# FL HU SnG opening range

• Bronze
Joined: 16.06.2011
Hi everyone,

recently I have started learning FL HU more thoroughly and I'm trying to understand why the opening range is so loose. I imagined two bots playing it, on the BB a calling station which calls you down with a 100% range no matter what, and on the SB a barrel monkey which bets down any hand which it opens.

The question: what kind of range can the SB open profitably ?

According to my calculations SB needs ~46,15% equity vs a BB-s range here and that manifests itself in the below range:

This is a 62.5% range, and considering that BB is a massive fish, I wonder how can you justify raising 83-85% from the SB vs a better player who can 3bet you raise you etc.. so not letting you realize your equity.

Ofc this is a very rough model, because vs a real opponent you have fold equity, implied odds, etc, but this true for you as well, so even if you need to add more bluff hands and such it is hard to imagine that you need +20%.

Do you know any kind of reasoning that implies a 80+%-ish range ?

Also I wonder how the SB opening range changes in a FL HUSG when the blinds become higher and the effective stacks get shorter and shorter. Do you have any info about this ?
• 25 replies
• Black
Joined: 30.07.2008
How did you calculate that 46% equity?
• Bronze
Joined: 28.04.2010
you should open about 85% - 90% SB standard
• Black
Joined: 03.02.2007
Originally posted by kavboj84
I imagined two bots playing it, on the BB a calling station which calls you down with a 100% range no matter what, and on the SB a barrel monkey which bets down any hand which it opens.
I don't see the point off calculate a strategy against a bot who's calling down 100% You probably don't need to change your preflop range in this situation (keeping something 85-100%), but your barreling range (IE if your opponents never folds, there is no point in bluffing anymore).

The main reason in opening that wide might be "When you have nothing, remember that it's the same for your opponent" and then the guy with initiative wins.

Even against a guy who's 3betting 100% on the big blind, you ca still open close to 100% if you know how to not fold too much and not get easily exploited postflop.

When the blinds becomes bigger, most players plays tighter, so it's even more profitable to openraise wide because you will win more pots preflop.
• Bronze
Joined: 16.06.2011
@Dawnfall26: My thought process is the following.

To be indiferrent to raising the amount you win with raising has to be equal to the amount you lose when you fold. I.e.

<raise>=<fold>

By 1/2 blind structure you put in 6.5 small bets into 6.5 when you raise, and lose 0.5 SB when you fold. Let the equity in question be called x.

6.5x-(1-x)6.5=-0.5

6.5x-6.5+6.5x=-0.5 = /+6.5

13x = 6

x= 6/13 ~46.15%

@Siliciom :

there is merit in it(at least for me) because this is an upper limit for your value hands vs the opponent of your dreams. Against someone who calls you down with any two you cant keep raising 85%, because the bottom of your range needs fold equity to be EV>0.
Vs a better player you have fold equity, but its hard to imagine you need +20-25% for bluffing, plus you wont have a 62.5% value range in that case,
because you play vs tighter ranges on each street. Plus you will get raises which will make your play more expensive, and because your costs increase you need to win more as well.

The main reason in opening that wide might be "When you have nothing, remember that it's the same for your opponent" and then the guy with initiative wins.

I don't think that an unexploitative strategy cares about the initiative. If it needs jack high to be called down then it calls down jack high, so if you are overbluffing in hope of a good opponent folds his 'nothing' when he shouldn't than I think you are too optimistic.
• Black
Joined: 03.02.2007
I'm not good with math, but even 72o has 34.5% equity against a random hand, so you will have to limp those hands. Right?

Other reasons I can see to raise those weak hands is to have something to bluff on some boards (ok, maybe not vs the bot who's calling down 100%, but against the vast majority of player) and have some hands that can hit ragged boards.

