Deep Stacked Play - Part 3

Below is a partial HH from a deep NL600 game that I played recently...I had quite a bit of discussion with Bruechips regarding this hand and the most optimal line to take in this spot considering the all the factors - stack sizes, board texture, virrains, etc. I think Bruechips is going to chime in a bit about his thoughts on the hand...but WTF would you do in this spot?

My reads are as follows...

MP1 - relatively unknown, but has been playing tight in the limited action I have seen from him
BB - ULTRA tight, his range consists of overpairs to the board

Full Tilt Poker, $3/$6 NL Hold'em Cash Game, 9 Players

UTG+1: $720.95
UTG+2: $1,200
MP1: $1,367.60
MP2: $642.45
CO: $298.80
Hero (BTN): $1,545.90
SB: $290.10
BB: $1,200
UTG: $1,433

Pre-Flop: dealt to Hero (BTN)
3 folds, MP1 raises to $14, 2 folds, Hero calls $14, SB folds, BB raises to $70, MP1 calls $56, Hero calls $56

Flop: ($213) (3 Players)
BB bets $150, MP1 calls $150, Hero ???

Thoughts? Comments from anyone other than FUEL55?

BRACKCHIPS

OK, here are my thoughts about the hand: I'm pretty sure BB is done with this hand once MP1 calls. He's folding if you raise every time (he MIGHT play for stacks with AdKd, but such a small part of his range, I'd just ignore it). He's also check-folding the turn. I'll be making that assumption for all that follows. The question is what MP1 has. Let's start off by assuming NOTHING about what MP1 has, and just let some letters serve as placeholders for what he'd do with his range. Let's also assume you've got three options available: shoving, calling, or folding (that is, I'm not considering a raise less than all-in, back to that later). My initial reaction was to call, but here's some math I've been doing on it (for those of you who aren't into this sort of thing, I aporogize).

If you fold, your EV is obviously -70 (you lose the $70 you put in pre-flop). Nothing fancy to calculate there.

Now let's figure out the EV of shoving. Let f be the probability that MP1 folds. Let q be your equity GIVEN that he calls. The EV of shoving is then:

f (143+300) + (1-f) (q (1367 + 220) - (1-q) (1367))

Now set this equal to -70 and solve for f (because I think q is easier to pin down than f). I get:

f = (1297 - 2954q)/(1810 - 2954q)

Now let's come up with a value for q, our equity vs. MP's calling range. MP's calling range definitely includes sets. 99's equity vs. just sets is 34.5%. (In case you're wondering, the diamond helps out a lot. 9s9c would have an equity of 31.8%). Add in T9s and we're down to 30.5%. Add in JdTd and we're back up to 32.5% . Add in AdQd and AdKd and we're back up to 35.3%. Add in 87s and you get up to 37.2%. It's hard to know without much of a history here whether MP would be calling the re-raise deep here with T9s, or whether he would 4-bet with the big diamond hands, or whether he'd be calling off 200bbs on the draw. But I think 33% or so is a pretty reasonable estimate for equity when called. f then comes out to be 38.6%.

Let's say you think his calling range for calling the 3-b and floating the flop is T9s, QQ-66, JdTd, AdQd, AdKd, 87s, and 67s (I'm open to other suggestions). 88-66, T9s, JdTd (which would give the 33% we assumed before) is only 32.5% of this range. The other 67.5% of the time he's folding. That's way more than we need to make a shove better than a fold. A huge amount of this is QQ-TT. If he just folds QQ and JJ to the BB's c-bet, then the fold % is only 53%, but still plenty profitable. If he calls your shove with 87s, AdQd and AdKd, then fold % is still 42.8%. So a shove is going to be better than a call pretty much all the time. With f at 42.8% and q at 33%, the EV of shoving is -$35. Bump f up to 60% and it's $109.

What about calling? Say you are willing to get it all-in whenever you hit one of your 8 non-diamond outs - any 9, any T, any 5. Say if a 9 comes you get it in vs. the undersets, TT,T9s,and JdTd. Your equity vs. this range is 58.5%. If a non-diamond T comes, you get it in vs. TT-66, JdTd, and T9s. In this case your equity is 72%. If a non-diamond 5 comes, you're in vs. 99-66 and T9s. You've got 61% equity here. Those are 8 non-diamond outs. Whenever you win, you win MP1's stack plus BB's dead money, for a total of 1567. When you lose, you lose the amount of MP1's stack, 1347. So here's your EV, GIVEN that you hit one of your outs:

2/8*(.585*1567-.415*1347)+3/8*(.72*1567-.28*1347)+3/8*(.61*1567-.39*1347) = $533

You get one of your 8 cards 8/45 of the time (let's assume that we know enough about the BB's range that he never has any T,9, or 5 in his hand). 533*(8/45) = 95.

The question is, what happens when a blank comes? Can you make a play in these cases? Also, what happens if a diamond comes? Let's assume for the time being that MP1 will check-fold most of the range he'd be folding to your shove on the flop if a non-diamond undercard to the board comes. That's 9 cards (offsuit fours, threes, and deuces). I'm pretty confident if you get checked to on a turn like that, you can bet 500 and win the pot pretty much every time. In this case, you win 443 (the preflop pot minus the 70 you put in, plus the 300 BB and MP1 put in on the flop). Then given a non-diamond undercard, you get f 443. For an f of .60, that's 266. You get this (9/45) of the time, and (9/45)*266 = 53.

Just this strategy, having to fold any other turn, already has an EV of 95+53-70 (preflop call) - 150 (the flop call) = -72, which is about as good as folding the flop. I think there are many other turns where you get checked to and can either bet profitably or take a free card and profitably play the river if you catch a good one. I'll have to do some more work on whether I can find enough equity on later streets to make calling better than shoving, and I haven't even considered if making a raise smaller than all-in is worth doing. But hopefully this is enough to get the conversation started.

BRUECHIPS