# River defend range vs 3 barrels

• Black
Joined: 05.08.2007
Board is K T 2
Preflop i open raise CO 28% range, BU unknown reg calls, all fold.

1) Once i check flop, what range do i defend on river vs 3 barrels 70% pot size bet?
I can cbet 3 streets KQ+, 2 streets other Kx. I want to check/call Tx and JJ QQ because no need to protect. So if i would bet Kx+, strongest hands in check range would be 2nd pair. This means that villian can bet huge with his top pairs and has high equity which is bad for my Check range EV.
To unable him to make huge bets with Kx+, i should check some % of Kx+. If i check with weakest Kx still he can bet big with most (or all) of Kx+. So it means i should check some of Kx+ which are stronger than his Kx. Agree so far?

2) what is the % of strong Kx+ hands that i should have in river defend range to unable villian to bet big with all Kx+ (I design river defend range vs 70% pot size bet)? If it is e.g 30% he will not be able to overbet, but can still value bet 3 streets with around pot size bet with all Kx+. So is that bad now?

3) obviously if he bets 70% 3 streets and strong Kx+ are making >= 50% river defend range, he cant value bet ANY of his Kx on river for value. Is that good cor my overall EV? Check range EV will be highest than in case 2) but can it be that i loose a lot of EV in bet range so that overall EV decreases vs optimal villian? It is for me not possible to conclude.

So final and key question, what is the % of strong Kx+ hands in river defend range?
• 4 replies
• Bronze
Joined: 10.06.2012
Good question.

A good starting point is, when you check and he bets 70% pot. You need to defend 1 - (.7/1.7) = ~60% to deny him autoprofit.

So on the river, if you only x/c each street, you would need to call down .6*.6*.6 = ~20% of you your flop checking range to deny BTN auto profit.
• Black
Joined: 05.08.2007
Originally posted by jules97
Good question.

A good starting point is, when you check and he bets 70% pot. You need to defend 1 - (.7/1.7) = ~60% to deny him autoprofit.

So on the river, if you only x/c each street, you would need to call down .6*.6*.6 = ~20% of you your flop checking range to deny BTN auto profit.
Yes i used this in the range construction.
• Bronze
Joined: 18.01.2010
Originally posted by jules97
Good question.

A good starting point is, when you check and he bets 70% pot. You need to defend 1 - (.7/1.7) = ~60% to deny him autoprofit.

So on the river, if you only x/c each street, you would need to call down .6*.6*.6 = ~20% of you your flop checking range to deny BTN auto profit.
I think that is not 100% correct unless you check 100% of your range on the flop. Even if opponent has some autoprift spots, that doesn't necessarily mean he is exploiting you. For example, I cbet 90% and I check fold 100% when I check.

You have to take into account the times you bet and opponent has to fold with his weakest hands. At least on the flop if you have a cbetting range, but even on the turn if you have a check/call donk range for example.

If you don't have a donking range, then you can defend 0.6*0.6 of the range you checked called on the flop on turn and river. But on the flop you can defend less than 60% of your checks depending on your cbet strategy.

does it make sense? correct me if I'm wrong!
• Black
Joined: 05.08.2007

I think that is not 100% correct unless you check 100% of your range on the flop. Even if opponent has some autoprift spots, that doesn't necessarily mean he is exploiting you. For example, I cbet 90% and I check fold 100% when I check.
Even if you check 100% range on the flop, it is still not 100% correct. It is only 100% correct if villian has 100% polarized range. Since in reality it rarely happens, also not in this example, then we actually need to defend more because his bluffs have equity. Also it depends how do we define autoprofit. Is it autoprofit for the whole hand (from preflop to the end of the hand), or autoprofit for the single observing play (e.g. bet flop). e.g. if you cbet 90% flop and fold 100% when you check, then when you check villian has +EV bet with any hand, and he should bluff 100% of the time. But did he play +EV the whole hand? probably not, because preflop he lost few BB when he cold called us, and postflop he gets only 10% in situation to bluff +EV.

So as a solution to this, I would on flop defend when I check in such a way that villian can't have +EV for the whole hand.
If e.g. pot is 7.5bb, we cbet 50%, and when we check villian bets 5bb and preflop calls 3bb open raise, and we assume he loses pot when we cbet (his equity is 0% and will give up turn), then his EV postflop is:

EV_preflop = -3BB

EV_postflop = P_cbet * 0 + (1-P_cbet) [FE * 7.5bb - (1-FE) * 5bb]
EV_postflop = (0.5) * [FE * 12.5bb - 5bb] = FE * 6.25BB - 2.5BB

Now, since we want to make his total EV = 0 :

EV_total = EV_preflop + EV_postflop = 0

Now we find required FE to unable villian to have autoprofit, by:

EV_postflop = +3BB

This means he can earn 3bb postflop because he lost them preflop:

FE * 6.25BB - 2.5BB = 3BB
FE = 5.5BB / 6.25BB = 0.88

So this means, that if he would have hand that has preflop 0% equity, he cant play whole hand +EV if we fold <= 0.88 once we check. In reality it is much more complex, because hands have equity preflop and on flop, so we cant simply say he lost 3bb preflop when he called us because sometimes he will hit a good hand, and on flop he will have equity when he doesnt hit. In practice, if I cbet 35-50%, I give up around 45-50% once I check, and turn and river defend standard 1-a.

Anyway, I think this is not the topic of the thread, we can make another topic for this, imo it is also interesting and important topic.

Anyone knows how this is calculated/approximated in reality, I mean how much we defend flop in such case?