SHOVE with PR (SH)

Where SHOVE vs SOR focuses on what we think Villain has and does, SHOVE with PR focuses more on what Villain thinks we have and what we do with it.

SHOVE with PR is useful in situations where we as Hero expect to have a well-defined perceived range in the eyes of the Villain. In these cases we can simulate Villain playing his range perfectly against our perceived range. We can then calculate the EV of shoving our actual holding.

This may sound very complicated but a couple examples should help clarify. In this article we will look at two common scenarios:
#1. We have 4bet preflop and we have a very tight perceived range. How do we calculate these EV of shoving on the flop.
#2. We call a 3bet in position and Villain cbets. If we shove we think we have a good grasp of the perceived range that Villain puts us on. What is the EV of shoving our hand.
Let's get to it.
Example #1
Using the GAME BUILDER I built a common scenario:
We are playing heads-up. We open a pretty hand from SB and get 3bet. We decide to 4bet. Flop comes Jc Qc 6d. We flop a gut-shot and a backdoor flush draw. Will it be profitable to shove the rest in here?
To analyze this situation we need to complete a series of steps:
1) Determine Villain's range on the flop
2) Determine our own perceived range.
Let's do it.
1) Determine Villain's range on the flop
We are playing heads-up and we expect this Villain to be 3betting about 12% out of position. He doesn't like to fold against 4bets and since he didn't 5bet so we rule out AA:
We also expect him to check his entire range to us, so we are not excluding any hands on the flop.
2) Determine our own perceived range.
We think Villain perceives us a tight and straightforward. We have not made a 4bet for the entire match so we are pretty sure that we get credit for having AA.
We are now ready to run SHOVE with PR. 
We open SHOVE and click the small caret down icon. We select SHOVE with Perceived range:
As we can see the player icon is now Hero and so we are asked to enter Hero's perceived range. We enter AA. 
Note: Hero's perceived range works as a sub range of Hero's main range.
In this case we have not altered Hero's main range and so it is still 100%. When we enter AA as Hero's perceived (sub) range this results in a combined perceived range of 100%:(AA).
Alternatively we could have changed Hero's main range to AA preflop and then entered * as Hero's perceived (sub) range and we would end up with a combined range of AA:(*).
They work out to be the same ranges and both approaches are fine.
Number of trials
Before we click the play button let's talk a bit about number of trials. All modules provide the option for the user to specify the number of trials he/she wants to run.
All modules come with a default number of trials. Be aware that the number of trials can vary a lot for each module. The default number of trials for SHOVE with PR is 500.
SHOVE with PR works very differently than SHOVE vs SOR and the calculations are a lot more expensive and the default number of trials therefore much lower. 
Note: Speed is very dependent on hardware! So a fast computer will make a world of difference.
The 500 strikes a balance between accuracy and speed. But in this example we would like to be more accurate. Let's set the number of trials to 2500:
We click the gear icon and we get a small popup. We enter 2500 and click save. PokerJuice will remember this next time you run the module.
We are now ready to run the module. We click the play button and after a little while we get results:
If we shove we can expect Villain to stack-off 74.88% of the time and only fold 25.12%. The times we get it in we stand to have 20% on average.
The total EV of shoving is $-10.76.
Conclusion: With the ranges we have assigned our best option is to check behind and hope we pick up sufficient equity on the turn.
Example #2
Let's try a slightly more advanced example. We are still heads-up and we defend vs. a 3bet. The flop comes:
We flop top pair + gutshot on a very drawy board. Villain cbets $14.00 into $18.00. We have decent equity and rather poor playability. We are tempted to shove. To analyze this in SHOVE with PR we need to complete a couple of steps:
1) Define a preflop range and cbet range for Villain
2) Define Hero's preflop range and what our perceived shoving range looks like in the eyes of Villain
Let's do it:
1) Define a preflop range and cbet range for Villain
We are playing heads-up so we expect this Villain to 3bet something like 12% oop.
Villain is the type of player to cbet a lot. We think he will cbet this flop with all his flush draws, all overpairs or better, all his nut open-enders with a pair and all his wraps:
We then expect him to fold some fraction of this range to a shove but generally play very well against a range.
2) Define Hero's preflop range and what our perceived shoving range looks like in the eyes of Villain
Hero's preflop range is pretty wide. Hero likes to call most 3bets in position rather than 4betting so we exclude only a small 4bet range:
Now comes the more tricky part. We need to define our perceived shoving range in the eyes of the Villain. We think he expects us to shove:
  • all two pair or better
  • decent open-enders with a flush draw or top pair
  • all overpairs with a flush draw or a decent open-ender
  • all nut flush draws
  • all 17 way wraps with a pair

Using PJ syntax the range look like this:


We open SHOVE with PR and enter this range as Hero's perceived range:

Anytime Villain has sufficient equity against our perceived range he will stack-off. If not he will fold. We run the module and we get:

The EV of shoving is $-12.18.

We can see that we can expect Villain to stack-off about 70% of the time and fold about 30%. When we get it in Hero only has 30% and so the total EV is negative.

But what if Villain perceived Hero to have a very tight shoving range? Let's assume that Hero is perceived as being very passive and to only shove top two pair or better:

Again this perceived range is a sub range of Hero's main range which we have defined as 80%!$4b4, so Hero's combined perceived range will be (80%!$4b4):(JT+).

We run the module once again and we get:

This time with a total EV of $-3.88.

The EV is clearly higher than before due to the increased fold equity. But it is still negative and by now it is probably safe assume that shoving this hand regardless of our perceived range is a bad play given Villain's range.

We have seen how to use SHOVE with PR in two different scenarios and we have seen how the EV depends on Hero's perceived range. The module is also very useful for testing equilibrium ranges, but this is a more of advanced topic. For more on this check out my blog where I plan to release more advanced How-To articles in the future.



I hope this article was useful. Please do not hesitate to contact us. You can find me on Skype or in the PokerJuice Community.

Skype: PokerJuice

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