• cardman021
      Joined: 12.04.2011 Posts: 110
      Hi Guys,

      Just have a question regarding hands like QQ/AK. If villain is going broke with a hand like QQ+/AK and you happen to face a shove w QQ or even AK. Is it positive EV to go broke here?

  • 4 replies
    • GoOnCal1
      Joined: 22.01.2015 Posts: 581
      Hi Cardman :-)

      Do you mean if villain and hero always get it in with identical ranges?
      AA KK AK QQ range vs... AA KK AK QQ = 50/50
      The rake is going to murder us

      AK = 39%
      AKs =42%
      QQ = 40%
      KK = 57%
      AA = 84%
    • DrDunne
      Joined: 29.12.2010 Posts: 3,337
      Well it's a bit meh really. The two situations are (1) you are the preflop raiser, face a 3bet from only QQ+ and AK, 4bet, and then face a jam from 100% of his 3betting range i.e. QQ+ and AK. The other situation is (2) you are facing an open raise, you 3bet, he 4bets and you jam with QQ+ and AK.

      I'll have a go at calculating the EVs since it's such a standard question and it's probably good practice for me to try out and good for you/someone to at least read if not try it out/check yourself. As a disclaimer I'm not good at maths and it's possible that I do something wrong. If you or anyone else notice anything then please let me know. I'll spoiler it because it's long.

      Blinds are posted (1.5bB) and villain opens (3bb+1.5bb), you 3bet (9bb+3bb+1.5bb) and he 4bets to around 22bb. The pot is currently 35.5 and you are either going to fold or jam for your remaining 91bb. You know he won't fold anyway, because he only 4bets his QQ+ and AK.

      EVjam = (pWin * vWin) – (pLose * vLose)
      EVjam = (.398 * 110.5) - (.602 * 91)
      EVjam = -10.803bb

      Where p = probability and v = value of that outcome.

      Blinds are posted (1.5), you open (1.5+3) he 3bets (1.5+3+9) and you 4bet (22bb) with the intention of calling a 5bet-shove. So instead of investing a further 91bb as we did above after 3betting 9bb, we have to invest a further 78bb. The pot that we are considering fighting for = 1.5+3+9+22+91 = 126.5bb. So:

      EV(calljam) = (pWin * vWin) – (pLose * vLose)
      EV(calljam) = (.398 * 126.5) - (.602 * 78)
      EV(calljam) = +3.391bb

      This is a really simplified question though. In situation 1, villain will have a 4bet-bluffing range. It wouldn't be right to assume that he doesn't. If you have information that he doesn't 4bet-bluff then why would you try and get it in with QQ+ and AK? That brings up the point that QQ+ and AK are profitable mainly due to the FE that they generate when villain has bluffs. For example if villain 3bets/5bets (or 4bets/calls) QQ+, AKs, A5s-A2s, AKo, AJo, KJo (5.58%), continuing only with QQ+ and AK (2.56%) and folding with the rest (54.12%) of his range, then the above situations are as follows:

      To calculate the EV of our 3bet/5bet with AK we need to know his opening range. We could give him a ~CO opening range of {22+, A2s+, K7s+, Q8s+, J8s+, T8s+, 97s+, 86s+, 76s, 65s, A8o+, K9o+, QTo+, JTo}[27.60%]. Thus, from this he is 4betting with, let’s say (5.58/27.60) = 20.21% of hands and folding 79.79% of his range.... Blinds are posted (1.5bb) and villain opens (3bb+1.5bb) with his 27.60% range, you 3bet (9bb+3bb+1.5bb) with your QQ/AK and he 4bets to around 22bb with that range 20.21% of the time, folding 79.79% of the time. The pot is currently 35.5 and you are either going to fold or jam vs his 4bet for your remaining 91bb. You know he calls it off only with QQ+ and AK, which represents 45.88% of his 4betting range, and folds the remaining 54.12% of his 4betting range.

