At first, bluffing with hands that have showdown value might seem unintuitive - we often choose our best bluffs from those hands at the bottom of our range that have no showdown value. But with modern solvers such as PioSOLVER, we often find opportunities to spot unconventional lines and ask ourselves “Why?” This can lead to deeper revelations that allow us to logically filter out the statistical noise inherent in a mathematical tool like PioSOLVER, and recognize solid theoretical concepts at work that we can apply ourselves in practice.
We'll talk more about how we accomplish this as our analysis goes more in-depth. First, let's take a broad look at PioSOLVER's overall approach to an example hand.
Hand Example 1
In this hand, we're playing $10/20 and are defending our BB from a SB open.We have the effective stack at just over 100bb.
Preflop
The table folds to the SB, who opens for 3x the BB. We defend with Q♠️J♣️.
Flop (6bb)
The flop comes 3♠️A♣️J♥️, and the SB c-bets just shy of 50% pot. We call with middle pair and a back-door straight draw.
Turn (11.85bb)
The turn is the 9♥️. The SB c-bets about 75% of the pot, and we call once more.
River (29.85bb)
The river is the Q♦️, giving us two pair. This time, the SB checks, and we fire off a 22.25bb bet - about 75% of the pot.
Up until the river, this hand seems more or less standard. But things aren't so clear on the river.
First, our intuition: on the one hand, QJ feels like a hand strength that should be able to bet another street with this run-out. But it's also a run-out where it’s difficult for us to find bluffs. In addition, villain could go for some check-shoves; hands like KT, QT or KQ make natural ‘bet, bet, check the river to check-shove’ hands.
Whenever villain’s going to have a real (and balanced) check-raising range, that always limits our ability to value bet, even if we’re ahead of the calling range. So, in practice, this river bet here can actually feel pretty thin.
Now, let's see what PioSOLVER has to say about this hand. For preflop ranges, we’ll just use standard Monker solver BvB ranges. We’ll also limit the flop bet sizing to our villain’s true action of a 1⁄2 pot bet, but we’ll allow a few more bet sizings, ranging from 33% to 150% pot, on the turn and river.
Figure 1 shows us what hands PioSOLVER thinks the in-position (IP) player should be betting on this Q♦️ river.
The first thing to notice is that QJ is solved as a mixed bet and check. It’s not at all a mandatory bet, and if we look at the villain’s range, we see that villain has a 15% check-raising range which is built mainly around AQ, with a few odd bluffs with hands like KQ or A8. This check-raising range is robust enough to cause the EV of QJ to fall close to 0. So our intuition was indeed correct.
On a superficial level, it may seem like there isn’t much more to say here. However, noting that PioSOLVER chooses the IP player’s bluffs from some low pairs and other hands that have some showdown value, and, furthermore, doesn’t necessarily triple barrel these hands on many rivers, we can see there might be more to learn from these choices than it might seem at first glance.
This brings us to the concept of “showdown value bluffs.” To better illustrate how these kinds of bluffs work, let’s take a step back and look at another example hand.
Hand Example 2
This time, we’ll look at a BTN vs BB sim with smaller effective starting stacks of 975 and a starting pot of 55. We’ll again use standard Monker solver ranges for our preflop hands and limit the flop bet sizing to 30% pot, while still being more flexible on later streets. Similarly to the last hand, the preflop aggressor, this time the IP player, c-bets the flop and gets a call.
Given the action thus far, in this hand we find ourselves on a board of A♥️7♣️4♠️T♦️ with an effective SPR of just over 11.
To best introduce showdown value bluffing, we want to focus on a specific part of the IP turn barreling range. It’s important that we don’t always skip ahead to our decision point when analyzing hands with solvers; in order to glean and properly utilize insight, we want to make sure we understand every step in the full chain of reasoning that incentivizes the entire decision tree.
Figure 2 shows PioSOLVER's IP float range on the turn. Specifically, we notice that we have some hands like 22, 33, 54s, and J4 barreling this turn. This might not seem out of the ordinary, as we often see a few pairs thrown into our betting range in situations like this, where we might expect some of these hands to be barreling with the intention of barreling some rivers as well.
However, we note that while these hands do barrel the turn when it’s a Broadway card, they drop to 0% barreling frequency on lower turn cards. And even on Broadway turns, we see these hands aren’t actually triple barreling on many of the lower rivers that we might expect; further, the EV difference between betting or checking on those rivers is not insignificant.
We could speculate that what’s going on here is connected to the calling range of our opponent on the turn. Specifically, when IP over-bets the turn here, the OOP player has some Broadway hands, and KQ specifically, in his range as high-frequency calls. This makes sense for OOP, because if IP’s bluffing range is polarized, as it should be when over-betting, then KQ beats all of villain’s bluffs, and also blocks AK and AQ.
