Raise Your Game #2: ARRRR-IN!!! How to Solve 3bet shove spots

    • LuckyLukePS
      Joined: 28.08.2014 Posts: 188
      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

      Originally 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) Hero has Q:spade: J:heart:

      fold, fold, fold, fold, CO raises to 6,000, Hero shove?
      Thanks to 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 does fold. So:

      %folds x $won@fold = FE (where $ stands for chips)

      To figure out how often he's likely to fold we need to estimate his opening range and his 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.

      Hand 0 16.9% [33+ A3s+ A7o+ KJs+ KQo QJs ]
      Hand 1 0.9% [QJo ]

      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 what we are risking, 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.

      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 ability 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.


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

      Yeah, that's the one :)


      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

  • 5 replies
    • SawyerNS
      Joined: 17.09.2010 Posts: 102
      Hi, LuckyLuke.
      Please correct article in sentence "In this spot villain is on the BTN, facing a 2x open from a big stack CO." Obviously, you mean "Hero" there.

      In general really helpful article to put yourself in a shape. And reach the idea where this numbers come from. Thanks a lot.
    • SDK1987
      Joined: 12.11.2008 Posts: 26,280
      Originally posted by SawyerNS
      Please correct article in sentence "In this spot villain is on the BTN, facing a 2x open from a big stack CO." Obviously, you mean "Hero" there.
      Nice you spotted that :f_thumbsup:
      I have fixed it.

    • dddq8842
      Joined: 09.12.2014 Posts: 50
      Thank you for sharing this.
      How can I practice this to become quick at it while I'm playing?

      Ranges below
      Hand 1, Is QJo shown as 0.9% for single hand selected?

      Hand 0 16.9% [33+ A3s+ A7o+ KJs+ KQo QJs ]
      Hand 1 0.9% [QJo ]

      Hand 0 62.390%
      Hand 1 37.610%
    • RedHeater
      Joined: 08.10.2010 Posts: 219
      Interesting article. Just on the mathematics, we are told that "we stand to lose what we are risking, which since villain covers us is 47,346 chips". So I don't get why when the numbers are plugged into the equation, 41,346 is put in for the amount we lose. This is the amount villain is due to win, but not the amount we put at risk?
    • SignOff1970
      Joined: 24.04.2011 Posts: 398
      CO: 152,520 (VPIP: 20.77, PFR: 18.43, 3Bet Preflop: 7.14, Hands: 262)
      I know that PFR is a summarized value, but I would like to ask if the opening range we assume with 31.8% is a value from your experience for a CO first in raiser with such PFR total or is the PFR irrelevant and we are assuming always this range?

      Sorry, if I am missing something vital here, but I am always struggling with ranges, my head just keeps spinning over and over the same issues, but I am trying :)