Studying Poker With Spreadsheets (Part 4): Increasing Complications

Last week, we looked at putting together a spreadsheet for looking at a turn semi-bluffing situation (link). This week, we’re going to look at our different options after checking. This is a complicated situation, and we’ll be continuing from the spreadsheet that we built last week.

Some Starting Parameters

We’re on the turn, heads-up, in position. We’re going to put in the stipulation that we have one bet left and that any bet is all-in for that amount. We looked at semi-bluffing with some amount of equity if called last week, and we’re going to assume that we have some sort of draw that we know will either be a strong enough hand to bluff or not. This week, we’re going to look at checking and what happens after we check based on these parameters.

After we check, the river will either make our hand or not. We’ll have some percentage chance of hitting our hand, and that will be the same percentage chance of hitting if we were called after shoving on the turn (cell B4). This breaks up the checking scenario into two main cases: We either hit on the river or we don’t. We’re going to add two spots for that information here like so.

Notice that both of these values are in the right-hand column because they are automatically calculated. Cell D8 consists of “=B4” without the quotes since we want it to be the same value as what’s in cell B4, and cell D9 is “=1-D8” since we want it to be 100 percent minus the percentage of the time that we do hit.

The Times We Hit on the River

Now suppose that we hit on the river. Our opponent can either bet into us or check. If he bets, we call and profit the pot plus the bet amount. If he checks, then we bet. If he calls us, we profit the pot plus the bet amount, and if he folds, then we profit the pot amount only. We need variables for the following:

% of the time our opponent bets
% of the time our opponent checks
% of the time our opponent folds after checking
% of the time our opponent calls after checking

We can add that information like so:

You’ll note that I put in a header for “We hit on river” to organize our two checking cases like I mentioned above, and you’ll notice that I abbreviated river to “R” to save some space on this for the sake of these screenshots fitting on the page. I also put in some dummy values of 0.333 for how often Villain bets and 0.7 for how often Villain folds just so that there were values in there and they weren’t blank.

As usual, we’ll input values in the left-hand column for the “Villain’s bet % on R” and “Villain’s fold % after R check,” and the corresponding values are updated in the right-hand column automatically.

The Times We Miss on the River

If we miss on the river, then our opponent will either bet or check. If our opponent bets, then we will always fold, and our profit for the play is zero. If our opponent checks, we will also check through, and we will win some small percentage of the time which will be our equity after it checks down. We’ll need the following variables to get the EV for the outcomes that come after we miss on the river:

% of the time our opponent bets
% of the time our opponent checks
Our equity when it checks through
Our opponent’s equity when it checks through

And again, we’ll add that information under a corresponding header:

I want to point out that it’s possible for us to have a profitable bluff on the river after our opponent checks down here, but that’s pretty easy to figure out based on the pot:bet size ratio and our opponent’s fold percentage, so I’m leaving it outside of the scope of what we’re working on here.

Calculating the Final EV of Checking

With the parameters we have set up here, we can set up our final EV equation. We’re going to walk through all of the possible outcomes and then fill in the corresponding cell values to get our calculated EV of checking. Here are the possible outcomes:

We hit river, Villain bets (we call), we profit pot + bet size
We hit river, Villain checks (we bet), Villain folds, we profit pot
We hit river, Villain checks (we bet), Villain calls, we profit pot + bet size
We miss river, Villain bets (we fold), we profit zero
We miss river, Villain checks (we check), we win on river, we profit pot
We miss river, Villain checks (we check), we lose on river, we profit zero

Now here is the respective EV of each of those possible outcomes that we get by just filling in the corresponding cell values:

D8 * B11 * (B1 + B2)
D8 * B13 * B12 * B1
D8 * B13 * D12 * (B1 + B2)
D9 * B15 * 0
D9 * D15 * B16 * B1
D9 * D15 * D16 * 0

Note that we can ignore the values of the fourth and sixth outcomes since they are multiplied by zero. This means that for us to get the total EV of checking, we need to add the first, second, third and fifth outcomes together in a formula like so:

“=(D8 * B11 * (B1 + B2)) + (D8 * B13 * B12 * B1) + (D8 * B13 * D12 * (B1 + B2)) + (D9 * D15 * B16 * B1)”

Remember that this is without the quotes. We stick that formula into cell D18, and we have the following:

This will give us the EV of checking the turn with the place-holder values that I put in for cells B11, B12, B15 and B16. You can continue to get more complicated with your spreadsheets if you want, but make sure to follow the organizational guidelines I’ve outlined in this series to help you to avoid mistakes.