One of the problems that some players, especially newer ones, run into is that they don’t quite understand the power of semi-bluffing. A lot of these players use the bet/(bet+pot) guideline to figure out about how often an opponent has to fold for a bluff to be profitable, but they don’t quite know how to compensate for the value of having outs to the nuts. It’s kind of anti-intuitive at times, and I’ve decided that we’re going to walk through some examples this week to help build your intuition.
An Instructive Example
The example I’m getting ready to give is extremely instructive, and I feel like all new players should study it with a good amount of effort trying different values and things to see how it works.
You’re heads-up, out of position on the turn with a $12 pot and a lot of money behind. The board is 298A rainbow, and you have either 54 or 63. You have four outs to the nuts, and you bet $8. If you hit your out, you never get value on the river (this seems like a strange parameter, but we’ll get to it in a minute).
With this example, there are three basic numbers you have to know. These three numbers are how often your opponent calls, folds and raises.
Using This Example to Illustrate the Value of Semi-Bluffing
To analyze this situation in a way that will help you to understand the value of semi-bluffing, you’ll need to calculate your EV based on two different scenarios. The first scenario would assume that you held some trash hand with no outs (63), and the second scenario would assume that you held some low hand that had a few outs to the nuts (54). When you look at the difference in the EV between these hands given how the opponent plays, then you start to develop a feel for how outs affect your EV in general.
With all of that having been said, let’s do the EV calculations for the two scenarios based on the following parameters: Villain folds 50 percent, raises 10 percent and calls 40 percent. If you aren’t familiar with how to do these EV calculations, then you can either just look at the results without worrying about the math or look back to my series on how to do EV calculations the easy way with just multiplication and addition.
Without the outs: .5(12) + .1(-8) + .4(-8) = $2.00
With the outs: .5(12) + .1(-8) + .4(4/46)(20) + .4(44/46)(-8) = $2.98
What you’ll see here is that we improve our overall EV by a considerable amount when we add just four outs, and this isn’t even including the times we get value on the river when we hit.
Let’s look at another set of parameters and see what happens: Villain folds 30 percent, raises 20 percent and calls 50 percent.
Without the outs: .3(12) + .2(-8) + .5(-8) = -$2.00
With the outs: .3(12) + .2(-8) + .5(4/46)(20) + .5(42/46)(-8) = -$0.78
Even though we’re losing money with these parameters, we can still see that we get a very sizable improvement with the addition of just four outs even if we don’t take into account the extra value we extract when we hit.
Compensating for Future Betting
In terms of the math, we can figure out how much more value we’ll get with a single bet on the river with the following quick calculation:
% of time Villain calls turn * chance of hitting our draw * % of time Villain calls river * our bet size on the river
Let’s suppose that we have four outs giving us a 4/46 chance of hitting on the river. The river pot in this scenario will be $28, so we can say the river bet size might be $18 or so, and we can adjust for the percent of time that we think our opponent will call the turn and the river based on whatever parameters we decide on. With that, let’s suppose our opponent calls the turn 40 percent of the time like in our first example scenario above, and let’s say he will also call our river bet 40 percent of the time when we hit. Our extra value from the river bet will be:
0.40 * 4/46 * 0.40 * 18 = $0.25
What you’ll notice is that this amount isn’t that big compared to the amount of extra value we received just from having the outs in the first place. The reason for this is that getting value from hitting our draws doesn’t happen all of that often since the opponent has to call the turn AND we have to hit our draw AND the opponent has to call the river. This idea holds true for situations where we have more than four outs, but I’ll let you examine that on your own.
It’s worth pointing out that the value we would get from betting the river and our opponent folding is already accounted for in the original equation.
How to Grow With These Examples
Here’s how you can grow your intuition with these examples. First, you’re going to want to come up with a specific set of parameters like the two sets we looked at before. Next, you’ll want to evaluate the bet/(bet+pot) amounts (aka the alpha value) for each spot and look at what the difference is between that value and how much our opponent is actually folding in the scenario. Finally, you’ll want to look at how much more value you get with different numbers of outs compared to having no outs at all, and you’ll also want to look at how much value you get from the river with different numbers of outs as well.
Next week, we’re going to get a little more in-depth with this type of situation and look at the effects of having outs that are not to the nuts. If you want to prepare for next week’s article, then you’ll want to read through my series on calculating the EV of poker scenarios.