V is a super station, he will raise only premiums and l/c 50% of hands preflop. will also also piece off with any piece including bottom pairs like 22 on a73, two overs, and any draw ranging from strong combos to weak gushots.

V limps and we iso with 88.

Stack are $500
FLOP(50) J93
V checks

What do we do and why?

Let me ask you a question...what's his range now, how much equity do we have against that and what's his continuing range?

You're going to get more out of this kind of thought experiment if you do some of the work to start with.

He will never raise, will peel flops with all pairs and draws from 22 to gutshots,

He probably has +40% equity

You said he raises premiums, now he doesn't raise? Where are you getting this equity figure from? What is his actual range in this spot?

are your questions towards preflop or OTF?

HU just B/B/B.

okay, why? sizing? value or bluff?

He's a station. Bet for value as big as he'll call.

40 otf anyway.

2/3 of the time you win a great pot.

1/3 of the time you own yourself.

if he calls 40 OTF, he has atleast 33% equity, so how is it value?

Our hand is just not strong enough for this unless we bet small enough to keep <= A-high in his range.

At no point is a bet by us pure value unless we improve or eliminate the stronger parts of V's range(or bet very small). His calling range is ahead of 88 unless he's calling down as weak as A-high, but the OP doesn't put that in his range.

There is some value in betting for protection and folding out stuff like unpaired Tx+. I don't think this is worth it on the flop, though.

We should check and evaluate his turn action. He's probably betting TP+ after a flop check, so his turn checking range is weak enough for us to value bet against. I would x/b/b on good runouts and fold to any aggression.

Explain...

Do I misunderstand your OP? Seems like you're saying he's continuing wide with a small piece, draw, W/E.

So what if he has 33% or 40%? Make him put $ in the pot.

Or stop isolating "lite".

Well, lets say he has 33% equity. we bet 100 into 100.

He is getting 2-1 and his range have atleast 33% equity so he is not making a mistake, he is calling correctly and is +EV for him to call.

We still make money when he calls by building the pot with an equity edge. Betting is better than checking in that scenario, even if calling is correct for him.

The true problem with betting is that we don't have an equity edge against his continuing range.

While that may be true, if he really is a station he's never thinking like this so it doesn't matter.

When faced with a station, stop bluffing and start value betting.

You're increasing your EV and decreasing his. If you check it down, your EV is +67, his is +33 (he wins 100 33 percent of the time, you win it 67 percent of the time). If you bet 100, and he calls, there's now 200 in the pot. Your EV is 134-33, or +101, his is 0. He's not making a mistake, but you're decreasing his EV all the way down to nothing.

If you are 2:1 to win, you get 1/3 of every dollar he puts in the pot. If you bet 100 and he calls, you win $133 on average. Just because he's not making a mistake by calling doesn't mean that betting isn't +EV for you.

Intuitively, this doesn't make sense to me. The math seems wrong. Somebody please explain.

If he's limp/calling 50% of hands than slightly less than 2/3 of the time he will not have a pair on the flop. Therefore we bet for value since he is calling so wide. Why would you let him outdraw you for free?

lets assume hand ends on turn, we have 66% equity and he has 33%

pot is 100

our EV of checking assuming he checksback is

EV=(W$*W%)-(L$*L%)

EV=(100*.66)-(100*.33)

EV=66-33= +33

lets do his

EV=(W$*W%)-(L$*L%)

EV=(100*.33)-(100*.66)

EV=33-66= -33

Is this correct?

No. The Ev of checking down is never negative for either player.

We are not losing the value of the pot 66% of the time by checking. We lose nothing because we aren't putting anything in the pot to potentially lose.

Our EV is $67 and his is $33 by checking.

If we bet $100 and he calls 100% of the time with 33% equity and no further action occurs, our EV is ($200*.67)-(100*.33) = $101, and his is -$1

If the pot is checked down, and you have 67 percent equity (2:1 favorite), that means you win 100 dollars 67 percent of the time, so ev=+67.

If you bet 100 into 100 and get called, you are wagering 100 to win 200. You have 67 percent equity, so you win 200 67 percent of the time, +134. You lose your 100 dollar wager 33 percent of the time, so that's -33. Ev=134-33=101.

From the other side, checking down $100 pot when you have 33 percent equity (2:1 dog), means your ev is +33.

Calling 100 to win 200 at 2:1 against odds results in Ev of 0, and it should be pretty clear why.

Basically, you're not "charging the draw" if you're checking it down. So the draw has a higher EV when it's not being charged. Betting anything when you're a favorite is better than betting nothing, even if your opponent does not make a mistake (meaning his EV is still positive or break-even).

Never mind

Impossible to have a negative EV when not facing a bet. Even if you're drawing dead, your EV of checking it down is 0 because you're not putting any more money into the pot. If you have any equity, checking it down realizes that equity without having to call a bet, so your EV is always positive.

How could one players EV remain positive or break even while the other players EV increases?