In this week’s column, we’re going to investigate the idea of betting to protect your hand. A number of people bet with the excuse of protecting their hand almost every chance that they get. On the other hand, a lot of people dismiss this concept as being something that doesn’t really work out because it doesn’t fall under the strict dichotomy of bets being either for value or as a bluff. We’re going to look at some fantasy scenarios and figure out if this is a viable strategy or not under certain sets of circumstances.
Note: If you are not familiar with the simple system that has been taught in this series for making EV calculations, then you’ll want to visit the EV Calculations Tutorial series before going any further.
The Factors That Come Into Play
When it comes to betting to protect our hand, we’re going to be looking at situations where our hand does not have enough equity to qualify as a pure value betting hand nor does it get enough better hands to fold for it to be seen as a viable bluffing hand. Instead of thinking along the lines of this dichotomy, we’re just going to look at the differences between what happens when we bet and what happens when we check in certain situations where checking isn’t necessarily pleasant. Let’s start with a model scenario to see if we can get something that we can work with.
Our Model Scenario
We’re going to start with a model scenario that’s fairly favorable for us in terms of the parameters used and use that as a jumping-off point. Suppose we’re heads-up on the turn with 77 against an opponent who holds AKo on a board of 2285 rainbow. The pot is $15 and we have $10 behind. If we go all-in, then our opponent will always correctly fold. If we check, then our opponent will always check. On the turn, we have an equity of 86 percent, and our opponent has an equity of 14 percent. Since our opponent is never going to call down on the river unless he has a better hand, and since we’re never going to check/call if an ace, king or eight comes on the river, then this is the same scenario as if there is never any betting allowed on the river at all.
Given this rather narrow scenario, we want to know the EV of checking and if it’s better than the EV of betting. We will always win the $15 pot when we bet, so the EV of betting can be seen as $15.
If we check, then there are two possible scenarios. The first possible outcome is that we still have the best hand on the river, and the second possible outcome is that we don’t. We will win $15 when we still have the best hand, and we will profit $0 when we do not. This gives us the following EV equation for checking:
EV of checking = EV of winning + EV of losing
EV of checking = (0.86)(15) + (0.14)(0)
EV of checking = $12.90
As we can see in this rather contributed example, betting is better than checking by a factor of $2.10.
Adding Betting Hands to Villain’s Range
One of the problems that can come up with betting on the turn in this type of scenario is that we’re sometimes going to be betting into a better hand. Let’s expand on this example scenario by saying that our opponent is actually going to have 88 for top set 10 percent of the time, and we will always lose when we shove. Note that he will only be calling this 10 percent of the time. When that happens, the EV of betting becomes the following:
EV of betting = EV of Villain folding + EV of Villain calling
EV of betting = (0.90)(15) + (0.10)(-10)
EV of betting = $13.50 – $1.00
EV of betting = $12.50
As you can see with this addition to our scenario, betting can very quickly lose some of its value if we’re running into better hands with any significant frequency.
Adding Bluffing Hands to Villain’s Range
Along similar lines, one of the problems that can come up with checking on the turn in situations like this is that our opponent gets the opportunity to bluff into us. Let’s keep the same stipulation that 10 percent of our opponent’s range is 88, but now let’s say that our opponent will bluff with a frequency that means 2.5 percent of his total range is bluffs with AK. That leaves another 87.5 percent of checks with AK.
Hero needs 28.6 percent equity to have a profitable call if we check in this scenario. He will only have 17.3 percent, so Hero will always check/fold and never check/call when facing a shove. This leads to the following EV of checking:
EV of checking = EV of winning at showdown + EV of losing at showdown + EV of Villain betting and we fold
EV of checking = (0.875)(0.86)(15) + (0.875)(0.14)(0) + (0.125)(0)
EV of checking = $11.29
With a minimal (ie: not exploitable by calling) percentage of bluffing by our opponent, we run into a situation where the value of checking is lowered overall. The point of these past two calculations is to demonstrate that there are multiple factors that can change the EV of checking and the EV of betting, and when these factors line up appropriately, it can be correct to bet purely to protect your hand, though maybe this is an inappropriate term for it. It’s more like you’re betting because checking gives up too much value.