Sunday, August 22, 2010

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.


SSProdigy said...

I am currently playing 23/23 at 50nl 6max. If I understand this article correctly, are you saying it's incorrect to 4-bet shove without very good to premium hands versus the type of 3-bettor in your example? Example, I minraise 22 on the BTN, typical solid TAG 3-bettor (who knows I steal a ton, etc) 3-bets me, and as a shortstack my options are to fold or shove. Would shoving ATo be incorrect here? According to PT3 and HEM, every time you minraise and fold to a 3-bet, you lose 1BB/hand. So, in order to profitably 4-bet shove, or call a 3-bet resteal shove, you need to win more than 1BB (2bb) per hand, including rake, when you shove. It seems like any solid player who knows you are stealing a good amount can crush you in this case. Is the solution to steal less-or does the positional advantage versus fish and frequency of nits folding still make it worth it?


Travis "The Dirrty" Rose said...

Without really looking at the math, my first impression/ answer to that would be to switch gears. As soon as they adapt you you, i.e. realize that you are stealing a certain percentage of the time, it will change their percentages and therefore the frequency and hand range with which you would 3 bet to begin with. I think that it is something that you always need to be aware with your regular opponents. They will either adapt to you or they are so shitty and un adaptive that they will probably go broke anyway. It all goes back to switching gears. Keep em guessing, it will drive them nuts to not be able to figure out why they can't beat you even though, according to your overall stats they think they have you figured out. Unless they take the time to look at your recent stats against them in particular, they will never be able to get a bead on you.

SSProdigy said...

I like your idea a lot. I think it's a good idea to have 2 or 3 various general strategies to use every few weeks or whenever you feel your opponents are adapting too much. One might be more mathematically solid but the other will confuse them once you think you're playing a certain style. There are no cut-and-dry answers in's taken me many years to realize this.

Lorin Yelle said...

Hi Jason,

Rather than address it directly, I was thinking that maybe it would be more helpful to point out the oft overlooked theory behind stealing.

We steal to either take advantage of tight pre flop play or bad post flop play. Essentially, we "steal" from those who are ineffective at protecting their property. When you look at it in this light, does it make sense to make light steal attempts against those players who have ramped-up home security?

Making bold calls against reshoves with less than premium hands has never been the path to success. If this player troubles you when you are in your most profitable spot, it is best to find another table.