Bluff Catching the River
Like most poker situations there is a theoretically correct decision and then there is the decision we should make in practice based on exploitative information or population reads.
Imagine that we have Ks2s and we have called 2 regular sized barrels on a Kh4c5s9h5d runout. In order for our hand to be considered a bluffcatcher we first need to establish whether we beat any of our opponents value-hands. If this is the case then we are not in a typical bluffcatching scenario. It seems pretty likely that in this scenario the absolute weakest hand that our opponent would be value-betting is AK, maybe even stronger. Anything weaker than AK will also be a buffcatcher. So there is not actually a huge amount of difference between K2s and KQo in this situation. Both hands lose to our opponents entire value-range and beat any bluffs that he can have.
River Bluffcatchers – ExploitationWe've identified that we hold a bluffcatcher, which essentially means that the only time we win the pot is when our opponent is bluffing. It should be logical to arrive at the conclusion that exploitatively the only thing we care about is our opponents bluffing frequency. So how often do we need our opponent to be bluffing for us to have a profitable call?
This will be a function of his bet sizing and hence our pot-odds. So if our opponent makes a 60% pot bet on the river and we call we'd be investing roughly 27% of the total pot. This means that we can call if we win over 27% of the time. Since we have identified that we only win when our opponent is bluffing, we need him to be bluffing over 27% of the time. But how do we know if he is bluffing this frequently?
Exploitation – Stats and Reads
Now unfortunately there is no easy way to know if our opponent is buffing without advanced tools. We can check his flop/turn/river cbetting frequencies to see if these are high. We can also check to see if his river Afq is above 30%. The problem is that these methods are unreliable and can be misleading. There are two better ways of collecting this information.
The first is by way of manual notes. If opponent 3barrels and shows up with a bluff, this is the kind of thing we want to be noting down, because it can help us dramatically in the future. We can keep a tally in the notes which will eventually reveal our opponents bluff:value ratio when we have enough of a sample.
The better way is to make use of modern technology such as Notecaddy. Notecaddy stats are more flexible than HM2 stats. HM2 stats are only capable of defining certain stats by the actions that our opponent takes (such as how often he fires the river), but not capable of defining certain stats by the hands that our opponent shows up with (such as how often he shows up with a bluff given that he has fired the river). With Notecaddy it's possible to create a custom stat which tells us explicitly how often our opponent shows up with a bluff on the river after he 3barrels. Bluffcatching decisions have never been easier. We simply cross reference our opponents bluffing frequency against the pot-odds we are getting and make the decision to call or fold depending on the price.
The downside to this method is that it doesn't necessarily take into account our opponents bet-sizing (unless we create an even more advanced Notecaddy stat which is possible). However Notecaddy does have a useful tool for this in the form of the Caddyscatter. This scatter graph will cross-reference our opponents river bet-sizing against his hand strength. For example perhaps our opponent overbets the river. We can check all of his previous overbets and see how frequently he is strong compared to how frequently he is weak.
Exploitation – Population ReadsThe good news for those of us that don't have or use Notecaddy is that there are some pretty good default assumptions we can have for lower limits when deciding whether or not to bluffcatch the river.
The average player is pretty passive at lower limits, so in most situations where we find ourselves with a river bluff-catcher facing 2 or 3 barrels, or an overbet, we can usually automatically hit the fold button.
This does of course mean that we are not playing a GTO correct strategy and will technically be over-folding the river. This will be represented in some of our stats such as river-fold-to-cbet and WTSD. We should be totally fine with this however since this simply happens as a result of exploiting our opponents. We know that in the vast majority of cases when a player at lower limits decides to 3barrel they have a value-hand, so we are actually making the game very difficult for them by folding super frequently in this scenario.
As a rough guide that any limit 50nl or below, our default approach should be to fold all bluffcatchers vs unknowns when facing either a 3barrel or a river overbet.
River Bluffcatchers – Game Theory Optimal
So what about higher limits against better players? We naturally want to be a lot more careful about folding all of our bluffcatchers in certain spots since we will be opening ourselves up to exploitation. It still wouldn't be a huge deal if we folded all our bluffcatchers initially, since whichever limit we play we should be adjusting our strategy pretty quickly as new information about our opponents comes to light.
However, assuming we want to start out with a balanced defense on the river with our bluffcatchers, what do we need to know?
The maths in itself is not overly complex. We use what is known as the “minimum fold-equity formula” which you are possibly already familiar with. If we know our opponent's river bet-sizing we can calculate how frequently we need to call overall. So assuming our opponent is betting 60% of the pot on the river, how frequently must we defend?
