I would check raise the river a ton vs this strategy both with slowplays and bluffs and completed draws.

I just think once you get called on the turn you're rarely against a worse hand so trying to showdown doesn't make sense. I think it makes sense to give up but you would be wholly expecting to lose so I guess in that regard I do agree there should be checkbooks but I wouldn't expect to win at showdown.


I wasn't commenting on the line as a whole I guess I was just saying that I wouldn't expect to win with those hands when we check back which is what I thought you were saying in your previous post.

Like I said above I agree they should be give checks to showdown but I guess I just read in your post you expect them to win some % of the time I would expect that to be really low %.

Edit: by really low % I mean almost 0.

Yes it's a low percentage, but considering that river bluffs in position are only slightly profitable, I think checking back 87s on the T45r, K, 7 runout is going to be slightly more profitable than bluffing the 87s.

I expect to win there maybe 10% of the time as the button. I think that's better than earning 5% with a bluff. However, I'm far from convinced that I'm right and if someone wants to solve the spot given these starting ranges, I'm all ears:

I raise cutoff for 3x: 22+, A2s+, A5o+, K2s+, K9o+, Q8s+, QTo+, J8s+, JTo, T8s+, 97s+, 86s+, 76s, 65s. Not sayin this is perfect, but I've had decent tourney success raising this range. Of course I'll tighten up vs players that 3 bet a lot and I'll loosen up vs players that are terribly passive. This is my default.

button calls 3x: 22-77, A6s-ATs, ATo, AJo, K9s, KTs, KJo, KQo, Q9s+, QJo, J9s+, T8s+, 97s+, 86s+, 76s, 65s. Maybe loose but I see these hands at showdown consistently. I think it's in the realm of ok preflop calls with a lot of chips behind, and it hints at what I consider a strong 3 betting strategy, but your mileage may vary.

I only know not to pass a +EV play. I find interesting the idea to bluff catch less bc Villain has a profitable check back. But vs a polarized range, there is not a profitable check back.

Vs a condensed range then ? does this make a difference ? Of course it's the frequency that is affected, not the EV. Not making a +EVcall is a mistake. Happens to everybody.

How is it affected tough ? Even Villain 'would' have a profitable check back, once he bets he either doN't have this profitable check back, or he's over bluffing ? Tough he could be 'under bluffing' because of the profitable check back. I'll think about it.

Out of position checking ranges should not be polarized.

What I meant was checking versus an opponent who bets Polarized. The in position player may have a polarized range. And you hold a bluffcatcher. If it s a situation where your range (oop) is capped, all your bluffcatchers would have the same ev versus an opponent who then bet polarized in position (blockers and other considerations aside).

What I was thinking was with depolarized ranges, all your calls are not only bluffcatchers. And then dont have all the same EV.

So I was thinking versus polarized range it's 'only' a question of frequency. While versus a condensed range it s very different.

Some runouts are better than others of course, but generally speaking when strong players face off heads up postflop, the fundamental law of chasing should apply.

Being capped is bad poker vs good opponents because it allows them to massively overbet for huge profit.

I'll think about it more in details later but I think we often have no choice to have a capped range. We don't like having a capped range but you can not always have what you want.

Indeed.
I think it's terrible to flat so wide. It may be common to do so, but I don't think it's good at all. I haven't studied the best way to play against such wide ranges, so it's probably best to ignore any of my strategic/theoretical input in the thread. :/
If you run a solve for those kind of ranges, it will presumably produce a strategy that is quite different to how I play by default, and it might even make 99 a +EV c-bet too. It's not a good c-bet if the BTN flats pre with a tight/strong range, however, because the flop floating/raising range is going to play so well on most runouts and give the OOP player all kinds of trouble. A T54r flop is very tricky to negotiate in COvBTN if both players are "good".

I completely agree. I'd check some Txs there as well.

That's ok with me. When strong players open 3x in the cutoff with no antes, I'm definitely folding some hands on that list. ATo, KJo, QJo, all come to mind as snap folds for me when a strong player opens. The difference in (calling %) if the button folds all of those 48 preflop combos is significant imo.

I used to think like this but now I believe that through mixing, we should have the nuts on every runout imaginable given every realistic action sequence or else:

Thread delivers by the way. Thanks for all the feedback. I figured that if we were gonna pick apart some river scenarios that there would be inevitable disagreement on which ranges we actually should get to the river with. I think that if we can come to agreement on these proper river ranges then we are in a great position to better understand where river profits come from.

I wouldn't dare ignore you Arty. To do so would be a major blunder. If giving opponents too much credit is your biggest leak? I think you're gonna be fine.

However, I do think that you should study how to play vs such ranges because this is likely how your opponents play. Perhaps this is the next step for you.

I’m in bed falling asleep but I want to put this thought down:

I think I was wrong earlier regarding the part about holding the nuts on every possible runout. Perhaps on boards that allow both players to hold the nuts it’s more important, so on such boards we will see the best possible hand taking passive lines. On boards that restrict the number of nut combos to the point that only one player can have the best possible hand, I think that the second nuts becomes the most important hand to be present in all realistic action sequences.

