Your pay off has to equal your investment and that is very often not true for many holdem hands vs an ep range.

good question

I hold pocket three's in the hijack and I call a raise from EP. We are both 100bb's deep and the raise that I called was 3bb's. Do I want the villain to have AA, KK and QQ in his range, or AA, AKs and AQs? Which range makes my set-mine more profitable?

That's something I've been thinking about lately, and I don't have a perfect answer. It initially seems like we should call often against tight ranges that will pay us off, but in practice I think that if we call pre too often, we put ourselves at such a range/equity disadvantage post-flop that we lose EV.

Against bad players, we should call in position with a lot of speculative hands, because of implied odds and our ability to outplay the opponent in position. Against good players, we shouldn't do a lot of calling, because good players don't bloat the pot when they are OOP, and can get away from overpairs etc.

GTO cold-calling ranges are probably a lot tighter than what is played as "standard", especially in the micros. If the opener is UTG, I think it's optimal to have a very low cold-call frequency, but the hands we do call with (mid pairs, some suited Broadways and small SCs) need to have decent board coverage, such that we'll have about 50% equity vs villain's range on most flops.

Fold pre.
You're gonna get overcalled or squeezed very often, have terrible relative position in multiway pots, get over-settted a bunch, and generally never win the PFR's stack unless he's terribad.
I think you need 77+ to call there.

You are, but you might be overestimating how much the BU's "responsibility" it is to defend vs EP steals. The primary defender of any steal is going to be the BB, followed distantly by the BU, then probably the SB and CO are close, with MP having the least amount of obligation.

Also, it should be noted that calling the EP player's open doesn't punish his strategy of opening too widely nearly as much as 3-betting does. QTo, 75s, and 64s are going to play so poorly as a call vs even a loose EP opening range that you're probably giving him value. You're definitely giving the blinds the ability to realize more equity than had you folded.

QTo plays terrible as a 3-bet though, folding to a min-raise sucks and so we are basically forced to call or give up EV.

It's easily possible (likely actually) that both 3-bet and call with QTo vs EP minraise are minus EV. Again, you're not the only defender, the responsibility is shared between all MP-BB players.

Does this mean that calling a 3bb open raise against this EP range is also -EV? I doubt this because I thought the general consensus was that calling suited broadways vs EP raises was +EV, in which case offsuit broadways should be a profitable call for 2.0x and maybe even 2.5x, since the suitedness factor is not over 50% of a hand's value, (whereas calling 3.0x pre-flop instead of 2.0x is a 50% increase in the cost to see a flop).

I imagine that calling 2.5x with QTo could be close to -EV, but calling 2.0x or 2.25x should be +EV right? You surely have to accept that the amount that we need to call to see a flop is very important in determining the hands that we can call the raise with, and that the common wisdom has always assumed 3.0x or even 3.5x and 4.0x. Now that open raises are generally getting smaller, (to allow cheaper EP and MP 'steals'), we should be calling way more liberally in my opinion in order to counteract this move from our opponents.

Also, if EP raises to 2.5x, and someone in EP or MP calls this raise, and we are in the CO with QTo, is this not a mandatory over call too due to the better implied odds and cheaper floppage? I accept that in practice these kinds of 'specific circumstance' calls might be tougher to identify when multi-tabling online, and it might be an easier thing to just fold and pass up on the EV, but I believe this to be a theoretical mistake when someone does this.

1) Since you have nothing invested in the pot and the risk of a squeeze from behind is present regardless of the size, there isn't as substantial of a difference in your effective pot odds calling the button for 3x, 2.5x, or 2x. For 2x you play for a smaller/deeper pot size so your price isn't that different really.

2) Suited broadways are profitable to call because your range prior to calling them was very strong. They weaken your ranges in spots where your ranges are too strong, and serve to balance value bets. Thus, they make a lot of their profit from being check/folded to. The thing about suited broadways is that they're relatively infrequent in your range, 4 combos per hand.

3) On the other hand, the more weak hands you add to your coldcall range, the weaker it becomes, and EP then becomes more comfortable two barreling or check/calling down on boards where your range is weak or has too many bluffs in it. As a general principle, adding too many marginal hands to your preflop range will weaken the postflop equity of all your marginal hands. QTo is 12 marginal combos added to your range.