One way or another, I don't see how you can fold 38% of your range pre. Even in a cashgame BvB situations which is pretty high raked, you open more than that being out of position

PS: You can raise pre, and still check on the flop if you think you have to.
• Bronze
Joined: 16.06.2011
I'm not good with math, but even 72o has 34.5% equity against a random hand, so you will have to limp those hands.

Yes, if the BB goes all in you can limp 72o, but this is not the case here. You need to see the river if you calculate with 34.5% equity because this is an all in equity, and seeing the river will cost you a lot more than 0.5 SB

Other reasons I can see to raise those weak hands is to have something to bluff on some boards

This 62.5% range also contains bluffs in that sense, what do you think what is 98o on an AKQ board. But there is no real postflop play in this model, because its a betdown vs calldown model. The reason why I'm using this is because my equity calculator uses static ranges, so I have to tailor the model onto the calculator unfortunately (static model to static ranges) and then make guesses how much it differs from reality and modify the ranges according to these.

You can raise pre, and still check on the flop if you think you have to

of course,thats why I said that it is a rough model, it uses only bet flop and thats it, and it is not real, but how can you calculate your equity in those cases when you have to x/f or x/c on the flop (plus you can b/3b x/r cap etc..)? Or if you cant, you should at least be able to roughly estimate the effect of adding x/f and x/c to your strategy, otherwise how can you decide how much more/less you can raise profitably ? I don't want a calculation that tells you that you need to raise x say exactly 85.8437267342354619342134...%, an approximation like the one I did with the value range above is absolutely fine for me. Because so you can see that what you can raise for value preflop is somewhere around 55-60 +/- a few %.
• Bronze
Joined: 22.09.2010
Unfortunately that model differs massively from reality, in fact so far it's almost useless

HUHU players tend to have WTSD's in the very late 40's to early 50's so 100% calldown is just as wrong as assuming they fold 100%.

Vs someone who'd calldown 100% of their range you're obviously just going to play exploitatively for value, even though I'd still raise and check with a lot of hands because a pair vs our opponent's calldown range is the nuts.

The generally accepted (i.e. what every single GTO bot give or take 0.5% raises with) range is around 82.5% in a rakeless environment vs an opponent of equivalent skill:

22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T4o+, 95o+, 85o+, 75o+, 65o, 54o

The only real place where there's big time disagreement pre-flop is 3-betting ranges as they can be very complex. The figure is generally similar (around 35%) but the distribution of hands (i.e. mixed strategy with different hands, pure hand value etc) is very different depending on which model is being used.
• Black
Joined: 30.07.2008
Kavboj:

I dont see how you can assume that when you raise preflop, you will inevitably go to SD and what I find even more false is that you will pay 6,5SB to go there. You will obviously not bet 100% postflop, you even have position so if nothing else you will be able to checkback on the river,let alone taking freecards or just giving up.
I would even make a bold claim that a guy who is going to have a WTSD of 100% you can raise any two preflop and just valuebet when you have a made hand.

And...did you include chance of him folding preflop and therefore winning 1,5SB in some %?
• Black
Joined: 30.07.2008
If you want to put this matter into equation I think its much better to just calculate your decition preflop alone.

So EV would be:

(chance of him folding)*1,5 SB +
(chance of him calling)*((% winning in raisedPot)*2,5 SB-(% of loosing in raisedPot)*1,5 SB +(% of tie in raisedPot)*1,25 SB +
(chance of him 3b)*((chance of you calling 3b)((% of winning in 3b)*3,5 SB-(% of loosing in 3b)*2,5SB + (% of tie in 3b)*1,75 SB)+
(chance of you 4b)*((% of you winning in 4b)*4,5 SB-(% of you loosing in 4b)*3,5 SB)+(% of tie in 4b)* 2,25SB)

Something like that. And since you have position its pretty safe to assume that the calculated EV will only be higher when you take postflop play in consideration.