Step 1 – Imagine villain is bluffing and calculate the break-even point on his bluff. So he is investing 60% of the pot to win 100% of what is in the middle (total of 160% pot). 60/160 = 37.5%.
This means that if our opponents river bluff works more than 37.5% of the time that he is generating automatic profit with his river bluff and he should be incentivised to fire every single time he reaches the river in this spot, assuming that we don't adjust.
Step 2 – Calculate how often we must defend to prevent our opponent from generating automatic profit. If we want to prevent our opponent's bluff from succeeding more than 37.5% of the time it's logical that we need to defend around 62.5% of the time. If we defend more than this then our opponent is no longer incentivised to bluff at all and will only value-bet the river assuming that we don't adjust.
Step 3 – Calculate our defending range. This is possibly the hardest step because it involves being aware of what our entire river range is. In other words we need to think the hand through from preflop and decide on all the possible hands that we get to the river with. Once we know exactly how many hands we get to the river with we can calculate exactly what 62.5% of this range looks like. This 62.5% defending range will likely include some bluff-catchers but not all. In this scenario we will pick the best bluffcatchers and fold the worst bluffcatchers.
Differentiation of BluffcatchersWe said in the earlier example that there was no real discernible difference between K2s and KQo. Both hands beat all of our opponents bluffs and lose to his value-bets. So what differentiates the two hands? Not really that much in this case, they are both extremely similar. KQo is likely slightly better just in case our opponent mistakenly overvalues something like KJo, but that's about it.
However in other cases there will be a more of a difference between two bluff-catchers. For example imagine we face a 3-barrel bluff on the following board texture.
Which of the following hands is a better bluffcatcher?
While initially these hands may seem much closer than the K2/KQ bluffcatchers, there is actually a much bigger difference. What is one of the hands that we are afraid might be in our opponent's 3-barreling range on this board texture? Heart flush-draws, including Ace-high heart-flush. However we know that when holding the Ah that there is simply no possible way that our opponent has an A-high flush. He will have a smaller value range as a result of the heart we hold in our hand. We can refer to this heart as a “blocker”.
When deciding which bluffcatchers to put in our range (assuming that there is not really much discernible difference in terms of relative value), we often look solely at blockers. There are two things that we are looking for.
1 – We want to block our opponent's potential value-range.
2 – We don't want to block our opponent's potential bluff-range.
So in the example above holding a heart was preferable because the heart-flush completed. But if we imagine another scenario where there are two hearts on the board and the flush-draw doesn't complete, is it still preferable for us to hold a heart in our hand? Holding a heart would actually be a bad blocker because it blocks some of the potential bluffing combos our opponent might select.
Absolute Strength of Bluffcatchers
By focusing purely on blockers we are really subscribing to the idea that all bluffcatchers have a similar relative strength in spots where our opponent is polarized. So in some cases we might fold a top-pair type hand with bad blockers and continue with a 2nd-pair type hand with good blockers. We have to be a little careful with this idea, since although it is theoretically correct there are a few things that can go wrong in practice.
Merged River Range – We often assume that when our opponent fires 3 big barrels that he has a polarized range. There is good reason for this assumption in most cases. But do we really know for certain what an unknown is doing? He may have no clue about poker and be 3barreling big with a weak top-pair. If we return to our KQ/K2 scenario we can see that there now is a really clear difference between the 2 hands because KQ beats some hands in our opponents merged range while K2 beats none of it.
Bluff-catchers Losing to Bluffs – It's also easy to fall into the trap of thinking that all buffcatchers will beat our opponents buffs. This is not the case – perhaps our opponent decides to 3barrel 66 on a K7422 board as a bluff. We might make the mistake of thinking that 7x and 4x hands are equivalent in this spot but they are not.
In other words, while blockers are potentially our primary interest in selecting river bluffcatchers, this is only correct in theory, and our decision making process should not completely factor out the absolute strength of our hand. The relative equivalence of bluff-catchers only applies if our opponent is perfectly polarized and we don't live in a perfect world. We don't want to put ourselves in the spot where we are calling a bunch of weak hands on the river more frequently than we call some of our stronger hands.
Putting it TogetherWe've talked primarily about facing 3barrels here. But our goal should be to make an outline for all the different river-bluffcatch situations we face. We'll find that much of the above exploitative information applies to situations where opponents raise vs our river bet also for example. It's nearly always correct to fold any bluffcatcher vs an unknown without doing any calculation. It's exactly the same when facing a river overbet.
Some scenarios are a little less clear and require more focused work. For example facing two barrels instead of three. Or perhaps facing a river bet after the turn goes check/check. So don't assume that you know everything about river-bluffcatching after reading this article, we have really just scratched the surface.