4) If you called an EP open with all offsuit broadways, pairs, and suited broadways/connectors, EP will have a range strength and range polarity advantage that he didn't have before. He will no longer check/fold as often in situations that are unfavorable for his range, and for that matter, few situations will be unfavorable to his range at all. When that happens, all hands in your range that aren't AQ+ 88+ will suffer.

It's kind of hard to measure how much suitedness is worth, but it's a LOT. If you have a tracker, run the "cold-called pre-flop" filter and compare your results with suited hands and offsuit hands. Much of the EV of suited hands (like QJs) comes from semi-bluffing with FDs (or backdoor flush draws), or actually making flushes. QJo is just trash, and in a raised pot it's barely profitable as a BB defence with great pot odds, let alone as a call in the cutoff.

I think the more important thing is that suited hands add bluffs, semibluffs, and value hands to your postflop ranges in a more equitable distribution than offsuit hands. Range vs range adjustment and counter-adjustment counts for much more than most people realize.

1) When we get squeezed, we lose more when calling 3.0x with QTs than we do if calling 2.0x with QTo, so surely the pre-flop raise size that we had to call does matter?

3) and 4) - If we are calling 2.0x with QTo, can't we just play fit-or-fold and only continue with decent draws top pair with gutshots and backdoor straight draws, two pair, trips etc.? If so, then we wouldn't need to be bluffing with all these extra combos of QTo, 75s etc. in our range.

Suitedness can't be THAT important because we don't call raises with 83s and Q4s. At some point, the relatively high rank of BOTH cards matter, as does the closeness/connectedness of the two cards, so that all-in-all suitedness is just one asset of a starting hand.

Now the high-card element of both cards is by far and away the most important in my opinion, because AKo and AQo are very profitable starting hands despite not being suited. In fact AKo and AQo are more profitable than most suited hands.

The much lesser elements of a non-paired starting hand are it's suitedness and connectedness, and this is why I can't see one of these elements on its own accounting for more than 50% of the starting hands effectiveness, whereby we can call 3.0x with QTs but apparently can't call 2.0x with QTo.

Obviously QTo is a -EV starting hand currently in today's games, because right now most raises that the hand faces are in the 3.0x ballpark. My theory is that if suddenly 2.0x or 2.5x raises become standard in tomorrow's games, then this should move more starting hands that are slightly -EV at the moment, into slightly +EV tomorrow.

If you assume that you will not be able to call a 3-bet, then you will be able to call the 2x open with any hand that will win at least (2bb)/x postflop, where X is the percentage of the time where you don't face a 3-bet. If it is a hu pot EP v BU, there will be a 5.5bb pot before rake. The rake is not insignificant, depending on your stakes, it will end up eating the entire SB usually. So for simplicity lets say 5bb pot, and lets say you fold to squeezes often enough that you would need to win 2.2bb of the 5bb pot. This is 44% of the pot, and when you have a hand that is actually pretty far behind an EP opening range, it is a tall order to realize that much equity, even with position.

And it becomes harder and harder to realize that equity the more and more weak hands you add, because your ranges post-flop will be saturated with weak pairs and bluffs. It will be harder to get to showdown with your mid pair type hands and harder to get credit for bluffing when you miss.

Also, I think you're overestimating the amount you will be able to extract from an EP range when you flop top pair with QTo. The hand will play out in many ways which will cause your top pair to be a bluff catcher and be thus only worth a small fraction of the pot. A big majority of you equity realized will be from 1) hitting 2 pair and better, and 2) from bluffing opportunities in position.

I don't fully agree with the maths in the first paragraph, because we will often win a good proportion of the EP player's continuation bet when we hit big, (let's say it's 3.5bb's and we win this 80% of the time), so the times that we decide to continue we can win 1 + 0.5 +2 + 3.5 x 80% -0.5 (rake) = 5.8bb

What we are risking is 2 + 3.5 x 20% = 2.7bb

This means that after accounting for occasional squeezes we would need roughly 35% equity right, and not 44%?

No. Just because I refer to the postflop EV figure in relation to the pot size doesn't mean that it doesn't account for the EV of future betting. I mean yeah if he's blindly c-betting flops with 80% of his range, you adjust the postflop value of your hand up to account for that, but its a double edged sword because if he cbets every flop then that's going to hurt your ability to realize the equity of your bad flops. Basically, he'll c/f to you less, give you free cards less often, etc.

