# GTO ranges OTR

• Bronze
Joined: 22.11.2008
First the theory:

We are HU on the river with a pot size bet left.

Our range OTR is as followed:
10 value combos
10 bluffs combos

Villain’s range OTR is made of 20 bluff catcher combos.

We assume for now that our value combos beat all his bluff catcher combos and that his bluff catcher combos beat our bluff combos.

As per GTO:

1) Villain should call at least with 10 combos otherwise we can shove our entire range and be profitable.

2) We shouldn’t shove more than 5 bluff combos otherwise villain can call with his entire range and be profitable since he needs 33% equity.

In this example, as per GTO, we make a +EV shove for a total of 15 combos (10 value and 5 bluffs) and villain will call with his entire range for a 0 EV call.

Before I go on is all the above correct?

In practice villain will have bluff catchers that beat our bluffs and don’t beat our value hands but also strong hands that beat some of our value hands. How do I define GTO ranges in that case?

Below is a hand I played where I wanted to define GTO ranges OTR for me and villain.

IPoker, \$0.50/\$1 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

MP: \$32.43 (32.4 bb)
CO: \$229.77 (229.8 bb)
Hero (BTN): \$143.13 (143.1 bb)
SB: \$77.42 (77.4 bb)
BB: \$102.30 (102.3 bb)

Preflop: Hero is BTN with K A
MP folds, CO raises to \$3, Hero raises to \$9, 2 folds, CO calls \$6

Flop: (\$19.50) 7 2 9 (2 players)
CO checks, Hero bets \$12, CO calls \$12

Turn: (\$43.50) Q (2 players)
CO checks, Hero bets \$28, CO calls \$28

River: (\$99.50) 6 (2 players)
CO checks, Hero bets \$94.13 and is all-in, CO ??

To make it simplier let's assume that I have exactly a pot size shove OTR.

From stats and reads, villain's range on the river is: 99, 77, 22, 7 8 , 8 9 , 9 T (12 combos) JJ, TT, 88, 66, 78s, 89s, 9Ts (30 combos) for a total of 42 combos

My range OTR is QQ+, AQ, A K (28 combos), AK (15 combos) for a total of 42 combos

All I know is that villain needs to be defending more than 50% of his range i.e 22, 77, 99, 7s8s, 8s9s, JJ, TT, 9Ts and another combo of 89s.

How do I define my range and villain's range from a GTO perspective?
• 11 replies
• Bronze
Joined: 05.02.2012
Why should he be defending more than 50% i dont see that. if he is calling more than that you should never bluff.

its not like im a lot into game theory or things like that so maybe im wrong.
i just moved up to nl25 so im not really focusing on gametheory.

in your example you should have 2/3 value combos QQ+ AQ AsKs and 1/3 bluffs
and villain should be defending 50% of his hands
he should always be calling 22 99 77 66 7s8s 8s9s 9sTs
and then just fill up with bluffcathers like JJ till you reach 50% of his range

then your bluffs has an EV of 0

and his bluffcatchers has an EV of 0

as far as i can see. but maybe im wrong
• Bronze
Joined: 22.11.2008
Originally posted by mkjmkjmkj
Why should he be defending more than 50% i dont see that. if he is calling more than that you should never bluff.

its not like im a lot into game theory or things like that so maybe im wrong.
i just moved up to nl25 so im not really focusing on gametheory.

in your example you should have 2/3 value combos QQ+ AQ AsKs and 1/3 bluffs
and villain should be defending 50% of his hands
he should always be calling 22 99 77 66 7s8s 8s9s 9sTs
and then just fill up with bluffcathers like JJ till you reach 50% of his range

then your bluffs has an EV of 0

and his bluffcatchers has an EV of 0

as far as i can see. but maybe im wrong
Yes you are right - not more than 50% just 50%

I would have 2:1 ratio value to bluffs if my value hands were beating all his range but that is not the case here.
• Bronze
Joined: 05.02.2012
but i think all the hands that is value is hands that has more than 0 equity vs the 50 % range he should be calling the rest is bluffs so its still the same ratio.

a hand with 0 equity vs his 50% range has an ev of 0 because of fold equity
lets say you have a hand with 1% equity vs a 50% range if villain starts calling more then the hand gains equity if he calls less it gains fold equity so all hands that has more than 0 equity vs villains 50% best hands is value the rest is bluffs.

and then you just use the same ratio.
• Bronze
Joined: 22.11.2008
ok let me reformulate my question:

How do I define my shoving range so that villain has a 0EV call
• Bronze
Joined: 19.06.2012
first off, in general you can't calculate river solutions without knowing how we got there. especially with tight ranges some hands can give up EV on earlier streets to get to profitable bluff spots on some cards and then the defender doesn't need to make the bluffs break even but the float-bluff line break even.

so whenever you are doing theory on a river spot I would tend to call it a local approximation. you look at the river as a subgame, like the game starts right there without any history.

alright so regarding your question. In the full polarization case you described the 10+5 betting range is right (its not quite exact as it's not a full pot sized bet, but close enough)

In the actual poker case, where ranges are not fully polarized, it is a lot more difficult. e.g in MOP syymetric [0,1] game you find the the cutoff bluffcatcher depends on the bet size in a non-linear way.

