Hello! Assuming we want to call 40% of our hands against a button minraise in a heads-up pot: How do we define the border of our calling-range? Would we rather call K2o than 92s or Q6o than 84s? Is there any way to figure this out easily?

Yeah, there’s a way to figure it out but it’s not easy and it depends on your hand ranking system.

I have a program that can do it – it’s called Call Hand Look (get it?, hint P.N.). For a villain mini-raise, the big blind needs equity of about 22% for break-even EV. I don’t know how you got a 40% call range but given that, it implies villain’s betting range is top 3.5% according to the hand ranking system I used (it values pairs somewhat higher than Poker Stove). The calculated 40% calling range to provide the 22% equity against a 3.5% betting range is

{A2o+,K6o+,QTo+,A2s+,K2s+,Q2s+,J8s+,T7s+,96s+,85s+ ,74s+,64s+,53s+,43s,22+}.

None of your 4 candidate border hands are included though 84s just misses.

I would think there are other ways/criteria to address the question.

thanks statmanhal! as always very happy to get an answere from you! Please check your PMs

edit: sorry I should've mentioned that I wanted to 3-Bet my premium hands. So assuming we would 3-Bet ~17% of Hands:

22+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,54s,AJo +,KQo

How would our 40% calling range look now?

Adding in the 3 bet possibility greatly complicates what is already a complex question.

What does villain do- fold, call, re-raise. I assume you will 3 bet the 17% range, call the 17-40% range and fold all else. Then you can use an equity calculator along with the applicable EV equation to do EV analysis given assumptions on future actions (the simplest of course being the hand is checked down after villain calls your raise or he folds).

Don't fold anything suited

K2o/K3o/K4o kinda close.

I don’t have the numbers crunched, but my range as the Big Blind would be any Ace, any pocket pair, any two suited cards, and any two cards 9 or higher (T9o through K9o).

I 3b rather narrowly, probably TT+ and AQo+.

This 3b is my personal strat, since HU has already been achieved, and I am raising for pure value, no deception.

thanks guys!

btw something that is confusing me a bit right now, its probably stupid:

I'm looking at my database trying to figure out which openraising size from which position performed best in the reg pool:

The bigger the raise size, the higher the winrate in terms of BB/100, which makes sense as they normally raise tighter. If they raise smaller they loosen up but their WR goes down.

Am I right if I'm saying:

We could have a small winrate but make more $/hourly by playing more hands with a lower winrate ?

If that is true, how do we best determine whether we should play tighter/looser in terms of better $/hourly? Is it right to say that we can only tell whether a 2BB or 3BB open raise performs better by playing the exact same range from the same positions over two large samples and then comparing winrates of the sample that played a 2BB open and the sample that played a 3BB open?

With regard to the player pool at large, be careful that 3x openers may just be better poker players, while some 2x players will be button clickers.

With regard to your own optimal play, you would add more tables with the superior winrate, not play more hands at the same number of tables.

The only thing that should ever lower your winrate is playing more tables than you can sustain your optimal strategy.

I developed a simple model that attempts to quantify this thought. It is described in the following thread:


https://forumserver.twoplustwo.com/3...?highlight=tef

Interesting, thanks statmanhal.

The variable will be non-linear, imo, and your system will need to be log based. Likely it goes something like .98, .97, .95, .90, .84, .77, .69, .58, .50.....,

assume a spectrum of players that all open for 2x with the same range:

passive........../\...........aggressive
......./.........../...\...............\
play wider.....play.............play tighter
range than.....same...........range than
opener...........range...........opener

postflop play affects proper big blind defense ranges as shown above. More passive postflop players give up free cards and charge you less to draw and or bluffcatch postflop on average. This allows us to defend a wider range vs a passive open raiser.

There is an undefined point in the middle where my folding range is the same as the opener's folding range, but even then the situation is asymmetric because of the way my 3 betting range affects the formation of my calling range. I do not think this point in the middle has any particular significance beyond its existence; it's just an inevitability of the effect of postflop play on defending ranges that folding frequencies will intersect this way.

More aggressive players don't give as many free cards and they charge more on average postflop. This should make us want to play a more showdownable range, a desire which is effected by folding more of the weaker drawing hands preflop.

Without this information, I typically will defend a range that is slightly tighter than (btn 2x unknown opening range) which is usually 45-60% in my experience. I think my hands from (45%-60%) the undefined 15% of hands are so close that we could fold or call by the flip of a coin, while maintaining a range that performs fine postflop. If there have been no showdowns, but my opponent has raised preflop frequently, then an application of Bayes Theorem will show a slight bias toward (my opponent is overaggressive) compared with (my opponent is a overly tight), in which case I would assume at least a 50% range and then reconsider the postflop tendencies.