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Defending our opens UTG, interesting results.

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Posted by posted in Mid Stakes

Defending our opens UTG, interesting results.

'Okay so I'll briefly explain it from UTG.
We open a reasonable range of; 66+,ATs+,A5s-A2s,KJs+,QJs,J9s+,T9s,98s,87s,AJo+,KQo
which is 12.5%.

Someone 3bets us to 9x (we open 3x). They are risking 9 to win 3 (our bet) + 1.50 (the blinds).
This means they have that if we fold 9/(9+4.5) or 63%, they automatically profit with any two cards. Which is bad for us, it means they are exploiting us.

So we set about defending roughly 37% of our 12.5% opening range. This is 0.37*12.5, 4.625%.

Right, now we'll assume that when the 3bettor 5bets all in he has roughly 30% equity with his bluffs. He invested 91bb extra to 5bet bluff, so his net loss when he 5bet bluffs and we call is (approx) 91-60=-31

We 4bet to 20, then he 5bets he is risking 31(the amount he loses when we call) to win 20 (our bet)+9 (his 3bet) +1.50 (the blinds). This means if we fold more than 31/100+20+9+1.50, 24%, he auto profits. So we need to 4bet with a 76% value, 24% bluff ratio.
0.76*4.625=3.515. This actually equates to AQs, JJ+, AKo roughly.
We then balance this with 24% bluffs 1.11%, roughly A2s, AJs, ATs, KQs.

and yada yada your range is protected perfectly.'

I recently wrote this for someone, and having never actually done the maths myself (lazy I know) was fairly suprised by the results. Basically all the articles I read in the past were fairly dated and based their ranges on bigger 4bets and 3bets. The implications of a smaller 3bet are fairly dramatic, especially when people 3bet to 8 or 7.5 even IP nowdays.

Could someone check my working, and also would anyone reccomend a different strategy, maybe involving calling? Basically would appreciate some opinions because I was pretty shocked we have to value shove AQs to protect a 12.5% opening range really.
Thanks and gl.

18 Comments

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Ace 12 years, 1 month ago
I also just worked out the optimal 3bet strategy vs UTG, pretty tired now so may well be wrong, but can anyone comment on this too?

Also when we are the 3bettor in late position, we need to 5bet enough that the 4bettor in early position cannot profit by 4betting any two cards. If they 4bet, they are risking 17 (20- their 3bb raise) to win 20 (their 4bet) + 10.5 (the blinds plus the 3bet) so we need to defend 1-20/30.5, 34% of our 3bet hands to stop them exploiting us.
This leaves us with a 34% value to 66% bluff range.

We can only 5bet hands for value that have >50% equity vs their calling range. The only two such hands are KK and AA.
We also have to 5bet bluff, enough to make villains weakest 4bet hands breakeven when they call off our 5bet. They need to call 80 into 121.5, so they need 80/201.5, 39.7% equity to call.
Thus we need to give JJ and AQs 39.7% equity, which can be done by making our 5bet range KK+, A5s 1/2*A2ss. That's right, I want you to use a randomiser every time you 3bet A2ss vs utg and get 4bet, and 5bet shove it 1/2 the time.

Anyway, we now have our 5bet for value range sorted as 1/2 *A2ss, KK+ A5ss. That equates to 16.5 combos, and should be 34% of our overall 3bet range. Thus we can 3bet bluff 32 combos ish, which obviously you can decide yourself but is something like; K8s-K7s A2s-A7s.
mike 12 years, 1 month ago
at a quick glance i think your math in first post about the EV fo 5B jam is off

you can use the formula i post here as a way to double check - http://www.runitonce.com/nlhe/creating-4bet-all-in-ranges-against-40bb/

also consider that you may sometimes want to flat some KK/AA combos not 3B then which of course changes the 3B range you are trying to construct
Phil Galfond 12 years, 1 month ago
"So we set about defending roughly 37% of our 12.5% opening range."

If we defend exactly enough to make their 3bet bluff immediately break even, they profit a great deal. When we call, they still have sizable equity in the pot.

We need to defend more than this.
remember 12 years, 1 month ago
If the oppenents 3bet us with narrow enough range (eg,AA) or optimal range,they always profit when they 3bet. If your oppenents are good,you lose more when you defend more.
I think what matters here is:
(the ratio we are not 3betted)x(the net when we are not 3betted)-(the ratio we are 3betted)x( the loss when we are 3beted)
We set up an open range to make sure this figure is the biggest and followed the strategy like Ace said.This is optimal I think.
BigFiszh 12 years, 1 month ago
That only holds true IF we elect to call the 3b oop, right? If we always 4bet or fold that should not matter anymore.
remember 12 years, 1 month ago
"Being 3betted" is equal to "someone defend you IP" here.If your oppenents have a optimal strategy,their EV is always plus when they do sth. against you. If their EV is minus by some actions,they'd better do nothing to keep their EV being 0.

However,that your oppenents'EV is plus does not strictly means that your EV is minus beacause of the blinds.

In order to set up optimal strategy,I think we should focous on EV both when we are defended and when we are not.

