HU SNG All in every hand

[dw33b]

So I sit down, and every hand my opponent shoves, if I limp they shove. I'm not sure how to calculate the math if I know future action. Obviously I can sit and wait for a big hand, but we start with 75BB's I don't know how much of an edge I give up for a possible better future edge.

[hra146]

Dont know where you play but that happens so rarely its not even worth doing the precise math. If you wanted to it looks like this:

You estimate the edge (x) you have over your opponent if you never limped. You choose a hand of which equity is <(x), limp with it and call his push.

This assumes you are definitely sure that his hand is random (i.e that he does push _every_ hand when you limp)

www.pokerstove.com for further investigation.

[dw33b]

Opponent is shoving every hand, not just when I limp. I don't know how I would determine my edge if there's no play to judge by. I have pokerstove, I know how to use it. What edge do I give up, if future action gives me a bigger one? Or maybe I misunderstood example.

[hra146]

Sorry, then I misunderstood it. So he only does not shove when you limp? He always shoves from the SB?

[ QUOTE ]
So I sit down, and every hand my opponent shoves, if I limp they shove.

[/ QUOTE ]

This is pretty confusing. However, if he shoves everytime in the SB its the same thing. You arent giving up a thing by waiting for a 60/40 vs. a random hand. I think I get your point though. However, I think to figure out a valid formula just for that example is a little over the top. Whether your edge is 10 or 15% vs. these guys wont affect your winrate in the longterm. Knowing when to fold your SB to a 3bet however does. (Just giving a random example for how to invest your study time better)

[hra146]

I think I finally got it. What you are trying to say is:

He shoves every hand pf.

Precise math on how long you can wait for what hand however would include information on tournament structure, blind structure, effective stacks, the time both of you take for your decisions and possibly more.

Just pick a top20 hand and call. Theres nothing more to it.

[jay_shark]

I've solved this problem a long time ago but the calculations can get tedious . The best way to work this problem is to work backwards .

I'll give you an example .

Lets play a simplified version of this game where you and your opponent have 3 BB's .

If your opponent is on the button and pushes with any two cards , then you're getting 4:2 odds which means you need to win at least 33% of the time to show a profit . This means you should call with any two cards except 3-2 o . So you should call with 1213 hands out of 1225 .

EV=1213/1225 [4*0.5016 - 2*0.4984] = 0.9997

Now say each player has 3.5BB's and you're in the sb. You would prefer to call with all hands that gives you an EV > 0.9997 . Since you're getting pot odds of 4:3 , you need 4x-3(1-x) >=0.9997
Solve for x>=0.5713 . Now use pokerstove to find all such hands with an equity versus a random hand greater than 57.13% .This range is about 24.7 % of all hands with an equity of 62.7%.

EV(3.5) = 0.247*[4*0.627 - 3*0.373] + Ev(3)
Ev(3.5) = 0.343 + Ev(3)
Ev(3.5) =~ 1.3427

Now all you have to do is continue until you reach Ev(75) [img]/images/graemlins/smile.gif[/img] which should give you your exact EV for this game assuming that you're playing optimally .

[phatjeffrey]

a very simplistic and most probably a "wrong" approach to this problem... if we believe we have a 15% edge against this guy .. by some sort of logic.. wed expect to win 65% of the time (15% more than a tie 50-50) .. then calling with a hand that is a 65%+ favorite against a random hand is the right play...

[phatjeffrey]

which on pokerstove translates to : (if villain is shoving random hand)

77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,QJo

[jay_shark]

I'm bored so I'll continue working this out .

With 4bb's you're getting pot odds of 5:3 so solve for
5x-3*(1-x)>=1.3427 , x>=54.283

Now use pokerstove to find all such hands with an equity >=54.282% .

Ev(4) = 0.32*[5*0.6088 - 3*0.3912] + Ev(3.5)
Ev(4) = 0.5985 + 1.3427
Ev(4) = 1.941228

-----------------------------------------------

5x-4(1-x) >=1.941228
x>=66.01%

Ev(4.5) = 0.042[5*.7448 - 4*.2552] +Ev(4)
Ev(4.5) = 0.1135 + 1.941228
Ev(4.5) = 2.0547624

---------------------------------------------------

6x-4*(1-x)>=2.0547624
x>=60.5476%

Ev(5) = .132*[6*.6635 - 4*.3365] + Ev(4.5)
Ev(5) = 2.4025824
--------------------------------------------------

6x-5*(1-x) >=2.4025824
x>=67.29620

Ev(5.5) = 0.032*[6*.772 - 5*.228] +Ev(5)
Ev(5.5)= 2.5143264

We can see what's happening here . You have to play significantly tighter from the sb than you would play from the BB . More often than not , you will be folding form the sb and calling from the bb . This is true if we assume that the player will raise all in or call all in no matter what .

[jay_shark]

I'll have to fix up my work later as I spotted an error .

My intuition tells me you should call with the top 10 % of hands or so but I haven't verified this .

I solved a similar problem but without any blinds in play . This question poses more of a challenge which has to be looked at carefully .