Extreme Draws in Lowball

Sometimes you have to make a desperation play in lowball that involves a draw – or standing pat – with negative expectation. You may have several choices, all of them bad, and your best – or only – decision is to choose the one that is the least bad. This is when lots of lowball players make mistakes, and never know it because they don't understand the principles.

If you or the other player is all in, for example, you have to make the draw with the best expectation. Sometimes the best expectation is the least negative. That is, if all your choices are bad, you take the least bad one. An example was my experience in the lowball event of the 2001 World Series of Poker, about which I wrote:

By now, I was one of the short stacks. When four tables still remained, I had been the chip leader at my table, and felt like I had a shot at the final table, but missed draws took their toll. At the $4,000-$8,000 level, I had 17 $500 chips left. I had to put eight of them in for my big blind. David Hoekstra opened for a raise, and I put in eight more chips on a one-card draw; David stood pat. I paired, and did not think I could win the pot on a one-chip bluff. I checked, and folded when David bet. He showed me that he had had an 8-5, so no way would I have gotten away with a bluff. If he had drawn, I might have tried it. The next hand was my small blind, for which I would have had to put in four chips if I had that many. Since I didn't, I put in my one remaining chip. Phil Hellmuth opened for $8,000. No one called till it got to me. I was already all in for my one chip, one-sixteenth of the bet. The big blind did not call. The house dealer now gave $11,000 back to Hellmuth, his bet plus $3,000 from the big blind. He already had a profit of $3,000 on the hand. Normally, the blinds would total $6,000; since I had only $500, they totaled $4,500, and I had action on $1,500.

I now made my brilliant play, a desperation move that enabled me to finish one ahead of Hellmuth. That wasn't worth any money, just a bit of satisfaction at having outlasted a brilliant tournament player, someone well deserving of the title of world-class champion. Hellmuth is to be congratulated for having made the money in a game that is not his specialty. I admire his achievements in every major form of poker, and going as far as he did in the WSOP lowball event is further attestation to his tournament skills.

I looked despondently at my cards. What a way to finish the tournament, I thought: K-Q-J-9-7. I did not want to draw three cards to a 9-7; if I did that, Phil could stand pat on a queen and still have the best of it. Drawing four to a 7 would be even more suicidal; two to a jack was just as ridiculous. My only choice was to stand pat, hope he was drawing, and then hope he paired. Not much chance, but better, I thought, than the multiple-card draw that was my only other choice. These choices all flashed through my mind, but as soon as the dealer asked how many cards I wished, I immediately indicated I was pat. If Phil had a pat hand, it was all over; I was resigned to getting up in that likelihood, figuring I'd given it my best shot with that last chip. Had he clearly had a pat hand, he likely would have just shown it down, but now Phil seemed to have a dilemma. He started talking out loud, meanwhile spreading his cards so the players next to him could see what he was thinking about, but I couldn't. "I could have you beat right now," he said. I realized what his dilemma was. He had either a pat jack or pat 10, and didn't want to give up those three chips without giving himself a chance. I didn't know whether saying anything would help or hinder me at this point, but figured silence might be too suspicious. After all, it's a classic move to say nothing when you're bluffing, so as not to precipitate unwanted action from your opponent, but I was sure Phil knew this, so I said something. "I couldn't very well indicate the strength of my hand by raising; I'm all in." Phil kept thinking, and finally threw the 10 away faceup. I then said, "Your 10 was good." It didn't matter at that point to reveal the strength – or rather, lack of it – of my hand. Phil disgustedly announced that he had paired threes. I rather triumphantly spread my horrible cards, and the gallery went wild. That is, the other players made admiring remarks and the three or four RGPers who were cheering me on from the rail applauded. I survived my all in with three chips. Phil had broken 10-8-5-3-joker to draw to the 8. RGPer Bill Chen, part of my rooting section, immediately informed Phil that even after breaking, he still was a 4-to-1 favorite on the pot. By breaking his hand, he had gone from 100 percent equity on the pot to 80 percent, still a huge favorite. Equally, though, my standing pat having convinced Phil to break his hand had changed my expectation from nothing to 20 percent. Phil said if he hadn't had the joker, he'd never have drawn. Everyone else at the table made sure to point out to Phil that they never would have broken a 10 in that spot. Well, everyone but me; I didn't say so, but I would not have broken a 10 against a desperation player with one chip remaining and forced in the small blind to play whatever cards fate happened to give him. There were far more hands worse than better than a 10-8 on which a player in such a position would stand pat. (By the way, I confirmed later with Poker Probe that of the multiple-card draws I was contemplating, drawing either three or four cards would have given me less than half the chance I had against the one-card draw.)

I would love to say that I was able to run those three chips into a victory, but I got no miracle hands. Phil went broke before I was forced to enter a pot, so I did manage to outlast him. Places 13 through 16 all paid $1,850, so my victory was essentially a Pyrrhic one. But that was $1,850 more than I had after buying in to the tournament, so I was pleased.

That's an example of making the least odious of several bad choices.

Another terrible hand is A-A-K-Q-J. What do you do with that one? You might think because of the similarity of this hand to the preceding, you should stand pat. After all, this hand is only one rank worse. But, although it doesn't seem intuitive, you should draw four cards. Again, we're talking of a situation in which no further money can be won after the draw. This could come up in a tournament or a live game when you're all in on one of the blinds – or your opponent is. If your opponent is first to draw and stands pat, of course you have no choice. You must draw four cards. But, against any one or two-card draw, taking four cards is better than standing pat. The rougher your opponent's draw, the better your chances. For example, A-A-K-Q-J against 7-6-4-2 wins about 27 percent of the time, while taking four cards wins about 30 percent of the time. But A-A-K-Q-J against 9-8-7-6 wins about 27 percent of the time, while taking four cards wins about 36 percent of the time. That's a big difference. And if you're all in, the average one-card draw against you is not likely to be as good as one to a 7. For examples against two-card draws, A-A-K-Q-J against 7-6-4 wins about 41 percent of the time, while taking four cards wins about 44 percent of the time. A-A-K-Q-J against 9-8-7 wins about 41 percent of the time, while taking four cards wins about 49 percent of the time. That's also a big difference.

Even if you're first, you're better off drawing four cards and hoping. Your opponent may stand pat behind you on a jack or even a queen, but you're still better off than if you stand pat and your opponent takes one or two cards. If your opponent has two pair, he still has to draw two cards. And if he has K-Q, most players still would draw two cards.

What you never do, and some would make this mistake, is throw the ace and draw one card. That is the worst of all possible choices. Drawing four cards is always better – and by a lot. You'd be better off standing pat than drawing one card. All you can beat is a pair. If your opponent doesn't pair, you have no better chance drawing one to that miserable hand than standing pat, because no card he catches that doesn't pair him would enable you to win. And if he does pair, your pair of aces is good, other than the rare chance of his pairing aces.

And if it comes up, standing pat on a J-10 is "less bad" than drawing two cards, whether your opponent takes one card or two. In fact, a J-10 is about a 2-to-1 favorite over most two-card draws. A J-10 takes the worst of it against almost any one-card draw, but always fares better than discarding the J-10 and taking two cards. So, against a one-card draw, as before, it's a case of doing the "less bad" thing.

Also, a rough pat queen is better than any three-card draw. No matter what your opponent does, standing pat against any draw with Q-J-10 is the lesser of two evils as compared with drawing three cards.