<aside> 🗞️ Welcome to the first edition of Nachos Monthly! Embrace the strategy as we present the very first interactive newsletter that is here to elevate your game to the next level. In each edition, we'll delve into the intricacies of the game, dissecting hands, exploring tactics, and uncovering data-driven insights that are often hidden from plain view.
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In this first installment, we will discuss the fundamentals of bluffing on the river. We will cover how different situations require different strategies and how you can improve your understanding.
To better understand how and when solvers bluff, we analyzed a database of hand histories generated by PIO. Using Hand2Note, we filtered for instances where the solver reached the river with J-high or worse. This does not necessarily mean that solvers cannot bluff with better hands; they often do. However, by choosing this low threshold, we can ensure that our results are not skewed by (very) thin value bets.
The chart below shows the results for bluffing the river in a single-raised pot (SRP) from the big blind (BB).
One thing that immediately stands out is that not every line gets bluffed at the same rate. Bluffing in a river probe line (XC-X-B) is rarely a mistake, whereas bluffing the river in a line like X-B-B is significantly worse. Why is this? The answer is, as always, EV.
When we are in a river probe line we often get to the river with a significant range advantage. The in position player had the opportunity to bet the turn after all, which he will almost always do with the top of his range. Checking behind loses a street of value and therefore slowplaying isn’t a great option (in contrary to spots where you are out-of-position with a strong hand, when you sometimes might make more money by checking as you have the option to build a bigger pot by check-raising). Let’s take a look a few equity graphs:
In one of these graphs we face a second barrel (BB vs BTN) on J♥️7♣️2♠️3♥️ and on the other one we get a check back and get to the river, which is the 6♥️. Can you guess which one is which?
If you guessed that the second one is the one where we face the second barrel then you were right! What immediately stands out is that in case the in position player checks back the turn, we have a range advantage throughout the entire range. This is exactly why the solver wants to bluff so often on this node: it leverages the range advantage and forces the in position player into a tough decision: either call and let the BB’s stronger range print money or fold a bit more and give away some EV to it’s bluffs. It often chooses to do the latter (especially in spots where the river does not improve IP’s range).
During one of our coaching calls, a student once asked the following question: "Where do they hide their air?" I thought this was a clever way of thinking about it. The answer is simple: in lines where they check (excluding checks to the aggressor). The fundamental truth about the way people play poker is that they typically check too weak and bet stronger than they should. This often results in overfolds in lines where they have a real option to bet (such as the second barrel spot in the hand that we just discussed), yet where they choose to check.
We can speculate on why players behave this way, but the most likely answer is also the simplest: humans are naturally greedy and therefore tend to make too many bets with their strong holdings. Regardless of the underlying reasons, what's important is being able to prove that this behavior is actually occurring. This is why I plotted the data for all the lines we discussed above in a chart:
Pool and PIO’s folding frequency vs a B75 river bet