      EV3b5b = (pFolds * vFolds) + p4bets * (EV5bet)
      EV5bet = (pFolds|5b * vFolds|5b) + pCalls * ((pWeWin * vWeWin) – (pWeLose * vWeLose))
      EV5bet = (.5412 * 35.5) + (.4588 * (.398 * 101.5) – (.602 * 91))
      EV5bet = -17.035

      So now that we have EV5bet, we can add this into our EV3b5b formula:

      EV3b5b = (pFolds * vFolds) + (p4bets * (EV5bet))
      EV3b5b = (.7979 * 4.5) + (.2021 *-17.035)
      EV3b5b = 3.591 + -3.443
      EV3b5b = +0.148

      The other situation involves us open raising (1.5+3), villain 3betting (9bb), us 4betting and investing a further 19bb (4bet to 22bb), villain jamming, and us calling. So we are interested in knowing the EV of our 4bet/call with AK and QQ.

      EV4bCall = (pFolds * vFolds) + pJams * (EV|heJams)

      So we calculate the EV given that he jams over our 4bet and we call off our remaining 78bb with our QQ and AK. The pot is 1.5+3+9+:
      EV|heJams = (pWin * vWin) - (pLose * vLose)
      EV|heJams = (.398 * 101.5) - (.602 * 78)
      EV|heJams = -6.559

      So now this leaves us with:

      EV4bCall = (pFolds * vFolds) + pJams * (EV|heJams)
      EV4bCall = (.5412 * 13.5) + (.4588 * -6.559)
      EV4bCall = +4.297

      This is not the EV of our single decision, but with our overall strategy with AK and QQ (i.e. to 3bet/5bet, or to raise/4bet/call).

      So to summarise this, the EV of our plan to 4bet and call with QQ and AK against a range of QQ+ and AK is +4.29bb. The EV of our plan to 3bet/5bet with QQ and AK against a 4betting range of 5.58% and a subsequent 5bet-calling range of 2.56% is +0.15bb. These both assume conservative bluffing ranges of villain. If we assume that villain has no bluffing range then the EV of jamming QQ and AK over villain's 4bet is -10.80bb, and the EV of raise/4bet/calling with QQ and AK against villain's range of QQ+ and AK is +3.39. In short, it is often quite close in this spot which ultimately means that whatever decision you make is very close to breakeven. It is also the case that sometimes you will be raped by rake. However, in aggro games it should be the better option for your entire range. If you only play aggressively with 12 combos (i.e. KK+) then villain will play close to perfectly against you, assuming he pays attention (which is much more likely in aggressive games where villains are a bit better). Other than that, it is DEFINITELY not an auto stack-off with QQ and AK. Finally, I've completely disregarded the EV calculations when villain calls our 3bet, or even calls our 4bet - which are 2 situations that are obviously going to happen a fair amount of the time. With AK and QQ we want a low SPR so it makes more sense to bloat the pot preflop.

      I hope I didn't make too many mistakes, it's pretty difficult without software. Even if I did I think the conclusions will be very similar anyway since nothing stands out to me and it is what I expected.
    • DrDunne
      Joined: 29.12.2010 Posts: 3,337
      That post is a bit of a side track, but hope it is useful... The main point is this: If you think that villain only 3bets you with QQ+, AK and won't fold anything to a 4bet, then don't 4bet with QQ and AK and then shit yourself when he obviously jams on you. You knew he would jam on you, so you shouldn't have 4bet it if you weren't prepared to call it off.

      If you 3bet and he just jams on you without 4betting to a normal size, just fold it: even with QQ, against a jam your EV is about -4.375bb assuming non-blind positions and 9bb 3bet over a 3x open. This is a good thing in a way, because you can now play perfectly against him, calling only KK+ for an EV of +44.982bb against his range.
    • cardman021
      Joined: 12.04.2011 Posts: 110
      Hey man, thanks! I haven't fully read it yet though. I'll read it tomorrow, have to go to work.. Thanks for taking the time.. :f_drink: