A response and my response...

Here is the response from one of the guys on the thread:

From: Responder 6

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Define p as % of time won before the flop with the 3-bet
Define c as % of time won after the flop with a continuation bet shove

EV = p*(25+25+2+3+5) + (1-p)*(EV when called before the flop) = p*60 +
(1-p)*(c*(135)+(1-c)*(-250))
EV = +$1.25

Note that the parameters are here are extremely generous, given that I
think you will win the pot before the flop significantly more than 50% of
the time and you will almost never be drawing dead when called on the flop;
you'll sometimes actually be ahead!

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On the contrary, I disagree here.  If he's not going to fold with 78s, he's
no where near folding 50% of the time pre-flop.  If he calls with a gutshot,
he's no where near folding 50% of the time post-flop.  Anything less than
50/50 and the equation above is a loss, so there was no proof offered.

If it's a solid player, then the math is very different because his chances
of an overpair calling your raise is much larger.

And my response:

I don't think this disagreement gets at the heart of the point that I was trying to make. The parameters of the situation as I presented it were just to show that given the stack depths and the villain's loose tendencies, squeezing with any reasonable hand is a +EV play. I can flesh things out a little further.

Let's examine Responder 6's two assertions a little more closely. They are pretty closely related, so let's consider their joint implications. If the villain is loose and aggressive pre-flop and is rarely folding on the flop, that means that his calling range of our shove on the flop is very wide. This means that when the villain calls on the flop, then we are nowhere near drawing dead. For example, if he's going to call with naked 8-high gutshots every time, then when you get your money in with Q high on the flop you will actually have the best hand a non-negligible part of the time and be a favorite to win. You managed to get all your money in with dead money in the pot as the favorite to win at showdown. This is a great cash-game situation.

If I change the parameters of the situation to:

%Chance of folding PF = 25%
%Chance of folding on the flop = 20%

Then giving the villain a loose range and giving me a random hand, I still have ~40% equity on the flop!

If these parameters are accepted as being reasonable, then you STILL make money on the move.

Let's talk about the hero's hand in particular. Since we have a decent hand, not any two cards, we have a more profitable spot to squeeze here. Given that the villain is very loose and aggressive in the hero's description, let us also suppose that he is opening any two big cards, any pair, any ace, any suited king, any suited connector, and any connector 67 or bigger. This makes his range:

22+,
A2s+, A2o+
K2s+,
QTs+,JTs,T9s,98s,87s,76s,65s,54s,43s,32s
KTo+,QTo+,JTo,T9o,98o,87o,76o

This turns out to be ~36% of hands

Let us also say that he only folds 25% of the time before the flop. This means that he will be playing approximately ~27% of hands when he gets to the flop.

On a Tx5h4h flop, ~80% of the hands that the villain has (assuming that he doesn't re-raise with the top of his range before the flop) are one pair or better, or any draw or a decent ace high.
When he calls, he range has ~51% equity against our 77.

Therefore, if we can model this situation as follows:

EV = $60*p+(1-p)*(c*$135+(1-c)*(.49*$285-.51*$250))

p=.25
c=.2

EV = +$42.54

Folding 77 in this spot is out of the question, since on average you will increase your stack by 17%. If you are routinely giving up your hand in spots like this, you are leaving a lot of money on the table.

Against a tighter player:

I want to point out how much the dead money in the pot affects the calculations here. Say that we are dealing with a tight player as Responder 6 contents, who is only raising from middle position with a tight range of 55+, AJo+,ATs+,KJs+, and KQo. This range constitutes only 10% of all hands. Furthermore, let's say that when re-raised, the player will only continue with AKo,AQs+, and TT or better. Also let's assume that he will re-raise all-in with any hand that he continues with. This is 3.8% of all hands and 38% of the player's opening range. This means that 62% of the time he will fold before the flop. Against this range, 77 has 33% equity. The pot will be $10+$25+$100+$250 = $385 and we will be being laid ~2.6 to 1, which makes this an easy call. Plugging these numbers in:

p = 62%
% Chance of winning when he does not fold = 33%

EV = $60*.62 + .38*( .33*$285 + .67*-$250) = +$9.29

Note that this continues to be +EV until the stack sizes hit about $322, or almost 30% deeper (i.e. reraising and calling the shove with 77 given the shoving range above).


So even if you know that a player is going to play as described above, re-raising with 77 is still a +EV play and strictly better than folding. The question against the tighter player is whether you can play the hand in such a way that your EV is greater by just calling. That depends both on you and the other player and is hard to model accurately.

I guess the main point here is that given stack depths, folding 77 is completely out of the question given almost any reasonable range of the opponent. Yes, you will sometimes get your money in as a significant underdog, but that is the cost of doing business in short-stacked cash games. As the stacks get deeper, the concerns that Responder 6 cite become much more relevant, since the dead money in the pot no longer offsets the money you lose by getting your money in as a 2-1 underdog.

I hope I haven't rambled too much; I didn't have anything to do tonight... Comments are appreciated.