Prolly full of errors,sooo tired will review again later and give and give an example.

so for 34s;
lets say he defends 100%(30% he 3bet,70% he flats)
vs 3bet:
Equity Win Tie
MP2 35.29% 34.84% 0.45% 43s
MP3 64.71% 64.26% 0.45% 55+, A2s+, K5s+, Q7s+, J8s+, T8s+, 98s, A7o+, A5o, K9o+, Q9o+, J9o+, T9o

vs call:
Equity Win Tie
MP2 40.23% 36.18% 4.05% 43s
MP3 59.77% 55.72% 4.05% 44-22, K4s-K2s, Q6s-Q2s, J7s-J2s, T7s-T2s, 97s-92s, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A6o, A4o-A2o, K8o-K2o, Q8o-Q2o, J8o-J2o, T8o-T2o, 92o+, 82o+, 72o+, 62o+, 52o+, 42o+, 32o

So now the math:

EV=
0*1,5+0,7*(0,3618*2,5-0,5572*1,5+0,0405*1,25)+0,3(0,3485*3,5-0,6426*2,5+0,0044*1,75)= -0,0301875 SB
May be mistakes,correct me please

So ya 43s is considering no postflop edge a loosing hand. Which doesnt really surprise me. But 43s is a pretty decent postflop hand to play in position, especially vs a guy who will calldown any two cards. We can simply just valuebet when we have an equity edge vs his range or play on odds and outs when we dont. Fact that we have postion is worth at least some % of that BB where we can make a good decition which should cover for this 0,015BB deficit.
• Bronze
Joined: 16.06.2011
@ Boomer2k10 :

Unfortunately that model differs massively from reality, in fact so far it's almost useless

I never said that I would use it in terms of playing this range IRL, nay I said that it is an artificial one, but it seems that I should have laid even more emphasis on that.

So again, the range is based on all-in equity, because this is the only quantity I have for estimating the chance of winning, and because of this every other factor is geared to it. Thats why things like x-ing is not allowed for the SB.
If we want to include more actions (for ex. allowing BB to fold or the SB to x ) , we need a better method for the calculation of the chance of winning, which can measure the effect of your future postflop actions (other than betting/calling) to your preflop chances. But this needs to work with dynamic ranges because after postflop actions neither SB-s/BB-s preflop range will remain intact.
So far I have not found such a method, but if you have one Im all ears.

I'd also like to know how GTO bot devs came to that opening range and where do you have it from.

even though I'd still raise and check with a lot of hands because a pair vs our opponent's calldown range is the nuts.

I just approached this in a different way, I didnt say I would x the flop when I dont hit, but that the model does not consider implied odds and fold equity.

@Dawnfall26 I think you may not have read the posts with enough attention because what you objected has been explained or answered previously.

The equation you posted is fine but the problems with it are the 'winning in' parts, and the reasons are expanded also above.
• Black
Joined: 30.07.2008
Yes sure winning will be problematic, but so will loosing be,wont it? He will still have to bet to make us fold...assuming that we need to invest full 6,5SB to seeSD is just plain wrong, also I have a feeling that you are somehow thinking that he will utilize his share of equity better than we are. I dont see how that can be true.

And my idea about developing a play that will be indifferent to what he does. That basically means that our overall EV vs him will be 0,am I right? If that is true we will end up huge losers as rake will eat us alive. Constructing such gameplan on rake heavy stakes is imo pretty destructive.
• Bronze
Joined: 22.09.2010
The ranges come from this Annual Poker AI competition which was dissected in Phil Newall's Further Limit Holdem book

Unfortunately I don't know the exact model used but if poker could be solved easily through a simple model it wouldn't have taken 20 years of research using super advanced bots and developing new a better modelling methods (which still involve bucket style methods) to get close to a solution.

