Situation: You are playing a hypothetical aggressive opponent who is raising his button 2/3rd of the time. Blinds are 25/50, effective stacks 1250 (25 BB).

Villain makes his raise. You have:

1) 2 2
2) A 2
3) J T
4) 7 5
5) 3 2 (for ****s and giggles)

Which of these hands are good to shove over his raise? Depends on what he's calling with:

Scenario 1: Villain is a solid (but a bit too tight) player, this is your first three bet shove, and he's going to respect your first raise. He's calling with 66+, ATo+, A9s, KQ.

This is 10.4% of hands. He's folding 1 - 10.4/66.7 = 84.4% of the time. You get 150 chips for free when this happens, so add 126.61 to your cEV for this move.

What if he calls, though? Here's the equity for each of those hands agaisnt this tight range:

1) 2 2 37.94% win, 61.31% lose
2) A 2 29.59% win, 66.68% lose
3) J T 36.52% win, 62.67% lose
4) 7 5 32.29% win, 67.07% lose
5) 3 2 25.46% win, 73.82% lose

So the 15.6% of the time you are called, you're obviously a dog. Here's the loss in cEV for each scenario (equals 15.6%*1250 chips lost * (%lose -%win)):

1) 2 2 -45.57
2) A 2 -72.33
3) J T -50.99
4) 7 5 -67.82
5) 3 2 -94.30 (!)

What have we learned from this? Well, if your opponent is opening wide and calling this tight, 3-bet shoving ANY TWO is +cEV. Also, against a tight calling range, the suited connector hands play better than the weak ace, but the pair is of course the best hand to shove against a tighter calling range. This is also why raising to 3x at 25 BB effective is generally a leak -- if you raise to 100 or 125, the P(fold) chip expectation falls to 84.4 and 105.5 respectively. As you can see, in the former case shoving 32o is now bad (lol). Of course, minraises will get called a bit more often, but this post will not deal with post-flop play for now. It's already going to be long enough.

Of course, you can't just keep shoving over this raise, because a smart villain is going to adjust, and a dumb villain is going to get pissed off that you're shoving so much and call lighter anyways.

Scenario 2: Either you've shoved a couple times over the villain in scenario 1, or you're playing someone who doesn't respect you as much. Villain is now calling 44+, A8o+, A5s+, KJo+, KTs.

We repeat the calculations. Villain is now calling with top 15.8% of his hands. You still get a fold 1 - 15.8/66.7 = 76.3% of the time, for a P(fold) chip EV of 114.47. Wooooo. Let's see how your shoving hands are holding up now if called.

1) 2 2 win 40.38%, lose 58.74%, cEV = -54.39
2) A 2 win 31.40%, lose 62.13%, cEV = -91.04
3) J T win 39.05%, lose 60.06%, cEV = -62.24
4) 7 5 win 34.51%, lose 64.75%, cEV = -89.59
5) 3 2 win 27.62%, lose 72.44%, cEV = -132.78

Everything but that 32o is still +EV here. The most surprising find is that A2o fares worse than the low suited connecter here, and that JTs isn't too far off the pair in equity. This is because A2o is crushed by all your opponent's range but the Kx hands, while JTs is still doing OK against the weak aces and low pairs. Moving on...

Scenario 3: Villain is tilting or just likes to gamble. He's calling your shove with any pair, any ace, KTo+, K9s+, QJ, QTs, JTs.

You know the drill: This is top 26.1%, so

P(fold) = 1 - (26.1/66.7) = 60.9%. cEV for folds is 91.3. Your shoving ranges will fare as follows:

1) 2 2 win 43.8%, lose 54.97%, cEV = - 54.59
2) A 2 win 32.1%, lose 53.3%, cEV = -103.615
3) J T win 31.12%, lose 53.09%, cEV = -107.38
4) 7 5 win 37.08%, lose 62.05%, cEV = -122.04
5) 3 2 win 27.95%, lose 71.06%, cEV = - 210.70

Yikes, now only the pocket pair is profitable against this range. Let's add a stronger but not amazing Ax hand to this mix:

6) A 8 win 41.98%, lose 47.75%, cEV = -28.2

A ha! Against a wide calling range, a middling A-rag hand fares pretty well. Better even than that low pair. Let's do two more examples before I get to the point:

Scenario 4: Villain is a drunk monkey. He's calling that shove with any pair, any ace, K7o+, any suited king, Q8o+, Q6s+, J9o+, J7s+, T7s+, 97s+, 87s, 76s.

This is a whopping 39.7% of hands! You only get a fold 1 - (39.7/66.7) = 40.8% of the time, and only have 60.72 in +cEV in folding. Let's see how your hands fare. I think I've convinced you that connector hands are bad against a wide call range, so I'll throw out 75s and 32o, and show 22, A2, A8, and JTs, along with a slightly better pair (55):

1) 2 2 win 45.71%, lose 53.04%, cEV = -54.242
2) A 2 win 41.24%, lose 49.54%, cEV = -61.42
3) J T win 43.56%, lose 53.39%, cEV = -72.74
6) A 8 win 48.88%, lose 44.41%, cEV = +33.078 (!)
7) 5 5 win 51.81%, lose 47.26%, cEV = +33.67 (!)

