An EV Calculation

I know I posted something similar a while back in “How to Analyze a Hand,” but I liked this spot that my buddy posted on Cardschat. You can find his thread here, which is pretty cool since it’s all live poker-oriented, but I’ve copied and pasted the hand itself below:

Sucks that I’m not deeper because I think it’d be an easy r/f. But I’m gii with my stack size right?

2/5 NL Live

Effective stacks: $500 (my stack)

Preflop:

UTG opens for $30.
Four callers to me in the SB, and I call with .
BB calls, and we go 7 ways to the flop.

Flop ($210): 

I check.
BB (solid reg) bets $65.
Folds to button (really loose fish), and he calls.
I jam all in.
BB goes all in.
Button folds.

Turn: 

River: 

 

 

Now, to most people this is a no-brainer gii or at least raise spot, but Sand (my buddy) correctly identified that he’s not necessarily in fantastic shape when he gets calls. My intuition told me that this was a guaranteed +EV spot, even though I know villain might only call with a very strong range. The reason? Well the pot is enormous. We make only a pot-sized raise or so when we jam over the $65 bet and call, so effectively we lay ourselves 1:1. If the villain ONLY led with hands that were ahead of us, and then called off that whole range (I assume the caller of the $65 bet always folds to the jam – debatable but not a terrible assumption), we’d not even be in terrible shape given we have basically 30% equity or better against any range that isn’t ONLY sets.

But why did I feel like it was profitable? Intuition is great, but it’s a lot better to do a full analysis when you have time, both to PROVE the spot is profitable, and to strengthen your intuition for on-table spots in the future. When you have time, doing as full an EV analysis as is reasonable can be quite helpful. Since I had some time this morning, I did that analysis for this spot. Here was my reply:

 

 

EV(jam) = (call%)[($210+$480+$65)(our equity) – ($480)(1 – our equity)] + (1 – call%)($210 + $65 + $65)

The pot is not of negligible size. We’re only making roughly a pot-sized raise when we jam, so taking the pot down with no call is fine. Let’s say he leads with every suited two pair (5 combos), every suited straight (8 combos), all sets (6 combos), 88 (6 combos), 98s (3 combos), 87s (3 combos), JT QT KT AT A8 A5 of diamonds (6 combos – we’ll say he doesn’t lead A4-A2dd). I think this is a pretty reasonable range, but you think that he plays close to all hands pre, so I’ll also give him all the 8x of diamonds that can make a straight using two cards (like I won’t include K8dd or 83dd), so Q8 J8 84 of diamonds (3 combos). That’s 40 combos total that he leads on the flop (some of them might be weighted not at 100%, but for simplicity we’ll say they are).

Now let’s say that we turn our hand over after we jam, and he has pokerstove in front of him. Ie he knows his exact equity, his pot odds, etc. And he’s ONLY going to call off with hands that he knows are +EV to call with. He has to call off $415 to win $210 from pot, $65+$65 from the bet and call, and $420 from our jam, so $760. 415/(415+760) = 0.3532, so he needs 35.32% equity to call.

To put this in perspective, JTdd has 34.7% equity, so in this situation would fold. 88 with one diamond also has 34.7% equity and would fold. A8hh has 39.2% and would call. AThh and all the other heart draws don’t have enough equity to call (for this scenario, in game I doubt he ever folds NFD + gutshot). Every OESD + FD hand has enough equity to call, at around 39-40%.

Hands that call:
A8, Q8, J8, 84, all of diamonds (4 combos)
99, 77 (6 combos)
T8s, 85s (8 combos)
Total: 18 combos

Hands that fold:
Everything else
Total: 22 combos

He’s calling with 45% of the hands that lead, and our equity when he calls is 34%. So plugging back into the EV equation:



EV(jam) = (call%)[($210+$480+$65)(our equity) – ($480)(1 – our equity)] + (1 – call%)($210 + $65 + $65)

EV(jam) = (0.45)[($755)(0.34) – ($480)(0.66)] + (0.55)($340)

EV(jam) = (0.45)[$256.70 – $316.80] + (0.55)($340)

EV(jam) = (0.45)(-$60.10)+ (0.55)($340)

EV(jam) = -$27.05 + $187

EV(jam) = $159.95


So definitely VERY +EV to jam, even when we’re screwed by his calling range and he plays perfectly. Interestingly, this shows that if he’s really folding that much, we can jam with pretty bad equity and print money in this spot if he thinks we always have a set or better. But I doubt he’s ever realistically folding things like gutshot + FD, so we probably can’t actually start bluff-jamming here unless he’s a good reg with a fold button who thinks we’re mega-tight and don’t bluff.

The good news is, for your actual hand, he’s probably calling off wider than just what’s +EV or better for him here, so we actually make more money. Plus, we have a really big EV buffer here (+32bb for a play is enormous), so even if we’re wrong and he doesn’t lead two pair or his pair + OESD combos or w/e, we’re still likely looking at a profitable jam.

 

 

So there you go. That’s my EV calc of the day. It’s something I really should do more often, but it can get to be somewhat cumbersome in more complex spots, and it’s really not practical for many multi-street scenarios. But it really helps you get a handle on spots off-table so that you have better handle on similar spots in-game.

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