**Hi guys, welcome to my primer on how to solve 3bet shove spots. If we can put villain on a decently accurate range, the rest is just maths and we should be able to solve these spots with a good deal of clarity.**

**But first of all, what are our options?**

A villain open raises and we're acting behind them and considering a 3bet shove. This will very much depend on stack depth and positions, but a good general rule is that we should expect to have a decent amount of fold equity (the chips we win when we get a fold from the opener) when we have 12+ bbs, and 12-16bbs deep is considered the "classic" reshove stack size since when we're deeper (though we may still fairly frequently do it) we will tend to face a somewhat stronger range when we get called, and when we're shallower, we have rapidly diminishing frequency of folds from villains. Still, there are spots we can reshove up to 25bbs or even higher, but far less frequently will it be optimal.

There are spots where we're reshoving shallower of course, but we tend to do it with a strong range, although sometimes we'll have a sliver of FE (fold equity) on 9-11bbs effective, it's unwise to rely on this being at all significant.

So today's thread is not aimed at addressing all the subtleties of when and where to 3bet shove, but just to show you how to calculate the profitability of the play manually. Of course one can use software such as HRC or Equilabs to run such calculations, but I think there's a lot to be said for running a few manual calcs - it helps us understand the nature of what we're calculating in a way which those sophisticated bits of kit which do it all for us (despite their great usefulness) just don't - as such they help us develop good instincts for use in game. We also have to create our own ranges when doing it from scratch, rather than just adjusting GTO ranges punched out by a hand calculator.

**A case study**

Thanks toOriginally posted by ronekinky

Never sure about these spots. At least he looked quite loose.

PokerStars - €9+€1|1500/3000 Ante 300 NL - Holdem - 8 players

Hand converted by PokerTracker 4

BB: 39,214 (VPIP: 12.78, PFR: 10.85, 3Bet Preflop: 3.64, Hands: 134)

UTG: 132,571 (VPIP: 15.15, PFR: 9.09, 3Bet Preflop: 0.00, Hands: 67)

UTG+1: 62,234 (VPIP: 35.66, PFR: 12.14, 3Bet Preflop: 6.67, Hands: 145)

MP: 65,678 (VPIP: 16.42, PFR: 16.67, 3Bet Preflop: 0.00, Hands: 67)

MP+1: 112,276 (VPIP: 11.43, PFR: 8.82, 3Bet Preflop: 0.00, Hands: 35)

CO: 152,520(VPIP: 20.77, PFR: 18.43, 3Bet Preflop: 7.14, Hands: 262)

Hero (BTN): 47,646

SB: 91,733 (VPIP: 24.72, PFR: 15.73, 3Bet Preflop: 11.43, Hands: 90)

8 players post ante of 300, SB posts SB 1,500, BB posts BB 3,000

Pre Flop:(pot: 6,900)Herohas Q J

fold,fold,fold,fold,COraises to 6,000,Heroshove?

**ronekinky**for the hand above, which I found in the hand discussion section. This will serve us perfectly well as a case study. In this spot Hero is on the BTN, facing a 2x open from a big stack CO. Villain looks reasonably active over a decent hand sample, though it would be nice to see a stealing statistic. BB looks somewhat tight. We have a 15-16bb stack, a perfect reshove stack size in fact. I would suggest that this shallow a flat would generally be a bad idea, especially as we can get squeezed by the blinds. We are too shallow to 3bet/fold (a subject for another time, but I'd suggest it's rarely a good idea to 3bet/fold in position <18bbs). So our options are shove or fold.

**Let's calculate!**

Typically in these sort of spots we expect our profit to come from a combination of fold equity and show down value. With a hand like QJo we'd expect to be behind when called, but that won't matter provided we get a sufficient number of folds. Remember, even if we only have 30% against villain's calling range, that 30% still makes a significant contribution to the overall profitability of the reshove.

