This is is more of a generalized discussion of the best play for maximum value and minimum variance, though I will be showing a specific hand.

Game is Commerce 1/2 blind game ($40 buy in, lol).

Profiles and stacks:

SB - $130 - old Asian gambolor, crazy action.
BB - $120 - hero, probably a TAG most of the time.
UTG - $20 - donk fish
+1 - $120 - good lag tag, most solid player at table.
The rest: about $40-$60 stacks, typical loose passives.

UTG goes all in DARK for $20.

Then HERO is dealt KK in the BB

+1 calls 20, two more callers, SB raises to 60. Hero goes ALL IN for 120.


Now, let's discuss the merits of shoving here versus flat calling the 60 and then shoving any non-ace flop.

When we SHOVE, we are trying to be heads up against the Asian guy. Asian guy has TT+ and AT+ in this spot, though might be tighter like JJ + and AJ+. All the other players probably have small pairs, connectors, any suited, etc.

If we are all in PF against Asian guy with his tightest range of JJ+,AJ+, then we are at most a 2:1 favorite as he gets a five card flop:

PokerCruncher-Advanced-iPad V.8.2.1

(Equity, Win, Tie)
Player 1: 2.03:1F 1.93:1F 46.4:1 [KsKd]
Player 2: 2.03:1 2.13:1 46.4:1 {JJ+, AJs+, AJo+}

Board: [? ? ? ? ?]
Deal To: River

Though in this scenario there is 120 in the main pot (three way) and 200 in the side pot (HU) (we risk 20 in the main and 100 in the side.)

Our equity for the main pot is 56%. (Side pot equity is 67%)

PokerCruncher-Advanced-iPad V.8.2.1

(Equity, Win, Tie)
Player 1: 56.6% 55.8% 1.76% [KsKd]
Player 2: 28.9% 27.9% 1.96% {JJ+, AJs+, AJo+}
Player 3: 14.5% 14.2% 0.73% [??]

Board: [? ? ? ? ?]
Deal To: River

So 100*.56 + 100*.67 = 123. We lose 20*.44 and 100*.33 = 41.8

so our EV is 81.2 with this line.


Now let's consider if instead we FLAT CALL the raise from said nutty Asian guy., with the plan for shoving our remaining 60 into any non-ace flop.

At least two of the other callers call when we flat the Asian guy. At least one of them ends up all in so we have two all in players to the flop (and now a main, side, and potential additional side pot).

The main pot is still 120, and the side pot is now 160 (200 if everyone calls) seeing the flop. Probably one more person is all in so further action will be in a second side pot. At the moment we have 20 into the main and 40 into the first side pot.

In this scenario we are 1.8:1 to see the flop (not counting any further cards). This is 65%.

21% of the time there is an ace on the flop and we check fold.

79% of the time we shove. We get called by top pair hands, some draws, and of course hands that beat us like sets and two pair and flopped straights.

Of the hands we shove and are losing immediately 14% (though we draw out on some of these around 30% of that 14%, so our loss is actually 10%) and the hands that call us when we are ahead draw out around 30% to 40% of the 65% which makes our wins 40% to 43% + the 4% we're behind and draw out.

We lose our flat called 60 the 21% we check fold an A high flop.

We lose our additional shoved 60 the 10% we're out flopped and the 22% ~ 25% we're outdrawn assuming no one folds their draws (and they would be wrong to fold any 4 out or better draw as they would be getting better than 5:1 on the call). But let's assume that gutshots fold, bottom/middle pair draws fold (I.e. 4 and 5 outters)

When we are called by a TPTK hand and a flush draw, then, we have to dodge about 14 outs.

Crunch of our flop equity:

PokerCruncher-Advanced-iPad V.8.2.1

(Equity, Win, Tie)
Player 1: 64.5% 63.8% 1.39% [KsKd]
Player 2: 20.3% 19.5% 1.48% {JJ+, AJs+, AJo+}
Player 3: 5.19% 5.14% 0.09% {TT-22, AJs-A2s, KJs-K2s, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, AJo-A2o, K8o+, Q8o+, J8o+, T8o+, 98o, 87o, 76o, 65o, 54o, 43o, 32o} [passive limp]
Player 4: 5.19% 5.15% 0.09% {TT-22, AJs-A2s, KJs-K2s, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, AJo-A2o, K8o+, Q8o+, J8o+, T8o+, 98o, 87o, 76o, 65o, 54o, 43o, 32o} [passive limp]
Player 5: 4.83% 4.76% 0.13% [??]

