Determining the Correct 3-Bet Calling Frequency

Compared to the previous examples, finding your correct 3-bet calling frequency against a specific opponent is easy, though it takes a large sample.  Unlike 3-bet shoving, however, the penalty for making the wrong decision here is quite severe, being that you are now limiting to only winning one way- showdown.  Other than your opponent's range, you have two other considerations: the rake and the effective stack size.  For this example, I will summon our old friend "KaySmash" with a 20BB effective stack size and a $2/4 setting.  The stakes are very important here and that is due to the impact of the rake, which you will soon see.  In case you don't recall, KaySmash has a 3-bet range of 18%.  For this exercise, we will treat all 3-bets as an all-in shove, particularly since the 4-bet re-shove gets called somewhere in excess of 90%, despite the size of the 3-bet.

Using NoahSD's method as discussed previously, we combine the 18% 3-bet frequency with a quick hand history review off all such hands that were shown down.  For this particular player, we have a range of approximately 22+, A7o+, A2s+, KJo+, and KTs+ (actually 18.5%).  This is a fairly strong and not uncommon re-steal range.

For the simulation, I open min-raised every hand and then called with every single hand against the 18.5% range.  Here is what we get:

Probably a little tighter that you would expect?  The good thing is that this information is not privy to all players and they frequently make mistakes in this category...even when they [think they] understand what a shortstacker is doing.  While a call with with KQs is just a marginal no-no, a call with KQo or KJs is just disastrous!  Take a look at similar calls that often seem correct to players, like 22, A7o, and KJo.  And they say that being suited is overrated?

Even when we reduce the effective stack size to 16BB, the calling range changes only slightly, with the addition that you can now also call with A9o, A8s, and KQs.

A much more dramatic thing happens when we begin begin tinkering with the stakes.  Let's now run the simulation with 20BB's in a $.50/1.00 game.  Here is what we get:

Looks like 44 is now a clear fold with the stronger impact of the rake.  The effects become much more dramatic as we increase the re-steal range, but the evidence is clear- the rake matters.  What's more is that it penalizes the calling player more, since the winning player is the one who pays it, and when you call you only have the option of winning at showdown.