Calling a Blind Bet in Lowball

Many lowball plays involve mathematics. For example, you can base your decision whether to call a blind bet entirely on math. Many players like to bet blind when they are drawing one card and their lone opponent is drawing two (or more) cards. Some bet blind against multiple opponents drawing two cards, and some against opponents drawing only one. Others bet blind drawing two, as long as their one or more opponents also are drawing at least two. You base your calling decision strictly on pot size and what the blind bettor is likely drawing to.

A typical situation is the one in which the middle blind has come in, in Southern California, for a raise, or, in Northern California, has merely opened the pot. In either case, though, the bet after the draw is the same size as the bet before the draw, so the figuring is the same in both games. Lowball is played in other areas, of course, but the structures of the limit games fall into one of two categories: double or single limit.

I refer here to ace-to-five lowball with a joker in the deck. Similar calculations could be made for deuce-to-seven, except that game is rarely played limit. It is normally played either pot-limit or no-limit. If it is played limit, it is played only in triple-draw lowball.

In this typical situation, usually there are three blinds, with one chip on the button (often called the dealer blind), one in the middle (or small) blind, and two in the big blind. Those chips could be worth $1, $5, $20, or $100. It doesn't matter; the principle is the same.

Everyone folds to the middle blind, who either comes in for a raise in the double-limit game or just opens in the single-limit game. The effect is the same. The player who has the small blind puts an extra three chips into the pot and the player with the big blind has to call two more chips. If the big blind has a reasonable two-card draw, he usually calls. The first player asks for one card and the second for two. As soon as the first player sees that the second is taking two, the first player says, "I bet blind," and tosses four chips into the pot, or, sometimes without saying anything, just tosses the chips in. But it is usually clear that the player is betting blind, because he makes the bet before receiving his draw card. It is now up to the player in the big blind to decide, after looking at his cards, what to do.

Let's look at the math. After the blind bet, there are 13 chips in the pot (including the dealer blind). If you are the player contemplating the call, you should realize that you don't have to win most of the times you call to profit. In fact, you don't even have to win a fourth of the time. Let's say you win exactly a fourth of the time. Then, out of four calls, you lose four chips three times, for a loss of 12, and win 13 one time, for a net of one chip in the four trials. You would break even by winning four out of 17 times (that is, slightly less than a fourth of the time). To guarantee a profit, then, you would call with whatever hand beats the average one-card draw a fourth of the time.

We can neglect the times you make a raising hand after the draw. You will lose with some of those hands and win multiple bets with others, and that needlessly complicates the calculations. All we need be concerned with is with which hand or better you should call, while still being aware that you can raise with some of those hands. And a discussion of which hands to raise with is beyond the scope of this column. (Here's something to think about, by the way. Game theory says that some of the hands with which you raise should be hands that cannot possibly win in a showdown, like two pair, three of a kind, or a pair higher than your opponent can possibly make.)

To have a positive expected value, your worst calling hand is whatever hand is better than the 25 percent of the worst hands your opponent can make. It's actually relatively easy to decide which hands those are, particularly if you know the other player does not have the joker. You would know this if another player flashed the joker when discarding his hand or if you yourself had the joker. In most cases, though, you can assume that the other player does not have the joker; a particular hand should have the joker a bit less than one time in 10. Although the actual compositions of the two hands affect the chances of the one-card draw making his hand, we can neglect those cards for the sake of this exercise. The cards in your hand actually make it somewhat less likely for your opponent to make his hand, so the figures here are actually somewhat conservative. Your edge will actually be somewhat higher than you might at first conclude. Specifically, let us say you have drawn two cards to A-2-3; since there are now fewer aces, deuces, and threes remaining in the deck, it is slightly less likely that your opponent started with those cards and, thus, slightly more likely that he needs those cards, meaning that the deck from which he is drawing actually has three fewer cards that help his hand. Nonetheless, let us ignore the cards in your hand. Your opponent has four small cards, and he discarded one unneeded card. He is drawing one card from 48 unseen cards. There remain three each of the cards that can pair him, for a total of 12. (Yes, it's possible that he broke a pair, which makes only 11 cards to pair him, but this is offset by the cards in your hand, leaving fewer good cards for his hand.) Thus, 36 cards help him and 12 hurt him. Interestingly, those 12 are one-fourth of the remaining cards. So, approximately one-fourth of the time, your opponent should pair. You need to call, then, with any hand that beats a pair. That is, you call whenever you end up with a king or better.

Knowledge of your opponent helps here. Some players bet blind when drawing one card only when they have the joker. If you know that for certain about your opponent, there need to be three more cards that would make him a loser. If you catch a smooth king, he can lose by pairing or by catching any of the three remaining kings. Thus, against such a player, you should call with about a K-6 or better. Even a K-7-5 would be worth a call, as long as you know your opponent would bet blind if drawing to a 7-6 with the joker. Some players bet blind only when drawing to a joker-6 or joker wheel; in such case, you would call only with K-6 or better.

Other players bet blind with any one-card draw, as long as their opponent is drawing two or more cards. Any one-card draw could be anything from a 9 or better. Against such a player, you can call with any king, even if you catch a king and a queen.

If other players are in the pot, you can call with worse hands, because you are getting improved odds on your call. For example, let's say you opened on the button with a good two-card draw and both the small blind and the big blind called. The small blind drew one card, and as soon as he saw that both the big blind and you drew two, he bet blind. The big blind folded. Now, instead of odds of 13-to-4 on your call, you are getting 16-to-4, or 4-to-1. This means you have to win one time out of five to break even, so now you can call with a hand that beats only a fifth of the worst hands he can make. Out of the 48 cards he can catch, then, the nine worst cards he can catch are those that pair any of the top three cards in his hand. You can call with any hand that is a pair of aces or better. In fact, if you threw an ace away and end up with a pair of deuces, you can probably afford to call with that, since he is less likely to have caught an ace to make his hand and more likely to have paired one of his higher cards.

What you also have to understand, and this is a key concept, is that against just the one opponent, you will lose approximately three-fourths of the time. I recently saw a poker writer state that you should fold in a given situation unless you have the best of it. That statement is true, but misleading. Many people find it hard to understand that you can lose a pot most of the time and still have the best of it. It is pure mathematics. In the situation with two opponents, one of whom folded for the blind bet, if you call with a small pair or better, you will lose approximately four-fifths of the time, yet your expectation will still be positive. The more bets in the pot, the fewer times you have to be right to profit.

If your opponent has drawn two cards and bets blind into your own two-card draw, you can call with even worse hands. When you are getting 13-to-4 for your call, you still call with a hand that beats the worst 25 percent of the hands he can make. Usually a player drawing two cards bets blind into another two-card draw only when he has the joker, so you can assume, lacking other evidence, that he does have it. However, if you have seen this player bet blind in this situation without having the joker, you can worsen your calling requirements. Here, the exact constitution of both hands is more important than in the earlier examples; nonetheless, calling with a pair of deuces or better should show a profit. If you know for certain the other player does not have the joker, or if you have seen him bet blind in this situation without having the joker when drawing two cards to hands like 6-5-4 or even 7-6-5, you can call with a pair of threes or better. This may seem counterintuitive, and you will find that most lowball players will call in this situation with any no-pair hand (even K-Q), but that is where they draw the line: They will not call even with a pair of aces. That is a mistake.