solver choose to c-bet nearly 100% of hands in this case?

I would argue this frequency is chosen by the solver because Hero is forcing Villain to overfold by 17% with a c-bet. All but the very strongest hands–which, of course, do not want to see a fold–will massively over-realize their equity since they force a lot of hands to fold that would otherwise have good equity.

The chart below maps the equity that each hand in Hero’s range had against Villain’s folding range:

equity denial heatmap

For example, you can see that 97s had 35.67% equity against the range that it forced to fold. This significant equity denial, when coupled with Villain’s inability to protect enough of her range, makes a c-bet extremely profitable.

Even when Hero is ahead with a hand like pocket fours (72.5% equity), a c-bet folds out a huge chunk of Villain’s range that had 27.5% equity. Plus, this ensures that Hero won’t be bluffed out of the pot on later streets–a strong possibility with a vulnerable hand like pocket fours.

Such is the power of equity denial. It’s very common on dry, paired boards like this one because Villain is forced to fold hands that otherwise have a decent amount of equity.

Equity Denial Conclusion

Equity denial is an essential concept for any poker player to understand, regardless of skill level.

Finally, it’s important to remember that decisions that are influenced by equity denial are also influenced by:

  • The potential value gained by betting.
  • The amount of value you might lose when you are called or raised by better hand.
  • The frequency with which you need to fold on the turn if you chose not to bet.

Thinking about all of this can be difficult, but, as with anything in poker or life, with practice you’ll become proficient.

That’s all for today! I hope you’ve enjoyed it, and as always if you have questions or feedback you can use the comment box below.

Good luck, grinders!

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