So basically you are suggesting that if we face an EP open raise of 3.0x we should call with X%, and if we are facing a 2.0x EP open raise consisting of the same range of hands for our opponent, then we should also call with X%.

However this seems at odds with the idea that when in the BB, we should call a 2.0x open from the button more often than we call an open to 2.5x or 3.0x. Unless this idea is also wrong?

Also, your assertion possibly goes against set-mining where we should call a 3.0x raise most of the time with 77 in position, 100bb's deep; but wouldn't call a 10.0x raise 100bb's deep, or 3.0x 30bb's deep.

Agreed. This was point you alluded to in part 3 of post #34, wasn't it?
I'd never really thought about it in that way before, so thanks.

I'm suggesting that the difference between facing a 2x open and a 3x button is more subtle than one being 50% bigger than the other. Definitely it is the case that you should play looser against the 2x open, but you shouldn't necessarily be playing a 50% wider range vs it. More like a 15-20% wider range.

The BB works differently because you close the action (squeezing is not a factor) and get a direct discount to your price, and the difference is MUCH sharper for a 2x vs a 3x. Button's price reduces by 33%, while the BB's price reduces by 50%

Long story short, what to vpip on the button is locked in by more factors than just the bb amount you face, and you have to factor the ranges of the SB and BB who will be attempting to maximize their equity just as much as you are. BB on the other hand is a direct pot odds check because there's just the dead money and you and him.

The squeeze difference is still fairly small as someone acting after your call in the CO, is attempting to 3-bet the EP opener, which they shouldn't be doing abnormal amounts of.

In general though your last post does seem to suggest that you now believe essentially the raise size that we face does indeed matter, and so we should be cold-calling in position with a 10%-15% wider range, (and not just in the BB), when facing smaller raises, and that 15% wider CO calling range just about includes 75s and QTo.

No one knows if QTo or 75s is worth +2bb worth of equity in position vs an ep raise. I would argue it's probably not and there may be ev charts out there by position that can give us clues to the profitability of those hands but they won't be focused on this specific scenario.

One thing is probably certain though if you think you can flat those hands profitably then you probably think you can flat many more hands profitability and you will certainly be opening yourself up for exploitation with a wide and weaker flatting range which overall would likely be -EV.

My personal opinion is that vs a decent player with a 15% EP opening range and average regs in the blinds, you could call something like 66+ AQo A9s+ KTs+ QTs+ 87s+ (10.1%) vs a 3x open and something like 44+ AQo KQo A6s+ KTs+ T8s+ 76ss+ vs 2x. (13.7%)

It is probable that you would be able to 3-bet a significantly wider range against the 2x, however, since it effectively plays like deeper stacks.


That all said, I think this has less to do with the price you get, and more to do with the deeper-stacked nature of minraised pots vs 3x pots.

This concept was given for all-in preflop situations. Probably in David Scalansky's Tournament Poker for Advanced Players.

As stacks get deeper, it holds less and less true. This is due to implied odds and reverse implied odds. For example a hand like ATo. Has significant reverse implied odds when facing better Ax hands with an ace on the board. On the other hand 56s has significant implied odds when catching a disguised monster which increase with the stacks but also with post flop skill factors where wider ranges will leverage not only hit or miss factors but will be bluffing and merging ranges to maximize those wins to yield the greatest implied odds, especially as effective stacks get beyond 200bbs.

FWIW, I can provide numbers from Snowie.
Assuming 6-max 100NL, and UTG opens for a minraise.
QTo in CO loses 0.38bb by calling. (QTs loses 0.10bb)
QTo OTB loses 0.37bb by calling. (QTs loses 0.03bb, and is break-even as a pot-sized 3-bet).

Versus 3bb UTG opens, QTo is -0.57bb in the CO and -0.55bb otb.
Snowie evaluates 75s as "better" than QTo in all spots, but it remains -EV in each one.

These numbers assume Snowie's approximation of "optimal" play thereafter (and by the blinds, who may squeeze or overcall). Against particularly exploitable players, or in games with lower rake, it may be possible to turn QTo or 75s into profitable calls.

Modern style is to never (or just very very tight like AA + bluffs or maaaaybe AA-KK + some bluffs) 3bet vs early position openers (like ~20%) and call 15%-25%. With this strategy you can get about -85bb/100 to -80bb/100 (assuming both play optimally postflop) and most top regulars these days settle for that. This is vs 2.5bb/3bb raise. Obviously vs minraise you should play more hands.