Lowball Situations

Limit lowball is a game of situations, many of which come up frequently. The seasoned player knows how to handle these situations automatically. But the new player, the infrequent player, or the poor player seems to handle each situation by whim or by guess, and usually guesses wrong.

Tight Larry opens from first position. Jim, a solid player, calls from the next position. Weak-tight Susie calls from the middle of the field. Crazy Willie calls, also. A nice pot is building. Clueless Bill is on the button, and raises. We happen to be totally omniscient, so we know what Bill has: 9-8-7-6-4. Now, if Bill is lucky, Larry does not have a pat hand. He is probably lucky, though, since Larry should have a one-card draw approximately 80 percent of the time here. Jim probably is drawing here, since he would have raised with any hand that he wanted to play pat. The only hand he might slow-play here would be a pat 6 or better, and that comes up less than 0.4 percent of the time, so we can neglect it. The others are drawing, for sure. We can use Mike Caro's Poker Probe to see how often Bill wins here. If everyone is drawing, Bill wins approximately 18 percent of the time. Of that 18 percent, though, Larry is pat maybe a fifth of the time; Bill loses most of those times, because Larry would not open from first position with a pat hand worse than 8-7. So, if Larry is pat, Bill would need to draw two cards to beat that hand, and he would make the winning hand less than 2 percent of the time. So, Bill doesn't win 18 percent of the time; he wins about four-fifths of 18 percent of the time, or 14 percent. (We should shade the 14.4 percent downward more than that to account for the times he draws two cards and beats the pat hand but not one of the other drawing hands.) Here's what happens in 100 trials: Approximately 80 of those times, everyone is drawing. Eighty times, Bill puts in $40. If he wins, he gets $175 (including the blinds); if he loses, he loses the $40. He actually loses more, because if only one player bets after the draw, he calls, and loses that bet most of the time. But, let's neglect the bet after the draw. His losses are 0.86 x $40 × 80 = $2,752. His wins are 0.14 x $175 × 80 = $1,960. Subtracting, we get $762. Twenty times, Bill puts in $60 and loses probably 99 percent of the time. His losses are 0.99 x $60 × 20 = $1,188. His wins are 0.01 x $275 × 20 = $55. (He wins one bet after the draw, on average. Actually, this win is too high. Often when Larry is pat, Bill doesn't win $275 because no one else calls Larry's reraise. But let's give Bill the benefit of the most favorable outcome.) Subtracting, we get $1,133. Altogether, then, he loses $762 + $1,133 = $1,895. Dividing by 100, we end up with his expectation, which is losing close to $20 per hand for every time he raises with a rough 9 in this situation.

Why did Bill raise? Because he was guessing. He has heard that a pat hand – any pat hand – has the best of it against players who draw, and he's guessing that he has the best of it here. He's wrong. A pat 9 frequently does not have the best of it against even three typical draws.

Cagey Cal is on the button with the same hand and with the same four players in the pot. What does he do? Raise? Nope. Call? Nope. He doesn't want to play a pot in which he has to put in approximately one-seventh of the money (he already has $5 in the pot for the dealer blind and $15 more is in the pot in the form of the small blind and big blind) with less than a one-seventh chance of winning. Cal raises with that hand here only if a maximum of two players are in, and he much prefers that at least one of them is someone like Crazy Willie, who is always subject either to be drawing two cards (and sometimes three!) or to a rough hand.

Here's another automatic situation that even the experienced player doesn't always get right, while the poor players invariably do it wrong.

Tight Larry opens from first position. You are next. Your hand is A-2-3-joker, the best one-card draw in lowball. You call. If you are Clueless Bill, you call because you always call with this hand. If you are Cal, you call because if you raise Larry, you will scare off all the potential customers. Everyone knows how tight Larry plays. If you just call, Susie will come in behind you with a draw to an 8-6 or better, and Willie will come in behind her with almost any two-card draw. But if you raise, neither will come in cold for two bets. Your wonderful drawing hand plays well against any number of drawing hands, whether one, two, three, or more. The fewer opponents there are, the better the chance of winning the pot; the more opponents there are, the better the chance of winning a large pot, even though the actual chance of winning goes down. Because of this potential, the hand does best against a larger field. As expected, Susie and Willie call. The button folds, and now Speedy Sam raises from the middle blind. Larry calls. This is wonderful information. You know Larry is drawing. He would reraise if he wasn't. Yes, there is a slight chance he has a rough 8 and would just call, but it is far more likely that he has a good one-card draw. Your one-card draw is much better than his, though. If you are Clueless Bill, you call, also, because you always call. You didn't raise to begin with, and now you're happy you didn't, because you figure you'd now have to be putting in three bets on a hand you haven't yet made. If you are Cal, though, you reraise. And you don't care whether Susie and Willie call the extra two bets, and you don't care if Sam is pat or drawing. You have a positive expectation in all of those situations. The only way you don't have by far the best of it is if Sam has a good pat 7 or better, and that is a rare situation. Against typical draws, if Sam is pat with about an 8, you win approximately 28 percent of the time, but you are putting in less than 20 percent of the money. (Specifically, since you already have $5 in the pot and since there is $15 more in blinds, you are putting up $55 to win $255, immediate pot odds of about 4.6-to-1 when it is only about 2.6-to-1 against your winning.) And here the bet after the draw is very important, because a substantial portion of that 28 percent of the time that you win, you win multiple bets, making your implied odds even higher. If either Susie or Willie folds, your chances of winning climb to well over 30 percent and there is dead money in the pot to win. What may well happen is that Susie folds and Willie stubbornly calls and still takes his two cards, which improves your chances vastly. If Sam reraises, that will surely drop players, but even if it doesn't, your chances of winning only drop to where you still have a positive expectation, and your chances of winning a huge pot go way up. If Sam reraises, it is with a hand he will probably bet after the draw, and you will win at least two bets after the draw, and maybe more. Clueless Bill has the same chance of winning, of course, but he has not maximized his potential win, because he didn't reraise. This is partially due to another misunderstanding. He doesn't understand that even though he loses the pot in this situation nearly half of the time, his expectation is positive. Losing players do not understand the concept that they can lose most of the time in a given situation and still make money in the long run in that situation.

Another play that most lowball players don't make is drawing three cards from the big blind. The live ones do it regularly, and they do it at the wrong time, and lose money. The tight players never do it, and they give up winning situations. But, in fact, when it costs only half a bet to get in (or half what the others put in, as long as the pot was just opened in a double-limit game or played with only one raise in a single-limit game), it is almost always correct to draw three cards against two or more opponents if you have one wheel card and the joker. Having the joker is critical. Against two very live opponents, one of whom is probably drawing two cards and the other likely drawing rough, drawing three to any two spokes (wheel cards) is also correct. In fact, against only one opponent who regularly draws two cards and is not smart enough to stand on a J-10 when you draw three, drawing three cards is correct, even if you don't have the joker. (Parenthetically, even if he does stand on the J-10, you still have a positive expectation.) Many otherwise good players who have been playing for decades have convinced themselves that drawing three cards is a sucker play, and they never do it. They're wrong.

Many other situations come up regularly in lowball. I'll talk about them soon.