You can now 3-bet shove A8 and 55 type hands for VALUE here, never mind the small chance you have of a fold! The difference between A8 and A2 and 55 and 22 is HUGE if villain is calling you mega-wide! One more example:

Scenario 5: Villain is tight from the button. He's only raising 25%, and calling the same range as the villain in scenario 1.

The equity calcs are the same, but your fold EV drops a lot:

P(fold) = 1 - (10.4/25) = 58.4%, cEV of a fold is 87.6.

Against this villain it is wrong to 3-bet shove A2, but not JTs. Hmmmmmm. Your edge against this opponent comes from him playing mega-passive on the button, of course.

What have we learned from this example?

1) Against an opponent you suspect is not calling your 3-bet very often, your edge in 3-bet shoving comes from FOLD EQUITY. On the off-chance you are called, it is best to have a pair or a middling suited connecting hand than a bad ace.
2) Against an opponent you suspect will call your 3-bet shove somewhat wide but not a lot, your edge is still in your fold equity, but suited connector hands drop a bit in value, and marginal aces increase in values.
3) Against an opponent you suspect will call with a lot of his raising range, your EV in shoving comes from the fact that a middling Ax hand or a low-ish pair is a FAVORITE against whatever trash he's calling with. Suited connectors should not be shoved against these opponents.
4) 3-bet shoving any pocket pair over a 3x raise with 25 BB effective is almost never a mistake.

Thanks for laying this out.

Nice post.

I think a lot of this people kinda already think, but having it all worked out and written is really good.

Interesting to see the maths in regards to the gap in difference between A2 and A8.

I have one query though. In your calculations for the times when villain folds are you not meant to add your big blind to his raise amount.

I.e. I think you should get 200 chips free if villain folds to our shove not 150.

I hope this doesnt mean you will have to do all the calculations again as i'm sure it was a lot of time and effort and regardless it is a very informative post.

By far the worst part of my game and something im going to work hard on in next couple of months hopefully.

reshoving with any two cards can be profitable in some situations obv; most of these things rely on gameflow though

damn. good post. sticky.

Insane!

Agreed. I don't think you need to redo the maths, though, just consider that the EV for folding is -50 instead of 0.

Also, the "win x%, lose x%" format isn't great imo, a simple equity % would be more useful and easier to read.
For instance the "win 41.98%, lose 47.75%" of A8o was quite misleading, because if you just look at the win, you think it does worse than 22.
And in scenario 3, JTs has "win 31.12%, lose 53.09%"... Seems bad to me, I don't see how JTs can split 16% here.

Very good post overall, though.

I used stove for all the equities, though I agree that JTs shouldn't chop that much. I'll redo that one.
EDIT: yea it's 40.90%/57.32%, but I can't edit OP.

Very nice work Steve.

And to think, about a month ago you posted this thread on shoving "light". Nice improvements!

Nice post Steve!

wow what an amazing post

should be stickied or something this area of the game is mega important and you've laid it out so well here

nice work

Hahaha, to be honest I think shoving JTs against that villian was better than A7o thinking about his possible calling ranges and what I just posted.

sorry, apparently i'm not a math guy.

why does the calculation equal 1 - (calling range)/66.7 ?

someone treat me like i'm a 6 year old and give me a simple answer why it isn't just 1 - (calling range). if villain's calling with say 10% of hands, isn't he folding 90%?

Villain is only raising 66.7% of his hands. In scenario 1, the probability villain calls GIVEN he raised preflop, P(call|raise), = P(call a shove)/P(raise preflop), and the probability of a fold is the complement, 1-P(call|raise).

There is a 10.4% chance he is given a hand he'll call a shove with preflop. When he raises, this means he does NOT have one of the bottom 1/3rd hands, so there's only 66.7% of the hands he's calling with. We also know that all of his calling hands he is raising before the flop.

Nice post,

its probably important to note the need to player-note people who will recognize this as a part of your game.

and people wonder why aggressive play is so rewarded...

Does this consider both sides of card removal effects: that is, the probability that Villain will raise given your hole cards as well the probability that Villain will call given your hole cards? I made a thread on this about nine months ago. The latter part is commonly known and calculated but I don't think the former is so much. The most interesting effect is that some middling cards may have a negative effect on fold equity. A hand like T9 might reduce the combinations of hands Villain raises with quite substantially, but if a considerable number of them are raise/folded it won't affect the number of hands Villain calls with all that much.

Hahaha, this thread is awesome. I was playing a villain who was opening 90% to 3x from the button and calling roughly scenario 3 (from past experience), and this guide helped me insta-value shove A7 with 26BB effective.

Wooooooo I made monies already with this concept!

This is a great post. I vote that it be stickied, i think this will be incredibly important for all HUSNGers whether they are experiences or inexperienced. It is a great breakdown of shoving ranges, apprecite it heaps mate!

http://forumserver.twoplustwo.com/45...ulator-121624/

If we have a reshove that shows 30 chips profit does that even pay rake? It does not seem a great idea to take such a small edge in a husng(given rake and that you could prolly find better spots)?

Yeah can we get a mod to sticky this please.

I'll add it to the sticky when I update it. There are a few other good threads to add there too I believe.

Didn't see this until today, good thread steve.

Just browsing through the HU forum again for a change and see this post. Such a quality post Insane_Steve! Really amazingly good info and also presented really well and simple which made it pleasant to read unlike many other math threads.

Cheers!