Board: [? ? ? ? ?]
Deal To: Flop

Crunch of our chance being outdraw by one caller with a strong draw:

PokerCruncher-Advanced-iPad V.8.2.1

(Equity, Win, Tie)
Player 1: 66.4% 66.4% 0% [KsKc]
Player 2: 33.6% 33.6% 0% [9cTc]

Board: [Jc 4c 2d ? ?]
Deal To: River

Crunch of our chance of being outdraw by two callers:

PokerCruncher-Advanced-iPad V.8.2.1

(Equity, Win, Tie)
Player 1: 54.2% 54.2% 0% [KsKc]
Player 2: 12.4% 12.4% 0% [QhJh]
Player 3: 33.4% 33.4% 0% [9c8c]

Board: [Jc 4c 2d ? ?]
Deal To: River

Thus we lose 60 about 21% of the time we check fold an A high flop.

We are called by at least one player that out flopped us 14% of the time, which breaks down to:

• We lose total 120 about 10% of the time we shove but we're out flopped and we don't redraw.
• 4% of the time we profit about 220 when we were outdraw but we hit our redraw.

But even when not out flopped, we still may get calls from one or more players that hit top pair or a draw. For this argument, let's say that 50% of the time all fold (except two all ins) 25% one call and 25% two calls. Also, we'll group the below estimates within the remaining 65% of events not listed above

• 50%: We win 160 about 72 % of the time (everyone folds to our shove and we are left with two others all in)
• 25%: We win 220 about 48% of the time when there are two all ins and one player calls with a big draw.
• 25%: We win 280 about 39% of the time that there are two callers to our shove (top pair and a strong draw) and two all ins.

About 5% to 10% of the time we only win one or both side pots, so we subtract $15 from these numbers.

145*0.5*0.72=52.2
205*0.25*0.48=24.6
265*0.25*0.39=25.8

=102.6 (won when called by draws)

-120*((.5*.28)+(.25*.52)+(.25*.61))=-50.7 (lost when drawn out by draws)

Totals:

-60*0.21 = -12.6

-120*0.1= -12
+220*0.04 = 8.8

+102.6*0.65= 66.7
-50.7*0.65 = -33

EV = 17.9

---------

Of course, the second line of action is full of estimates, but the upshot is that we let in a lot of other people and that substantially reduces our chance of winning.

21% of the time we cut our variance in half when we avoid an ace on the flop.

But 79% of the time we become a coin flip against 2,3, or 4 opponents.

In short it's better to be a 2:1 favorite 100% of the time than a 1:1 coin flip 79% of the time.

---------


WHY THIS POST

If you are wondering why I am posting this, it's becuase of the above hand last night. I was wondering to myself if it's better to get all in PF and give Villain a 5 card flop, OR to wait for a flop and then shove into several players.

Rather than guessing I wanted to work it out, and did so in the form of this post.

All comments and further discussion appreciated.

---------

CLIFFS NOTES:

Yes, is best to ship it in PREFLOP and NOT go for overcalls here. While the final pot may be 80 to 160 SMALLER (20-40% smaller), you are more than twice as likely to win.

Even though you reduce your variance by $60 21% of the time, you increase variance by 50%, 79% of the time.

LINE 1 (PF shove) we lose 120 about 35% of the time. We profit 200 65% of the time.

LINE 2 (flat and shove flop, fold ace flop) we lose 60 21% of the time, PLUS still lose 120 35% of the time. We profit ~300 only 44% of the time.

Nice anal-ysis. Is deeper worse for Hero when shoving PF?

In thinking about this, I think the deeper the effective stacks, the more we should be inclined to push here.

The deeper we are, the more likely we are to fold out A high hands. The pot is big enough we should be happy to be HU against the reckless fish that went all in blind with 10 bb.

If the stacks behind us are big, we don't want to be playinga one pair hand out of position.

What the analysis above shows is (what we all should know intuitively) is that our equity plummets the more players we face. We don't want to be OOP against a bunch of other deep stacks.

Also, if we flat and there are a bunch of deep stacks after us we can't just shove the flop (when we're too deep) because a flop shove when DEEP is probay getting called by hands that beat us, and we don't get value from top pair hands.

So if we flat PF, we can certainly lead the flop, but the possibility of making post flop mistakes becomes much greater.

So when deep, I think we are still shipping it in or at least 4 betting half our stack PF.

This applies to the ABOVE scenario, when one player has raised all in with essential any two cards, there are several callers, and there is a three bet from a loose agressive player.

If I was on the button, and stacks were really deep, I could better get behind a flat call PF.

But even then I'd prefer to 4 bet to reduce the field.

