Studying Poker With Spreadsheets (Part 5): Checking to Induce

Following the same organizational ideas as we have used so far in this series, this week we’re going to look at one of my favorite topics in poker: checking to induce a bluff. We’re going to make a simple spreadsheet along the lines of what we have made in the previous four weeks of this series to analyze an example river situation.

Details of the Scenario

For our example checking situation, we’re going to be on the river against a single opponent with one bet left. We have the option to check or shove. If we shove, our opponent will call some percentage of the time, and when he calls, we will have a certain amount of equity that determines if we win or lose. Alternatively, we can check. From that point, our opponent will either check or shove himself, and we’re planning to always call if he shoves. We will then have some amount of equity against this opponent’s shove.

First Thing’s First

As always, our first place to begin is by breaking down all of the possible outcomes of each of our strategic decisions. Here is a complete list of what can happen after we shove along with our profit for each outcome:

Villain folds, we profit the pot
Villain calls, we win the hand, we profit the pot + bet size
Villain calls, we lose the hand, we lose our bet size

This lends itself to the following EV equation:

EV of betting = (Villain’s fold %)(pot size) + (Villain’s call %)(our equity when called)(pot + bet size) + (Villain’s call %)(Villain’s equity when called)(-bet size)

Along these lines, here are the possible outcomes if we check:

Villain checks, we win the hand, we profit the pot
Villain checks, we lose the hand, we profit zero
Villain bets and we call, we win the hand, we profit the pot + bet size
Villain bets and we call, we lose the hand, we lose our bet size

And again, we get an EV equation for checking from these outcomes:

EV of checking = (Villain’s check %)(our equity when checked thru)(pot size) + (Villain’s check %)(Villain’s equity when checked thru)(zero) + (Villain’s bet %)(our equity when check-call)(pot + bet size) + (Villain’s bet %)(Villain’s equity when check-call)(-bet size)

The idea is that we want to have an EV equation for each of these options (betting and checking) so that our spreadsheet will automatically calculate the EV of each of the options for easy comparison. We will more or less copy and paste these EV equations and put in the cells for the appropriate variables when we set up our spreadsheet.

Setting Up the Spreadsheet

To set up the spreadsheet, we need to set up spots for the variables that we need. Like in the previous installments of this series, we’ll put variables we input on the left column and variables that are calculated by the spreadsheet in the right column for the sake of organization. We figure out which variables we need from the EV equations we created above, and then we make spots for those variables as needed. Only then do we put together the EV equation inside of the spreadsheet.

Here’s what things should look like when we have the EV equation for betting together:

I’ve added some test values that are kind of arbitrary, but I’ve also highlighted the formula used for the EV equation in the image so that you can check it against your own results. If you don’t know how to do this, or if you’re completely lost, then go back through the EV Calculations series and the Studying Poker With Spreadsheets series after that.

Now we’ll want to add a section with the appropriate variables for what happens when we check:

Again, I’ve added arbitrary test values and have highlighted the EV equation used for you to cross-reference. Now we’re going to put this spreadsheet to use to study situations where we might want to check to induce river bluffs instead of betting ourselves.

How Does Each Variable Affect the Whole

One way to study these situations is to see what effects changing a single variable will have on the entire situation. From our arbitrary values, what if we change our equity when we bet and are called from 60 percent to 55 percent. It’s not hard to figure out that this will lower the EV of betting, and in turn, this will make it more likely for checking to be the correct play.

After we check, if our equity when it checks through or our equity when it goes check-call increases, then that will obviously increase the EV of checking the river as a whole. However, each of these equities will contribute to the total EV of checking differently based on how often Villain checks and how often Villain bets. Along similar lines, it will also be affected by the fact that the pot is bigger when it goes check-call as opposed to when it goes check-bet, so we can see that the scenario where we actually get our opponent to bet on the river is going to be weighted more heavily. This is even moreso the case if we can get him to bet more often than he would have called if we had bet ourselves.

Putting in Specific Scenarios

Your homework for this week’s column is the following. Find a situation in your own play where you have had the option to shove the river or check against a single opponent. Decide on your opponent’s ranges at this point in the hand, and fill in the percentages in the spreadsheet accordingly. Use the spreadsheet to decide if you should have checked or if you should have bet.