Out Now
×

Defending blinds equity math question

Posted by

Posted by posted in Low Stakes

Defending blinds equity math question

So i was trying to work out how i can calculate math for defending ranges vs various sizings and opening percentages. Once i have the technique for this sorted i will be fine to work it all out myself. I am stuck on the relationship between the preflop raising range and how that should affect my defending range. Of course theres the issue of hands that are flat called vs 3B, and how that effects our equity realised. Anway heres where i got to earlier:

BB Vs BTN min raise (assume SB folds).
Blinds= 1.5
Btn=2
Our call=1

We risk 1 to win 4.5 so 1/4.5=0.2222 so in theory we can defend 78% of hands

However since we our OOP so can't realise 100% of our equity so let's say we can realise 70% of our equity. So 70% of 78*0.7=54.6%

This theory is (I think) for a 100% button open. If button opens less we need to defend less bc they are letting us collect the blinds when they fold, but not entirely sure on this point and would be greatful if someone in the know could discuss it

That means if button opens:50% Range we need to defend:
50x0.78=39… 39x0.7=27.3% of hands

So am i correct in thinking that if buttons a tighter range we should defend less hands (seems pretty obvious but not entirely sure) even vs a min raise? I defend really wide and was surprised that math wise it seems i should maybe be folding much more than i am. I mean defending 27% vs a regs button min raise of 50% just seems crazy tight to me, i generally defend more like 60% of hands in this spot.

3 Comments

Loading 3 Comments...

Slava Brat 9 years, 9 months ago

My general thoughts on it (no ranges, sorry, just thoughts):
1)BU opening range is affected by SB and BB defends. SB defends ~20% of his range against BU open, so when SB folds, you are playing against a range that was constructed to be good vs average of 2 players, not against you only. That will affect your decision in vacuum situation to play more tight. In reality, when you have exact BU opening%, you dont need to worry about that and you can construct your range according to his % (basically you are exploiting his frequency at this point if he doesnt change his range at all).
2)Against BU 50% range and minraise you can defend pretty wide. Most suited connectors, most K and Q highs, offsuted connectors with high cards. Problem is, there is a postflop left. With wider range, you become more vulnerable on typical broadway-high-card flop since you will not have a pair very often, which requires you to defend Ahigh and sometimes even Khigh and Qhigh with backdoors, which leads to a lot of tough turn situations where opponent can still play pretty straightforward against your range.
It leads to the point where adding more low-equity combos to your range doesnt affect your EV of calling preflop at all.
3)In reality, though most players still play weak on BU vs BB, they will cbet more often then they will check. High-cbetting strategy negates part of equity of your hands (f.e. K4o has decent equity against BU open, but most of it is Showdown-equity and not Pair-equity, and you will not simply see showdown with your Khigh ever). To take advantage of that strategy, your strategy must implement some loose x/raises with unbalanced frequency towards bluffs. Playing this strategy is dangerous, since you might make some big mistakes chosing wrong flops and turns to bluff.

sw_kaizer 9 years, 9 months ago

Yeah i'm a little bit aware of how difficult it is play a very wide range oop since have played a decent bit of HU vs 100% button players who CB a ton, what i was really trying to do was use math to come up with some default ranges vs different percentages. Thanks for the input though definitely tough problem thats hurting my brain today :p

Slava Brat 9 years, 9 months ago

What I would do to try and solve this problem (if I have resources):
1) look at winning players at database and see ev of defending borderline hands at large sample
2) use equity distribution software to see most important type of flops for you hand, then use gto solving software for each of those flops to see ev of your hand for those flops. Then apply simple math to calculate ev of preflop call.

Be the first to add a comment

Runitonce.com uses cookies to give you the best experience. Learn more about our Cookie Policy