Navigating BvB OOP
After Check-Calling the Flop

B-X-B Refresher (Equity Advantages)

A key point to consider when playing rivers is how the equities stack up. Very broadly speaking, the player with the equity advantage will have more made hands relative to their opponent, so they can bet thinner/more often to extract value. When a player calls a bet on a given street, typically the equity shifts in their favor (barring the scenarios where the turn/river are extremely good for the bettor).

In the B-X-B line, the flop caller will almost always have an equity advantage across most runouts. This enables them to bet more often, especially in wide-range scenarios where certain runouts won’t be drastically better for one player over the other.

What Makes This Spot Unique?

This spot is going to play a bit differently than some adjacent lines, such as the B-X-? or X-XC-? scenarios. The main reason is that on many board textures, the OOP (SB) player will be more capped and/or heavier on high cards/showdown value hands than if it were BTN vs BB, where the flop caller (BB) was also the preflop caller. (Think: OOP will usually be seeing a turn after having defended against a flop stab when they hold AK/AQ, even on wet/scary boards).

Consider the SB vs BB in an SRP scenario where the OOP preflop raiser (PFR) check-calls a 50% pot flop stab. The PFR will be much heavier in high-card hands when they check-called flop, since their high cards have significantly more equity vs. the stabbing range as opposed to the BTN vs BB scenario, where the high-card region has less equity vs. the c-betting range (of the IP PFR) that contains stronger high cards, causing them to usually over-fold.

Check-Calling (XC) on Low Boards

Let’s take a look at the XC strategy on a low board, such as 963r first (SRP between the Blinds):

This is the response from OOP vs. the stab. On a raggy rainbow board such as this one, OOP will be continuing tons of naked high-card hands due to their greater ability to showdown or value bet across later streets if they hit a made hand (in addition to OOP c-betting more middling/low pairs on rainbow boards).

To demonstrate the point, here’s OOP’s response vs. the stab on 963tt:

Notice that OOP is folding slightly more and calling slightly less. If you look closely, you’ll see high-card hands like K8s, K4s, A7s, etc. mostly folding due to the decrease in their ability to value bet later streets if they make pairs (since more draws will complete on two-toned boards).

The result is that on two-toned boards, OOP will XC flop with more showdown-oriented hands (good Ace-highs, low/middling pairs). Whereas on rainbow boards, OOP will be floating more weak high-card air with backdoors. The effect on how the B-X-B line plays is difficult to summarize in short bullet points without demonstration first, so let’s get our hands dirty.

This is the range breakdown of 2 scenarios for the boards given above. On the left, we have the range matchups for the 9♠6♠3♣ 2♥5♦ runout. And on the right, 9♠6♥3♣ 2♣5♦. Essentially, the same board with a non-flush runout, with the difference being that one flop is two-toned. SB range is on the left, BB on the right side of each graphic.

On the two-toned board (left), what sticks out to you about the range matchups relative to the rainbow board (right)?

The big idea is simply that on wet boards, OOP will XC less air on the flop. However, don’t get ahead of yourself. It would be easy to leap to the conclusion that they should be betting quite often, but this is not necessarily the case. Remember, the hands worth betting are the ones that gain value by betting; you don’t magically profit from thin value bets just because your range is more protected. The thin value hands make money by betting small enough to squeak out value from worse.

Constructing OOP’s River Checking Range

Consider the XC-X-? line on 963♠♠ 2oT♠:

While it is true we arrive at the river with less air when check-calling on a two-toned flop, the middling hands (77, 6-x, 3-x, etc.) are no longer worth value betting when flushes come in. Take a look at the high-card region:

So while OOP has a huge equity advantage, IP will reopen this river Ten more often than if it was a King or Ace, giving us more incentive to check. On cards IP is less likely to reopen, we need to do more betting ourselves.

The interesting part of the OOP strategy is how the solver plays flushes:

OOP is checking their flush combos over 50% of the time. Notice the flushes that strongly prefer checking are AX♠♠, namely A♠K♠, and the lower sidecard combos. The flush combos with a Queen or Jack in them bet much more often (notice Q♠J♠ is a pure bet). To understand why, think about the range IP will reopen. Combos like QTo/JTo that bet flop get here much more often than their counterparts without the suit of the flush draw, so when we have a flush with a Queen or Jack of ♠ in hand we get bet into much less often. Also, when we have a hand like A♠7♠, A♠4♠, etc., we unblock combinations of Ten-x since the Ten is a spade.

Speaking of unblockers, there’s one more related concept: unblocking air. Think about it like this: if IP has a potential turn bluff candidate without a ♠, this type of air will get put into the turn check line to possibly bluff rivers much more often than similar hands with a ♠, since flush draws (and offsuit hands that block flush draws) tend to take preference in the bluff selection on the turn. After it goes X-X on the turn, it’s much more beneficial to check a made hand OOP with a ♠ as a trap regardless of whether the flush completes on the river. For example, if we XC the flop with K♦Q♦ and the turn checks through, it’s more likely IP has a hand that’s trying to get to showdown because we block the hands that are going to slow down on the turn and possibly bluff river, hands like Q♦7♦ or K♦8♦.

Exercise for the Reader

In this custom AI solution for the same spot discussed above in the BXB line on 9♠6♣3♦ 2♥T♠. Given what we learned about OOP trapping some flushes and two pairs (T6, 96 mainly), try altering IP’s betting strategy when OOP checks river using the nodelocking feature. Force IP to play a bit more aggressively (value betting thinner, allowing overbets, etc.) and take notes on how that changes OOP’s response. Then do the same for a Villain that’s too passive (not value betting thin enough, only using up to pot-sized bets, etc.).

Building on what we’ve covered here, let’s take a look at how to construct betting ranges on runouts that are better for OOP (and so will feature higher betting frequencies from OOP).

Constructing OOP’s River Betting Range

The main exception would be when we have a massive advantage in a nutted hand class, making IP less likely to reopen. A prime example would be a non-flush board like 963 6J, where IP bets flop for a larger size (like 75% pot). IP isn’t betting 6-x for this size on the flop, so we have significantly more trip Sixes than IP.

On high-card rivers, OOP will certainly make significantly more new hands, but how does that affect our betting strategy?

It is very reasonable to have overbets in this line, but it’s important to keep your entire range in view here, and not immediately go for the overbet button just because your current hand rivered a good pair. Tons of your range will want to check or block, always consider “trapping” your good made hands on the river by assigning them to those two ranges. You can do this by using your side card and an RNG. For instance, if you river an offsuit Queen in the hand outlined just above. In the case of AQ, laying the occasional trap with a check and then springing it with a click on the raise button is an option worthy of consideration. A nice property of this hand is the sidecard Ace, which blocks your opponents check backs. When holding Q6s, you could put it in the blocking line to go along with other, weaker hands that can bet for thin value (like 6-x).

Study Question

We talked about unblockers and their relevance to playing flushes. How might unblockers play a role in the line that thin value hands decide to take?

Summary