Shoving Trash in the blinds 100 bb's deep to a 4x button raise
Nope, you didn't misread the title. I'm convinced that against a reasonably TAG or LAG player that this is profitable as long as it is not overdone.
Let's look at some ranges. Since preflop raise from the button is the one variable, we'll leave that alone for now. First we need to look at the ranges needed to call such a move. You're on the button, you raise 4x, SB folds and BB shoves. What will you call with? Obviously AA/KK, and maybe AK/QQ. If they've done it a few times before MAYBE with JJ. Let's assume they'll do it with this range, which makes up just over 3% (3.01%, we'll estimate 3% for this).
Now we need to calculate the equity here. If we do this with ATC the button has 75% equity when he calls. As an alternative, let's also look at the AA/KK and the AA/KK/AK ranges for tighter players. AA/KK is 0.9% and AA/KK/AK is 2.1%. Equity of AA/KK is 83.8% and equity of AA/KK/AK is 73.5%.
So our table looks like this:
Range Equity % of hands
AA/KK 83.8% 0.9%
AA/KK/AK 73.5% 2.1%
JJ+/AK 75% 3%
Now the odds
we get when bluffing
are 99:5.5 = 18:1. This means that if we can win 18/19 of hands we don't even have to have any equity in the pots we get called. Note that 18/19 is just under 95% and none of our ranges are higher than 5%. First off we'll do the calculation for a hypothetical button who raises ATC unopened and only calls AA/KK.
99.1% of the time we win the pot right there and the other 0.9% we win (1-.838) of the time. So we win 0.991*5.5 + 0.009*(1-.838)*(5.5+96) - 0.009*(.838)*99 = 4.85 bb's. Now let's see just how tight the range of button stealing would have to be for us not to be able to profitably shove here:
First I'll do a general expression, a=preflop button open raising range, b=range of calling shove (as a subset of overall, not subset of preflop open raising range), c=equity of range against ATC.
(1-b/a)*5.5 + (b/a)*(1-c)*102.5 - (b/a)*c*99 = 0. - b/a = range of calling shove from range raised preflop.
5.5 - 5.5b/a + 102.5*b/a - 102.5*cb/a - 99cb/a = 0
5.5a - 5.5b + 102.5b - 102.5bc - 99bc = 0
5.5a + 97b - 201bc = 0
5.5a = 201bc - 97b
a = 36.54bc - 17.64b
Since b and c are completely correlated, mainly we're looking at the kind of a we would need to have for various b's (from which we can get c).
So let's start with AA/KK. b=0.9%, c=83.8%
a = 0.117
Yes if you are playing someone who only calls a shove with AA/KK and they raise any more than 12% on the button, you can profitably shove with ATC.
AA/KK/AK. b = 2.1%, c = 73.5%
a = 0.193
Here we need someone stealing on the button 20+%
AA/KK/QQ/JJ/AK. b = 3%, c = 75%
a = .292
So if we have someone calling this wide of a range for a shove, it's now profitable against someone who steals a lot in position, but no longer profitable if we have a tighter player who doesn't steal a ton.
Also note that since we most likely wouldn't be straight shoving AA/KK/AK/AQ/22+/KQ/etc. we can't really use those ranges, but take a look at for example 84s against these ranges. It actually does BETTER than ATC against the AA/KK range. In fact it is probably better to be shoving trash hands rather than hands with an A or K because you'll so likely be dominated when called with those hands.
Now of course the thing we need to look at is that even if shoving is +ev, could 3-betting light be MORE +ev?
Basically looking at it 3-betting light seems to be the answer against not so good players, but if we get a tricky player that knows you and will use position to outplay you with a wide range of small pockets and suited connectors, it gets worse. The other thing is you can't do it every time, because if they realize that your range when shoving is actually ATC or even worse ATC aside from AA/KK/AK/etc. then they can profitably call much wider and our play is no longer +ev. Even still though, do you know of a single player who will call with 88 to a 100 bb shove just thinking they're ahead of our range? Or someone who will call with KQ?
The easiest defense is actually to tighten up preflop, but as shown above, they would have to tighten up a ton, and if we're talking about frequent multi-tablers, they're not likely to tighten up that much just because you are in the big blind.
Thoughts on this, and whether it could ever be practically used or whether you just think the light 3-bet is always better?