An interesting hand. Thoughts?
Live 3/6 game at my place of employment. I'm off the clock and not in uniform, but the regulars all know me as a dealer. They know I'm required to bet hands straight-up (no slowplaying or check-raising), and that when I bet hard I always have the hand to justify it.
I'm in mid-position with KK.
UTG (moderately tight) raises, folded around to me, I 3-bet, two very loose players cold-call the 3-bet, UTG calls.
Pot : 12 small bets.
Flop : ATx, two clubs. I have the Kc, and the Ac is on board.
UTG bets, I call, cold-callers call.
Turn : small club.
UTG bets, I call, one cold-caller folds.
River : club.
UTG checks, I bet, remaining cold-caller folds, UTG calls.
I win with nut flush.
Now, the real question :
Should I have called the flop?
Bear in mind that I was getting at least 13:1 odds (possibly as high as 15:1, based on my expectation of the subsequent action).
My reasoning at the time: on the flop, **assuming that my opponent has an ace** (he actually had AK), I have about 4 outs (two kings + RRFD + RRSD). That's a little less than 12:1 against, and I'm getting 13:1 in immediate odds from the pot.
However, giving it further thought, I realize that not all outs are created equal. The two kings cost 1 small bet each to draw to (either I hit them on the turn or I don't). But the RR draws (weak as they are) cost at least 3 small bets to draw to (calling both turn and river), so they should be discounted appropriately. OTOH, if I miss on the turn, then I can safely save that river bet, so the discount isn't exactly 1:3. There are 10 cards that make me the nut flush draw, which will then leave 9 for me to draw to on the turn.
So, to my reasoning, that means I have 2 cards (the two kings) that are straight-up draws. I also have 10 cards (the RRFD cards) that will cost me 3 bets, with a hit-rate of about 20% on the river. I have 6 additional cards (the RRSD gutshots) that will cost me 3 bets, with a hit-rate of about 10% on the river. The remaining cards (29) will cost me one bet only, because they'll miss me and I'll folds the turn.
So, what I'm seeing is this :
kings : 2 times I win the pot.
clean misses : 29 times I lose 1 bet.
RRFD hit-then-misses : 7.5 times I lose 3 bets.
RRFD hits : 2.5 times I win the pot.
RRSD hit-then-misses : 5.4 times I lose 3 bets.
RDSD hits : 0.6 times I win the pot.
Expected pot size (ie: what I stand to win) : at least 13 small bets already in the pot, plus at least 1 big bet on the turn and 1 big bet on the river (this is not counting my own contributions, since I only recoup those, not win them). Add it up, this comes to at least 17 small bets.
The final math, in terms of small bets :
immediate misses : -29
hit-then-misses : -38.7
immediate hits : +34
RR-hits : +52.7
net EV of flop call : +19 small bets for every 52 calls, or, equivalently, +0.36 small bets per call.
So, by my math, every time I call this flop with 13 small bets in the pot, I'm making about $1 (in a 3/6 game).
The situation :
The guy I "sucked out on" (ie: the AK) was very upset that I would make this call, and simply refused to believe that it could be a "legitimate" call. I laid out a simplified version of this math for him, but he just didn't want to believe that all those little draws could add up to a "legitimate" draw in a pot of that size.
So, I'm asking the good folks of the 2+2 Small Stakes forum for some feedback. Is my math correct on this? This is basically an "Ed Miller" call (ie: I would never have made this call before reading SSH). Have I misread SSH somehow?
If there's an error in my reasoning here, I'd be interested in finding it out.
Also, note that I'm evaluating the "runner-runner" outs a little bit differently than Ed Miller does. He assigns them an "equivalent" number of outs, but it doesn't seem to me that this is viable unless you weight the different outcomes according to their (cumulative) expense on both the flop *and* on the turn. It actually turns out to be a clearer call this way (ironically), but I'm still interested in 2+2'ers thoughts on this method vs. the straight-weighting that Ed uses in SSH.
Also, note that the rake drops the pot by about 1.3 small bets ($3 rake + $1 jackpot drop). This drops the expected pot-size from 17 sb to 15.7 sb, and drops the overall EV from +19/52 to +15/52 (a 14% drop in EV -- from $1/call to $0.86/call !). I found this angle interesting, and would be interested in others' thoughts on this, too. Clearly, the bigger the rake is in proportion to the final pot (ie: the lower the limit), the less correct this call will be. Again, I just found that very interesting, because it means that any so-called "suckout" call would be more viable at higher limits than at lower limits. Maybe there's something I'm missing here (?).
Lastly, I'm curious as to the less-quantifiable elements of this call -- particularly those related to the fact that I'm an employee at the establishment in question. On the one hand, I bet the hand straight-up. On the other hand, my income is highly dependent on tips from my opponents, including the guy who held AK in this hand. We're still on good terms, but he was cleary upset with me for a couple of days after this call (he'd been running bad, which didn't help matters). I'm not clear whether the marginal value gained by making this call was worth the marginal loss in tips (if any?) that I risk by making it. On the other hand, if it becomes clear to my patrons that I never make redraws, even when the pot odds favor it, then that just encourages them to hang onto their rag draws when I raise, right?
So many angles, so many angles.
Thoughts, anyone?
q/q
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