If preflop is standard then I have no idea why we didn't limp/reraise (and meanwhile seeing a limped multiway high SPR is also a fine alternative). We got the expected result and the worse one; a low SPR where we'll have a tough time with TP (the most likely hand we'll end up with) and yet gave 4 opponents awesome 28+ IO.

Weird flop because even though we have decent equity there's a bunch of hands that could have smashed this flop (especially ones that call an EP raise preflop). So basically if anyone is cool with getting in stacks on the flop we're likely behind to the point where we'd rather not get in stacks (although with our equity will likely be forced to). I would have actually checked this flop (we have showdown value, fear almost no draw, and would rather not get in stacks UI).

As played, I haven't mathed it, but I'm assuming we have enough equity to snap this off.

As for ranging, this is mostly AJ/AT/JT/KQ/JJ/TT/98hh/Q9hh/Q8hh/87hh (noting that JJ/TT often don't 3bet in a lot of games).

GcluelessNLnoobG

I don't understand the advocacy for checking the flop.

If a scare card peels off on the turn (any heart, Q, or K) it will be more difficult to get paid off. We want to get money in the middle ASAP against the hands we have dominated (AK,AQ, 89hh,Q9hh - 16 combos) and the hands we're a 55-45 favorite against (AJ, AT, JT - 21 combos). If we wait until the turn to bet, and the turn is a blank, we're no longer a favorite against the 2 pair hands. This is why it's better to bet flop -- we're ahead of a larger chunk of the opponents range on the flop. I don't really like check/raising flop, because we lose value against the dominated hands in the first category which are likely to check back. If we get stacks in using a x/r we're going to be in bad shape against two pair+ (and never pair+gutshots or FDs).

If you run the equity, we're more than a 55% favorite against hands that can call a bet on the flop. So make a bet that you think a hand like AQ will be able to call. 40ish seems right.

One of the benefits to checking is that we can see who does what and make the best decision possible. If like the tightest nit at the table bets large and it gets HU, we know we should probably be playing pretty passively UI. If like an action guy bets and gets a bunch of calls, we know we have huge dead money in the pot where we're a lot cooler fastplaying with our equity.

I'm guessing whichever way we play it will be EV, but it's just not immediately obvious to me which line is the most EV. Checking has the benefit of perhaps helping us figure that out. Although it admittedly does have the downside of sometimes missing value from hands that would have payed off a bet (but that only happens when no one decides to bet this flop, and that parlay off someone-having-something-worth-paying-off-a-bet-plus-no-one-betting-this-flop is an unlikely one).

GimoG

Okay, this post attempts to carry out the mathematical comparison between the bet/call flop line and the check/call flop line, to see whether the value lost from the flop checking around is compensated for by the value won when we are able to get away from our hand on the turn (Say, when the board pairs and an opponent shows aggressions). Here goes:

Tl;dr: The aggressive bet/call line is favored to the passive check/call line.

If we check the flop, it is usually going to check around, and we are going to miss value from worse flush draws and worse combos draws which would otherwise call a flop bet. How often will it check around? Well, it will only check around if no opponent holds a hand in the two categories: C1 = {JJ,TT,QK} or C2 = {AJ,AT,JT}. These make up 18+21=39 combos out of ~1300 combos, so the probability any one player holds such a hand is 39/1300=3%. So, the probability one of the 9 players holds a C1 or C2 hand is 1-(0.97)^9 = 24%.

Assuming the flop is bet (again, 24% of the time), the cautious route of x/c on the flop will be followed by turn action. If the turn pairs the board, we can get away from the hand on the turn and preserve our stack -- we save like $250 when this happens. But, given that our opponent has bet the flop, the turn will pair only 10% of the time (it's a bit less than the usual 12% because the opponent will hold blockers due to their 2pair and set combos).

So 10% of 24% of the time, the cautious route saves us $250. The EV gain for the cautious route in this case is roughly (0.1)*(0.24)*250 = $6.

