Calculating Pot Odds in Omaha Hi/Lo

This is quite likely an elementary concept to a lot you reading here. In fact, some of you are going to read this and think "Jebus! Can this idiot please come play with me every day?" But I've been bouncing around playing some O8 on and off for several years now, and I just had an epiphany Saturday night.

We had switched our game from NLHE to PLO8 at midnight, and the stacks were deep. The blinds were constant at $.25/.50, but there were several stacks over $300 around the table. I limped in with Kd-Jd-10x-x, because this was a limp-friendly game preflop. Flop comes down with two low cards and two diamonds, so I'm on a high-only draw with the 2nd nut flush. There's a pot-sized bet of $3.50, and several of us called because the guy who fired had been betting out pot on almost every flop, and didn't really know what he was doing. He was catching everything under the sun, but I felt like if I hit my flush, I'd be good, so I called. The table at that point was composed of four solid players, one solid players who was on a bad run, one aggro-donk and one uber-calling station. Three of the solid players folded, leaving me (I'm calling myself the 4th solid player, and it's my blog, so I get to call myself that), the calling station, the decent player on a bad run (rough night, Jim) and the aggro-donk.

Turn brings a non-diamond 5, which paired the board. If any of the other three players I considered solid were still in, I would have been worried about the boat. But when the Aggro bet pot again, I didn't really care, and when Jim just called, I didn't put him on a boat, because he's not going to flat-call $30 in a four-way pot with me still to act behind him if he's made the boat. So there's a bet and two calls in front of me, and I'm getting exactly 4:1 on my money to make the call for a 2nd nut flush that I'm certain will get me the high hand if I hit.

Now in NLHE, that's an insta-call. And as I flashed my hand to the player next to me, I said "How bad would this call be?" He replied "8.75" and I said "Yeah, but what's the scale?" as I made the call. At the time, I thought that the math made it a good call, but upon further review (i.e. after the vodka wore off) I realized that it was actually an amazingly BAD call.

Here's the deal. With a high-only hand, and two low cards on the board, I had to have a diamond bigger than 8 to make my hand. So that goes from 9 outs down to 6 right there. But wait, the Ace doesn't count, because it goes low and makes me not scoop. So that's 5 outs.

But wait, I have the King and the Jack. So that's three outs. And the 10d was on the board, so I only had two outs to make my hand good for the whole pot, which is what I was thinking when I made the call based on 4-1 odds. I did indeed have 9 outs to get half the pot, but to make that a mathematically correct call I would have to be getting 8-1 on my money, which I most certainly was not. So I did not hit my 2-outer, and that was a fine example of throwing good money after bad. By the way, my read was right, and I would have gotten the high half if any diamond had come, as the high hand was a rivered straight.

Now I'm not posting this to say that I would have seen that had I been sober. I wouldn't have. This was a real epiphany for me in O8, and it probably comes hundreds of dollars later for me than for many of you. Fortunately for me, I play low stakes Omaha, so I've only thrown away hundreds of dollars with this miscalculation rather than thousands, but it's an important consideration nonetheless.

So in essence what I've saying is this - when you have a hand that is only going for half the pot on your best day, you need double the pot odds to make a call in O8 that you need in Hold 'Em, since you're only going to get half the money. So if you are like me, drunk and stupid and calling off on a flush draw thinking 4-1 is good odds, you actually need 8-1, because the low cuts the pot in half. Just something to think about in a rare and exceedingly elementary strategy post from the Falstaff homegame.