Thursday, February 16, 2012

Poker Quiz Question #48

Q#48: You're in a 9-handed $5/10 NL cash game. Everyone has $1500 stacks. A TAg MP player open-raises to $40. Another TAg player on the button RR's to $140. You're in the big blind with Ah-Kc. Your image is TAg, but you were recently caught bluffing. What should you do?
  1. Fold
  2. Call
  3. Re-raise
  4. Shove all-in


A#48: And now back to Q#48, in which you're in a 9-handed $5/10 NL cash game. Everyone has $1500 stacks. A TAg MP player open-raises to $40. Another TAg player on the button RR's to $140. You're in the big blind with A-K♣. Your image is TAg, but you were recently caught bluffing. What should you do? Fold, Call, Re-raise, or Shove all-in?

Interesting hand. My gut reaction is to re-raise (either 2.5x or all-in), but I'm also leaning toward a fold. Sounds weird doesn't it? RR seems reasonable.... but fold? With an offsuit big slick? It's the 4th or 5th strongest starting hand? Really? Yeah, really.

Anyway, I don't think calling is smart, as the best that can happen is that TAg #1 calls behind and I see a multiway pot OOP with a hand that plays best heads-up. This leaves either RRing or Folding. Hmmm.... Let's see what REDi tells us.

  • TAg #1: Without any other info, a TAg open raising in MP in a 9-handed game generally means a PFR of around 15% or so. I'm thinking essentially all pocket pairs and nearly all broadways (with the exception of some of the weaker unsuited broadway cards). Call it: 22+,ATs+,KTs+,QTs+,JTs,ATo+,KJo+,QJo
  • TAg #2: The second TAg repops to $140. We will assume he has put the first TAg on the same range as us. He's reraising, so he's either trying to isolate and/or trying to build value. With only the blinds left to act, I'm going to lean toward the latter. Typically 3bet ranges for TAgs run around 6-7%, but that number is an average against all opponents. Against another TAg, I'm going to drop TAg#2's PFR down to 4% or so. Call it: 99+,AQs+,AKo
  • Hand Equity: Hot-and-cold against these two ranges, our AKo has a tad over 30% equity. TAg #1's equity is close to ours at 27.3%, and TAg#2's equity is 42.3%. In other words, our equity is just so-so if we're multiway. Heads-up against TAg#1 (an unlikely scenario), we're a 57:43 favorite. Heads-up against TAg#2, however, the tables are turned and we're the 44:56 dog. 
  • Fold Equity: Normally, I'd say we have decent FE against TAg#1 (because of his range, and the strength we'd project by 4betting here) but we've been caught bluffing recently, so our image isn't very good. Our FE against TAg #2 is not great either, simply given his hand range.
  • SPR: If we call or reraise to anything but all-in, we have to consider whether we get ourselves pot committed or not. The standard way to estimate this is via our stack-to-pot (SPR) ratio, which is just our assumed effective stack size on the flop, divided by the pot size on the flop. 
    • Reraise. If we RR to, say, 2.5x and (miraculously) just get called by the other two players, the pot would be around (2.5 x $140) x 3 = $1050. The effective stack size would then be $1500 - (2.5 x $140) = $1150. Therefore the SPR would be 1150/1050 = 1.1.
    • Call. If we call (and TAg #1 doesn't 4bet), the pot will be (3 x $140) = 420, and the effective stack size will be $1500 - $140 = $1360. Our SPR would then be 1360/420 = 3.2.
  • Our RR SPR reads total commitment, so RRs to anything less than all-in is silly. 
  • If we RR all-in, and get called by both players, our equity is less than the 33% needed to break even. If we RR all-in and get called only by TAg#2, we're a dog in the hand. In other words, if only one of these guys call, they're probably going to do so with only big pairs and maybe AKs that have us beaten pretty squarely.
  • Calling is even worse, as we'll be OOP with an SPR that also says we're committed. Unless we hit the flop really hard we won't know where we're at, but the SPR says we should get it in. 
  • I think this all implies pretty strongly that we're on a fold line.
Implement: Muck, and then pay attention to what kinds of hands either player turns over if it goes to showdown.

Answer: Fold

All-in for now...


  1. Are you kidding me? 4 betting is definitely the play, even w/ the ranges you specified. The way you did your math was completely wrong. You don't just calculate the equity of AK vs the other two ranges to find out if the play is plus EV or not. I did some basic calcs w/ the starting ranges. Honestly player 1 is probably only shoving qq+/AK and player 2 will probably call a player 1 shove w/ a similar range, but shove a little wider when folded to him. Therefore, we do have to fold when they both get it in, but you can expect that to happen less than 10% of the time. W/ a 2.5x 4bet you profit when you get it in vs a single player as well as when they both fold. The total ev of 4betting is around +60, or 6BB! that's a good hourly winrate you are sacrificing if you fold AK here.

  2. I think you're correct... only if this was a 6max instead of FR AND the fact you just got caught bluffing which would induce, imo, lighter shoves from the initial raiser.