The fact that the top 3 bots analysed use pretty much exactly the same range details to me that this is near as makes no difference a solved situation.
• Bronze
Joined: 15.06.2009
It might be possible that some marginally unprofitable hands should be played as well. Sounds strange, but the reasoning would be that the complete range might benefit because the better hands may get better paid off. But this effect is probably quite small if it is there at all.
• Bronze
Joined: 16.06.2011
@Dawnfall26 :

It seems to me that you still have not read the thread thoroughly enough, or just can interpret it right.

I have a feeling that you are somehow thinking that he will utilize his share of equity better than we are.

Can you quote the part that makes you think that ?

That basically means that our overall EV vs him will be 0,am I right?

Why would it be, how did you come to this conclusion ?

Constructing such gameplan...

This is not meant to be a gameplan. This is an attempt of estimation of an upper limit for the SB opening (value)range. Can you understand the difference between the two ?

assuming that we need to invest full 6,5SB to seeSD is just plain wrong

Regarding the whole game it is, but the purpose of this thought experiment is not to be precise.

vs 3bet:
Equity Win Tie
MP2 35.29% 34.84% 0.45% 43s
MP3 64.71% 64.26% 0.45% 55+, A2s+, K5s+, Q7s+, J8s+, T8s+, 98s, A7o+, A5o, K9o+, Q9o+, J9o+, T9o

Have you realized that the problem you disapprove appears here as well ?

@Boomer2k10:

Isnt the method they used described in the book ? Or at least just outlined somewhat ?
• Bronze
Joined: 22.09.2010
Unfortunately no the model wasn't there to look at but 3 of the strongest bots, each capable of addressing billions of decision nodes in their game trees came to the same conclusions:

1) Always raise when first in
2) Never Cap when 3-bet
3) Fold between 7.5-8% of hands in BB
4) Raise between 82.2-82.8% of hands in SB
5) Maintain both a calling and 3-betting range which can hit a wide range of flops
6) Go batshit insane when someone limps in (i.e. 65%+ raising range)

In 3-betting they're wildly different (7% difference in ranges and difference between pure and mixed strategies) inferring that the lines get more blurred when the pot is inflated or that certain hands are so marginal whether to 3-bet or not that hyper small differences lead to a change in line.
• Bronze
Joined: 28.04.2010
Originally posted by Boomer2k10
Unfortunately no the model wasn't there to look at but 3 of the strongest bots, each capable of addressing billions of decision nodes in their game trees came to the same conclusions:

1) Always raise when first in
2) Never Cap when 3-bet
3) Fold between 7.5-8% of hands in BB
4) Raise between 82.2-82.8% of hands in SB
5) Maintain both a calling and 3-betting range which can hit a wide range of flops
6) Go batshit insane when someone limps in (i.e. 65%+ raising range)

In 3-betting they're wildly different (7% difference in ranges and difference between pure and mixed strategies) inferring that the lines get more blurred when the pot is inflated or that certain hands are so marginal whether to 3-bet or not that hyper small differences lead to a change in line.
*died laughing*
• Bronze
Joined: 16.06.2011
Originally posted by Boomer2k10

6) Go batshit insane when someone limps in (i.e. 65%+ raising range)

What if SB open limps his entire range ?

BTW since Ive played Neo Im a bit sceptic about these bots. I won its chips 2 times within an hour and I quit because I didnt see anythig special I could learn from. Its hard to believe that it would be a winning player vs a slightly trained human.
• Bronze
Joined: 28.04.2010
Originally posted by kavboj84
Originally posted by Boomer2k10

6) Go batshit insane when someone limps in (i.e. 65%+ raising range)

What if SB open limps his entire range ?

BTW since Ive played Neo Im a bit sceptic about these bots. I won its chips 2 times within an hour and I quit because I didnt see anythig special I could learn from. Its hard to believe that it would be a winning player vs a slightly trained human.
try polaris. I beat Neo aswell even in NL mode.
• Bronze
Joined: 16.06.2011
How can you get your hands on polaris ?

BTW Neo won 1 gold and something like 5 bronze medals on the Annual Poker Competition.