The basic idea is that the singular nut combo will always be able to overbet, and that’s precisely the reason for needing to have the second nuts in range on such boards.

So for example: the KK9 2 3 runout allows KK to overbet quite large, but K9 can’t bet quite as big. Since both players can hold K9, it’s the most important hand to mix with as the player facing the bet. Not KK.

Contrast that with a board that contains five of the same suit. The second nuts must be present in all lines for the player that is facing the bet.

On unpaired non flushing boards that allow straights, the second nuts is again the most important hand to have in range.

I think that’s good but I’m gonna fall asleep now.

Hi Bob, I think the KK923 board is kind of too easy. I was thinking about boards that kind of 'force' you to check-raise the nuts at some point to get more EV. Because the EV is really what we are competing for.

I would look more for a kind of double suited J 8 9 T with KQ or even a Qx. and the river brick.

Would you really check-call the turn there ? The Kk923.... I don't know about the 'nuts', but it's sometimes difficult to get worst value even you hold a K and check call check call still have K in your range.

But really I think theoretically if you never check-raise the nuts even on a wet board. It may be good to do it a tiny fraction so your opponent can overbet in it. But think of all the free cards you give, your action killed, etc...

But sometimes, your +EV bring you on another line and it's more important than just being balanced. I think 'correct unbalance' is good too. I don't know if it's a real concept. But we are looking more for EV than for balance.

Just thinking

I also think a xKK often favour the IP, who has more K (from pretty much any 2 positions except SB vs BB full ring) and it could be good to check call check call a K if you want to protect another part of your range.

Yeah I was half asleep when I wrote those last two posts haha.

Looking back, I think the point that I was trying to make was this:

If only one player can hold the nuts due to the nature of the board, then the player holding the nuts can force the second nuts into a bluffcatcher situation by betting big, assuming that stacks allow such a betsize.

If both players can hold the nuts due to the nature of the board, then the out of position player has to have the nuts in all realistic action sequences or else the in position player can massively overbet for huge profit.

But that shouldn't matter if you are facing an opponent who bluffs appropriately (i.e. has the appropriate ratio of bluffs to value bets).

There is no way to 1 always reach the river with the nuts and 2 spread that over all available action sequences without making mistakes somewhere along the way before the river.

That's just simply due to the probabilistic nature of the game. Sometimes the cards come down bad no matter how well you play and you just have to deal with the shirt sitiations as best you can.

I agree that we can't always have the nuts in our range, that's not what I meant. Sorry for not being clear.

Try thinking about it in (0,1) game terms, since every river situation can be described as such a game.

All I meant was that there should be a noted difference when comparing these situations:

a) only one player can hold the nuts
b) more than one player can hold the nuts

Taken to the extreme:

If there's an Ace high straight on the board, how should one play?

I think the answer is very different than how one should play in situation (a).

So how does the fact your opponent has showdown value with some of his range affect your calling frequency ?

Great thread, really interesting. I think the actionable edge in this river scenario will boil down to the sliver of card removal. Card removal is only known by one of the two, and is the edge in otherwise perfectly balanced river scenarios, especially when a caller is holding one or two important nut blockers.

It gives the player in position incentive to check back for a profit that is greater than the profits earned by bluffing vs an opponent that will call at minimum defense frequency or more often.

That’s why everyone learns to not bluff vs calling stations.

Depends on how you look at it I think. The player that holds more value hands will probably be the long term winner. To see why, think about the profitability of a bluffcatcher after the opponent has bet. You’re really only winning a fraction of the bet, while the bettor is earning the existing pot plus a fraction of the bet back.

Even when the caller can beat some value hands this is true. In order to earn a fraction of the existing pot in addition to the bet, the caller needs a really strong hand. I’m not exactly sure, but I think that the caller needs to beat (bet)/(pot) of the bettors value range in order to actually dig into the existing pot and profit from both the bet and the pot.

For example:

pot = 1

player A: out of position players range = (0.4, 0.5, 0.6, 0.7)

player B: in position players range = (0, 0.65, 1)

player A checks, player B bets 1 pot with 100% of the listed range, player A?

ev of calling for player A:

(0.4) = 0ev call

(0.5) = 0ev call

(0.6) = 0ev call

(0.7) = 1 pot +ev call

-----

What if we give player B this range?: (0.4, 0.65, 1)

and keep player A's range the same: (0.4, 0.5, 0.6, 0.7)

player A checks, player B bets 1 pot with 100% of the listed range, player A?

here are the evs for the listed hands:

(0.4) = -0.5 pots -ev call

(0.5) = 0ev call

(0.6) = 0ev call

(0.7) = 1 pot + ev call

notice here that if player B checks with (0.4), he chops 25% of the time, which equals 12.5% equity, which equals a profitable checkback of 0.125 pots + ev. So if player A wants to make player B indifferent to checking or betting with (0.4), then player A should allow player B's bluffs to profit exactly 12.5% of the pot. Thus player A should call with 43.75% of his entire range, which allows such a profit for player B. This means that player A should check call at these frequencies:

(0.4) = 0% call

(0.5) = 0% call

(0.6) = 75% call

(0.7) = 100% call

With these frequencies, player A may not be exploited by player B.