Which means that this
All I know is that villain needs to be defending more than 50% of his range

must not be true. I think they did bet pot sized bet actually and there you can see more than 50% folds. The simple reason for this is that the IP doesnt have enough bluffs, he has to bluff with hands like 0.0 to 0.1 which have some showdown value, hence the bluffcatch is only trying to make checking = bluffing not folding = bluffing.

What you should do is construct some more simple range games and solve those. The example you posted is already a bit too complex for me to go over here unfortunately. (And you are missing your air hands / how many air combos you have, but i assume you mean you have enough pure air to bluff with so that 87s is a bluffcatcher)
• Bronze
Joined: 15.06.2009
Are you asking about how to exploit villains deviation from GTO? If so, you should shove 100% or 0% depending on how he deviates.

EDIT: I suppose you knew that. I think you need to sharpen your question a bit.

/Johan
• Bronze
Joined: 22.11.2008
Originally posted by lnternet
first off, in general you can't calculate river solutions without knowing how we got there. especially with tight ranges some hands can give up EV on earlier streets to get to profitable bluff spots on some cards and then the defender doesn't need to make the bluffs break even but the float-bluff line break even.

so whenever you are doing theory on a river spot I would tend to call it a local approximation. you look at the river as a subgame, like the game starts right there without any history.

alright so regarding your question. In the full polarization case you described the 10+5 betting range is right (its not quite exact as it's not a full pot sized bet, but close enough)

In the actual poker case, where ranges are not fully polarized, it is a lot more difficult. e.g in MOP syymetric [0,1] game you find the the cutoff bluffcatcher depends on the bet size in a non-linear way.

Which means that this
All I know is that villain needs to be defending more than 50% of his range

must not be true. I think they did bet pot sized bet actually and there you can see more than 50% folds. The simple reason for this is that the IP doesnt have enough bluffs, he has to bluff with hands like 0.0 to 0.1 which have some showdown value, hence the bluffcatch is only trying to make checking = bluffing not folding = bluffing.

What you should do is construct some more simple range games and solve those. The example you posted is already a bit too complex for me to go over here unfortunately. (And you are missing your air hands / how many air combos you have, but i assume you mean you have enough pure air to bluff with so that 87s is a bluffcatcher)
Don't really know about the MOP symetric game....

With the River range that I gave to myself (ok I should prob have included TT-JJ but let's park that for now) versus a bluffcatcher like 87s I have 28 combos of value hands and I need 14 combos of "air" to make him indifferent to calling or folding (and I have 15 combos of AK). So yes I have enough air combos in my range.

I know it is a bit more complex that a simple theoretical example since ranges are not fully polarized but this is an actual hand I played so that makes it more interesting too

Can you give me any tip on how I should build my shoving range to make villain indifferent to calling or folding?
• Bronze
Joined: 22.11.2008
Originally posted by YohanN7
Are you asking about how to exploit villains deviation from GTO? If so, you should shove 100% or 0% depending on how he deviates.

EDIT: I suppose you knew that. I think you need to sharpen your question a bit.

/Johan
I think this is right but I dont know his calling frequency
• Bronze
Joined: 05.02.2012

so if i understand internets answer we should be checking a lot of hands on the river because the ev is higher than betting them and villain should be calling less than 50% because we are betting so few hands.
is this the right thinking?
• Bronze
Joined: 22.11.2008
If we know villain's calling frequency (i.e his calling range) from stats or reads we can play perfectly.
If he calls 50% or less then I should shove my whole range
If he calls more than 50% I should shove a range that has more than 50% equity vs his calling range.

What I wanted to determine was my shoving range so that villain is indifferent to calling or folding. In the theoretical case of the OP where villain only has bluff catchers (that beat my bluffs and lose to all my value hands) I know I can accomplish that by shoving a range with a 2:1 ratio value to bluffs.

In this practical example, ranges aren't perfectly polarized which makes it more complicated. But yet I am sure there is a way to determine my shoving range so that villain has a 0 EV call.
• Bronze
Joined: 22.11.2008
Anyone on this?