Trying to do sth. to make your oppenents'EV be minus when they defend you IP is impossible.
remember 12 years, 1 month ago
1 ) "This means if we fold more than 31/100+20+9+1.50, 24%, he auto profits."
supose z is the ratio we fold.
(z)x(30.5)+(1-z)x(-31)=0
z is about 50% ,not 24%

2)"If they 4bet, they are risking 17 (20- their 3bb raise) to win 20 (their 4bet) + 10.5 (the blinds plus the 3bet) so we need to defend 1-20/30.5, 34% of our 3bet hands to stop them exploiting us."

There 4bet will auto profits when we fold 17/(20 +9+1.5)=56%.We need defend 44%,not 34%

3)"We can only 5bet hands for value that have >50% equity vs their calling range."

hands which have >39.7% equity is value hand, eg AK QQ.

4)"We open a reasonable range of; 66+,ATs+,A5s-A2s,KJs+,QJs,J9s+,T9s,98s,87s,AJo+,KQo
which is 12.5%."

You said "reasonable",without reason.
I think the reason is here:
(the ratio we are not 3betted)x(the net when we are not 3betted)-(the ratio we are 3betted)x( the loss when we are 3beted)
We set up an open range to make sure this figure is the biggest and followe the strategy by your analysis process
Ace 12 years, 1 month ago
Yeah legit point, you are definitely right on point 2).
I don't really get what you are saying on point 1) though,? could you explain it abit clearer?

Also, point 3). I am not sure I follow. I agree it will be +EV to get them in, but I don't think it's the most +EV action.
Surely there is no point taking a path with QQ/ AK that leads to us getting them in vs an underdog when we can 3bet enough vs him without doing so?
remember 12 years, 1 month ago
1) Let's calculate your oppenet's EV when he 5bet all in.
EV= (the percents you fold) x (binds's 1.5+your 20+his 9) - (the percents you call) x (his loss)
=(z)x(30.5)+(1-z)x(-31)
When EV=0,we get a ballace frequence:50%

3)3bet\5bet AK\QQ is +EV at least.
It's hard to say clearly that 3bet\5bet AK\QQ is better or just flat them is better.
But if you want a wider 3bet\5bet range,you have to do that with AK\QQ.This make you can add more bluff hands in your 3bet\5bet range.
Ace 12 years, 1 month ago
Yeah I hear you on point 2).

I think your original equation on point 1) seems correct, but rearranging it quickly I get z=(-)62.
I'm still super confused because I can't see what was wrong in my 4bet calcs, can you spot it?
Juan Copani 12 years, 1 month ago
I supposed this is a good point when we are facing opponents who are actually exploiting (good regs) our fold3betUTG%
Because if it´s not..

What´s the reason on being unexplotable when people is not exploting this fact ?

I didn't see a single opponent 5b jamming bluff to UTG, may be im playing really tight in this aspect ?
james 12 years, 1 month ago
I haven't check all your numbers but there's no way 4 bet calling AQ is going to be necessary to "protect" a 12.5% opening range. I did some quick math for your 12.5% range with 4 betting QQ+, A10s+, AQo+ where we call it off with QQ+, AK and it seems to do pretty well vs any strategy. Also, not sure if this has been mentioned but you're going to need to protect less of your range than you might think because this isn't a hu scenario and in 6 max there are people behind the 3 bettor (usually) who can cold 4 bet to "protect" your range too meaning that you won't need to 4 bet quite as much as you might initially think.
thedoors 12 years, 1 month ago
which 3bet range did you assinng to the 3bettor vs a 12.5% utg range? because i dont see that much and i chose to never do it to be balancerd so i call even AA KK... vs an utg range,
any thoughts? thanks
james 12 years, 1 month ago
I can't remember exactly because I didn't save the file but it ended up consisting of a lot of Ax blocker type hands and then a bunch of pocket pairs as low as 22-33 as well as the obvious value hands. Remember though, that even if it's +ev to 3 bet a bunch of those pairs to 5 bet jam them vs a balanced range it's somewhat likely that it's more +ev to flat with them.
Grouchy 12 years, 1 month ago
Ace

I did not read all the posts but here it is (I guess :) ):

As u said when he 5bet bluffs he gets back around 60bb from the 200bb pot, so he's risking 31bb to win 31/(31+20+9+1.5) = 50%; our 4bet range should be 1/1 bluff to value ratio .

Also 9/(9+4.5)= 66% not 63% so we should defend around 34% of our opening range and 4.2% of a 12.5% range, so we could 4bet for value QQ+/AK and as bluffs AQs, AJs, ATs, AQo and AJo.

Actually the smaller 3bet and smaller 4bet is beneficial to the opener in this case because when villain decides to 5bet jam he's risking more money to win less; if he instead raised to 10.5bb and we 4bet to 23bb he would have risked 29.5 to win 35bb so his 5bet jam to breakeven has to work 29.5/(29.5+23+10.5+1.5)=45%, so the opener's 4betting range should consist of 55% value hands.

This is actually surprising to me; I knew that the 4betting range should consist of 60% value/40% bluffs (this is true when opening is 3.5bb and 3bet is 12bb) but I never realized that a smaller 3bet will let you defend your opening range "easier". However, if the 3bet is much smaller (7bb for ex), i think it gets to a point where u need to have a calling range OOP.

James Hudson has a video on Dealing w/ Small 3Bets in NL, u could check it.

Hope one of the pros gives us his thoughts on this.

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