Where else does the cautious route save us money except in the situation where the turn is paired? It's not clear to me that there are any other situations where it is beneficial. If the turn is a blank (like 4), we will be forced to call any reasonable-sized turn bet, up to the size of the pot (our equity against the range of C1 and C2 is 33% on a blank turn). We're gonna lose an additional 100-150 dollars, and at that point, we may feel pot committed on the river and have to call of our last $100. If we hit our flush or straight on the turn, we're going to be in the awkward position of trying to get stacks in from out of position when our opponent is the aggressor -- clearly there is no benefit to the passive line in this case.

On the other hand, the cautious route loses money relative to the aggressive bet/call flop line in every situation where the flop checks around (this will happen 75% of the time) and where one of our opponents has a hand that we crush -- let's call these hands C3. There are like 12+ combos of worse flush draws out there (hands like 68,78, etc.), 12 combos of AQ, 12 combos of QJ, 9 combos of KJ, 12 combos of QT, and some fraction of the 16 combos of Q9 (I don't know if players at 1/2 NL love calling EP raises with trash hands like this, but my guess is they do, so maybe close to the max 16 combos) -- all of these hands would call a $40 flop bet. How often are these C3 hands in our opponents range? -- for a very conservative estimate, we are going to say 60 combos of C3 hands -- so, 60/1300 ~ 5% chance of a C3 hand per opponent, and 1-(0.95)^9 = 36% chance that one opponent has a C3 hand and can call a flop bet. We're an 85-15 equity favorite against the C3 hand range.

So the value of the aggressive betting route relative to the cautious route is at least

(probability no opponent has a C1 or C2 hand)*(probability some opponent has a C3 hand)*(equity advantage against C3 hand)*(size of bet) =
(0.75)*(0.36)*(.85-.15)*40= $7.5.

Plus, if one of our opponents hits their draw and it is second best to our completed draw, we can try to squeeze additional money from them on the turn (e.g., in flush over flush, or straight over straight+redraw situations). These turn bets will be much larger in proportion to the size of the pot, due to our flop bet.

It seems like the value of the aggressive route will end up being considerably more than $7.5 (and anyway, certainly greater than the $6 benefit of the cautious route).

The aggressive route also has the benefit that we never have to worry about the opponent bluffing us off of the best hand -- e.g.,we might get owned if we hit our two pair on the turn, and one of the 5 opponents with position on us decides to turn their hand into a bluff and represent the Queen. In general, it is for this reason that we prefer to take aggressive betting lines in EP -- it negates the opponent's positional advantage.

We are never folding this hand at any point ever. The point of checking is not to preserve our stack when we have the worst of it.

We're in a 5-way pot completely readless. You can't just go around saying these randos will never bet hands when we know nothing about any of the players.

There is also loads of value to be had *IF* the flop checks around and we bomb brick turns. Hands that would turbo muck the flop if we c-bet, like QT, are now going to be exponentially more sticky when it looks like we can be stabbing with ATC that QT is often ahead of. I can't tell you how many times I check AA on really raggedy disconnected boards, the turn connects the board a little more and I bomb it and get called down light or shoved on and you GII with loads of equity.

If the most likely result of betting is folding everyone on the flop or GII and stacking off as a 55/45 favorite versus reasonable ranges, then there's probably a more +EV line out there.

That's ridiculous. What sort of 1/2 game are you playing in where players turbo-muck a pair+gutshot draw to a $40 c-bet? These *are* sticky players. That's why we got 5 callers when we opened in EP. These players aren't thinking about our range here. They're thinking "pair plus gutshot LOLZ I call".

If your assumption is that we're never folding this hand on any turn card, it becomes even more straightforward that we should bet out. There is literally no value to taking a passive route if this is our assumption.

If our opponent has the nuts, stacks are going in on the turn either way, and the EV of both options are identical.

If our opponent doesn't have the nuts, but a dominated hand (like AK, AQ, and worse flush draws), then we get to put the money in ourselves and gain value when they would otherwise check behind for pot control.

We should be checking a HUGE portion of our range OOP vs 4 players. Checking this flop with this particular hand is completey fine. Bet hands like KQ, sets, etc that need more protection for fat value.

Checking this hand is completely fine.

Betting this hand is also obviously completely fine.

If we were heads up, or even 3 ways I'd definitely advocate a bet.