Don't have time to read and think about the math part just now, possible you explain everything so I comment at the risk of appearing an idiot (which is close to reality):

Don't we want as many callers as possible? If we flatted the $60, the first caller is getting direct odds of 5:1. Even if all of the remaining stacks are counted as implied odds he is only getting like 10:1 implied. PP's are maybe getting the implied odds to call. Everything else, not so much. Broadway type hands that make TP have bad RIO. IMO, the range of hands in the field are going to be making big mistakes by calling.

I don't mind the raise but I don't think it is to ''thin the herd'', rather it is to get as much money into the pot as possible.

Looking forward to reading though your math.

Where are all the short posts?

Ah cliff notes, thank you, shove cowboys pre-flop, don't let 4 people go to the flop. Got it, theory confirmed.

*click back button*

Kookie, I agree with everything... *if* we had AA and not KK.

We usually play AA and KK the same pre-flop, so we don't often witness / intuitively understand the difference between AA and KK. There is actually a massive difference in strength, and this hand illustrates that difference, and we should do something different with the two hands.

KK is far more vulnerable because all Ax has OK equity vs KK. You talked about pocket pairs and broadway cards... but what about, say, A9o? A9o is a bit worse than 2:1 dog against KK. A5s is actually exactly a 2:1 dog. That's a lot of equity.

And there are also fewer broadway cards available for RIO when you hold KK because, of course, we hold two K's.

When we hold AA, there's far more villain RIO post-flop than when we hold KK.

I'll have to look at the OP situation in more detail, but my guess is we actually benefit from wielding *fold equity* and getting people to fold Ax pre-flop. We make more money by getting them to fold Ax and abandon quite decent equity than we do by letting them in. If they call our shove with Ax, they're probably not making a mistake. It's still profitable for us, so it's fine. But the right play should be to shove.

If we held AA, everything you said should be 100% spot on.

Again, I haven't reviewed the OP situation closely enough yet, but AA is probably an excellent pre-flop flat here.

Though for sure, we can't just look at hot/cold equity Ax vs KK because Ax might not see 5 cards.

Makes sense.

Though, OP said SB's range was like TT+/AT+ which is 25 combos of pp's and 56 combos of Ax. Given he is Ax heavy, would this not be an argument for keeping Ax in the hand? With 5 players plus hero putting $20+ into the pot, it would seem likely there is more than one Ax hand out there. No?

Equity Win Tie
UTG 68.89% 67.95% 0.94% { KK }
UTG+1 31.11% 30.17% 0.94% { TT+, ATo+ }

Equity Win Tie
UTG 62.97% 62.37% 0.60% { KsKc }
UTG+1 19.42% 17.54% 1.88% { TT+, ATs+, ATo+ }
UTG+2 17.61% 16.19% 1.42% { A2s+, ATo+ }

Indeed, if I have AA in this exact spot I am flat calling PF, and then open shoving nearly any flop.

playing AA hyperfast might be decent anyway because their TT might flop an overcard or their Ax might not catch anything to continue

by jamming now we pick up this value

also people wont just fold here after calling 1/6 of their stack and even if, then they are huge donks

For sure, that's a consideration as well.

After I shoved, Everyone but crazy old Asian folded. He called with AQo.

I'll let you figure out the rest LOL.

I think the breakdown of hands to play and shove or flat in this spot is like:

AA - flat and shove all non-A flops, shove A-high coordinated flops (monotone or two to a flush or straight), and checkraise all-in all other A-high flops.

KK QQ JJ - shove pre-flop in this spot always. This range flops an overpair or set 78%, 61%, and 47% of the time. Pop this range is about 66% or better against villains range.

AK - shove pre-flop in this spot always. We are dominating all other A-high hands that villain has (most of his range), and we really want this heads up. We want to fold out all small pairs. When villain calls us with a pair we're only a 44% dog getting a 5 card flop.

77 to TT - either fold or flat pre flop and shove when we flop an overpair or set. This range flops an overpair or set about 18% to 37%. If we fold 77 and 88, and only flat 99 TT, we flop an overpair or set 28% or 37%. A case could be made for flatting 77/88 and shoving a flopped op/set, and shoving PF with 99/TT instead of flatting.

These middle pairs are troublesome in this spot. I don't think it's a terrible mistake to fold them, I don't think it's too horrid to flat and shove a favorable flop, and not too bad to shove pre flop when we are typically 55% against an A high hand like AT+.

In short we fold them to lower variance, and we play them to push a small edge.

22 to 66 - fold. This range flops an overpair or set less than 15% of the time.

AQs probably fold, it's almost as bad as a small pair, and not really better than 77.

AJs and below, KQs and below, and all other hands - definitely fold. These hands will scoop the pot less than 15% of the time. They are garbage.