So first we need to calculate our fold equity, then our show down value, and add them together to calculate our chip equity value (cEV) of the play. Bear in mind we aren't looking at ICM or anything else in this example, just plain old chip equity. So:

**FE + SD = cEV**Fold equity consists of how often villain will fold, multiplied by the amount of chips we win when he

*fold. So:*

**does***(where $ stands for chips)*

**%folds x $won@fold = FE**To figure out how often he's likely to fold we need to estimate his

**and his**

*opening range*

*range for calling a shove.*Let's use some simple examples in this case study. Let's say villain is opening this range:

And furthermore, let's say when we shove and it folds back to him, he's calling this range:

Now we can figure out how often we get folds. If we divide 16.9 by 31.8 we get 0.531, or ~53%, which is how often he's calling. So in this example we estimate we're getting 47% folds. Now we just multiply 0.47 x $won@fold. The $won@fold is just the pot before we shove, which is 6,000 + blinds + antes, so 6,000 + 4,500 + (8 x 300) = 12,900.

**0.47 x 12,900 = 6,063 chips in FE.**

Now for the showdown part. We simply check in a hand calculator the equity our hand has vs. the calling range we've defined.

**Ranges:**

Hand 0 16.9% [33+ A3s+ A7o+ KJs+ KQo QJs ]

Hand 1 0.9% [QJo ]

Equity:

Hand 0 62.390%

Hand 1 37.610%

Hand 0 16.9% [33+ A3s+ A7o+ KJs+ KQo QJs ]

Hand 1 0.9% [QJo ]

Equity:

Hand 0 62.390%

Hand 1 37.610%

So when we go to showdown we win 37.6% of the time. Now we simply check the amount we win when we win at showdown, the amount we lose when we lose at showdown, and multiply it all through in the following equation:

%called ((%win@SD x $won@SD) - (%lose@SD x $lost@SD))

As for the amounts, we stand to lose

**which since villain covers us is 47,346 chips. We stand to win what villain has to call of our shove, plus the pot as it is now (the same pot we win @fold, so 12,900 chips). Villain has to call our stack less the 6,000 he's put in already, so 47,346 - 6,000 = 41,346. Add the 12,900 and we can see we stand to win 54,246 chips.**

*what we are risking,*So to punch the numbers into the equation, the SD calculation is:

0.53 ((0.376 x 54,246) - (0.624 x 41,346)) = 0.53 (20,396 - 25,800) = 0.53 x -5404 = -2,864.

Note that this number is negative, not unusual in a fold equity reshove calculation.

Now we simply add the FE to the SD.

6,063 - 2,864 = 3,199 chips +cEV, or just over 1bb +cEV, which when we have a 15-16bb stack is a huge benefit, and well worth taking.

**What about players behind?**

What, you may well ask, about the two players behind? A few % of the time one of them is going to wake up with a monster, and granted this is going to take away some of our edge. In fact it will significantly impact it, and needs to be accounted for carefully. At this point we turn to our trusty friend HRC to check just how much it will impact our equity, since calculating such things manually is a big pain in the arse. Running that quickly through HRC and assuming tight overcalling ranges of AQo+ 77+ for the blinds, we find that QJo will still have reshove equity of 0.33bbs.

Now of course, the more players left to act behind, the more likely we'll be dependent on checking such things using software, rather than by manual checks. If we're in the big blind, the manual calc. will always be accurate (but we may be able to consider flatting of course). The point is that having the

*to run a manual calculation, and look at the math involved, and consider how often we need to get folds for a play to make sense, will give us the wherewithal to start exploring widening our 3bet shoving ranges in appropriate spots.*

**ability****Finally...**

And what face are you gonna pull when villain flips over AA and you get there?

Yeah, that's the one

**Questions?**

Please post any questions, examples of your own hands, spots where you're unsure, calculations you'd like to double-check, criticisms, hell post whatever you feel inclined to That's what the thread is here for.

Until next time then... good luck at the felt

LuckyLuke