A hand like A9 is similar in this respect – in fact, both A9 and KQ are close to 0 EV calls for OOP here - but KQ has a draw to the nuts, while A9 pretty much remains a bluff-catcher on the river. This can be a very important distinction.
In response, what PioSOLVER seems to be doing is adding some showdown value bluff hands to the IP turn betting range, up to a point where the OOP player’s KQ is indifferent to calling. If none of those showdown value bluffs were present – if we take, say, 22, 33, and some 4x out of our IP barreling range – then the OOP player’s KQ/KJ/QJ hands become +EV calls.
This incentivizes the IP player to barrel with some of these hands on those Broadway turns. Doing so not only denies equity to some of our opponent’s hands that we can’t beat, like 7x hands, or higher pocket pairs, but it also allows us to check back on rivers and rely on our showdown value to take the pot from those K-high hands that stuck around but whiffed.
In short, when our villain’s range has some of these types of showdown value draws, we counter by adding some showdown value bluffs to our range.
With this concept under our belt, let’s revisit out first hand example, where we were considering whether or not to float our two pair with QJ on a Broadway completing river.
Hand Example 1 (Revisited)
Recall that, in this hand, we defended our BB from a SB open with Q♠️J♣️, and after calling both flop and turn c-bets on a board of 3♠️A♣️J♥️9♥️, our OOP opponent checks to us.
One assumption we can make here is that most people who bet 50% pot when BvB on this kind of flop texture are not heavy PioSOLVER users - that’s the archetype we often expect at these levels. It follows then that betting 50% instead of 33% of the pot probably indicates that there won't be much overbet barreling on the turn. In addition, the river is kind of bad for hands like AK and AT; we see PioSOLVER going 33% with them, but realistically it's not a bad guess to say that this kind of player would not have that kind of bet size in his arsenal.
With this in mind, this time we simplify our sim by limiting OOP turn/river bets to 75%/(75%, 150%) pot sizes, respectively. Limiting our opponent’s bet sizes in this fashion doesn’t change much, but one important change to notice is that now that PioSOLVER can’t block bet with a 33% pot sizing on the river, all of its AK and AT type hands go into its checking range. This in turn makes betting QJ a significantly more EV line for our IP range.
But let’s look at villain’s OOP turn barreling range in Figure 3. We notice 22 barreling at a high frequency, and hands like Q3s, K3s, and even KQ are barreling at 100% or near 100% frequencies. Now that we’ve talked about showdown value bluffing, we can better understand why these hands are chosen – it’s because our IP calling range on this board again has some of these premium bluff-catching hands that also have showdown value drawing power. As before, on this kind of board, this means hands like KQ, KT, and QT.
And just like it did in our instructional example, we see PioSOLVER again adding showdown value bluff combos to its OOP barreling range in order to combat the showdown value draw part of the IP turn calling range, stopping at a point when a hand like KT becomes indifferent to calling.
Furthermore, when we see these showdown value bluff hands barreling the turn, we should now immediately recognize that they won’t often barrel rivers that are bad for the IP bluffing range. They might still barrel on a Broadway river, such as a Q, but on blank rivers, such as a 6, they'll simply check and call.
Similarly, on Broadway rivers, the IP player will be incentivized to turn some of his 3x, 9x, and 7x hands into river bluffs rather than checking back, simply because these hands will almost never win at showdown.
This is the essence of showdown value bluffing.
We’ll close out our article with one final word of warning: these spots can be very player-dependent. When you’re OOP and you go bet-bet-check at levels < 500NL, most of your opponents are going to be playing multiple tables. Often they’re going to have a J or a 9 in a spot like this and will check back the river without giving it a moment’s thought. Because that’s how the hand type plays; why wouldn’t they check back? And that’s why at lower stakes, as the OOP player, hands like AK/AT are roughly 0 EV calls - against quite a Figure 3: PioSOLVER's OOP turn c-bet range for our BvB spot from hand example 1. decent amount of the people you’re playing with, you’re better off just never calling with those hands. (Which would in turn make the QJ value bet fairly bad for IP.) But the higher stakes you go, the more you encounter people who realize their Jx, 9x, or 3x have no showdown value, but who are still not aware of how much they get to bluff. So they just do it with all of those hands, and spots like this become amazing bluff-catching spots for OOP.
With this in mind, we mustn’t forget to pay attention to, and take proper notes on, our opponents, as we can gain or lose a lot of EV depending on how well we adjust to who we’re playing against. At higher stakes, with more savvy players, we need to make sure to stay balanced and to choose the appropriate amount of bluffing combos for our betting sizes. Other factors like blockers can help us decide which of our strongest bluff-catchers that also have equity vs our opponent’s drawing hands we should barrel on the turn, and perhaps tend to check the river, so we don’t end up over-bluffing with too many of our weak pair type hands.
