Playing Tens From the Big Blind in Lowball

Here's a limit lowball situation that comes up frequently. You have the big blind. In a double-limit game, someone opens for a raise; in a single-limit game, someone just opens. No one raises, but two other players call. Your hand is 10-9-8-7-2. What should you do?

I know a few players who do the absolute wrong thing: They dump the hand. They say, "I can't win with a straight 10 against three players." Why are they wrong?

I used Mike Caro's Poker Probe to compare lots of four-player situations with one player holding a pat 10 with no possible draw, or at least no good draw. Against three typical draws, the pat 10 wins approximately 24 percent of the time. Odds against winning are about 3.2-to-1, but you're getting odds of at least 7-to-1 to play. Now, this is a little misleading. Approximately one-fifth of the time, the opener has a pat hand, and you can assume that the pat hand is better than yours 100 percent of that time. This cuts your win rate from 24 percent to approximately 19.2 percent. But your bet (the $10 you put in to "make the blind good") is one-eighth of the pot; if you win more than 12.5 percent of the time, you have a positive expectation. Those players who look at the situation incorrectly have not kept exact track of the results. All they know is that they lose most of the time. That's certainly true. They lose more than 80 percent of the time. But look what happens in 100 times the situation comes up in either a $10-$20 double-limit game or a $20 single-limit game. If you fold every time, you neither win nor lose anything. (You might think you lose $1,000, but that's not the right way to look at it. Once that $10 is out there, it no longer belongs to you.) If, instead, you call $10, 80.8 times you lose $10, or $808; 19.2 times you win $70, or $1,344. Your overall profit is $536. Divide that by 100 and you get a hefty $5.36 for that $10 investment. That's $5.36 more than you get by throwing the hand away and "saving" $10.

Yes, it's certainly disheartening to stand pat on a rough 10 and have the opener stand pat right behind you. That's when your 24 percent win gets whittled down to 19.2 percent. It's also disheartening to have everyone draw, and, after you check, have someone bet. Should you call? Rarely, if at all. You have revealed extreme weakness by not raising, standing pat, and then checking, but it doesn't matter. Three others are in the pot. They know that someone will bet a rough hand, thinking, correctly, that you will fold. So, they check and call with those nines and even tens, or, if the first player bets, they call with hands that have you beat. Knowing this, players rarely try to steal the pot, fearing someone will "keep them honest." That is, your hand is "protected" the times that it is the best. You can assume that any bet represents a hand that falls into the greater than 80 percent of the time you actually are beat, and you can safely fold. But there's that sweet 19.2 percent (approximately) of the time that no one is pat, everyone draws, everyone misses, everyone checks, and your rough 10 takes down the pot. Someone is sure to say, "How can you play a hand like that against three players?" or "You sure are lucky that hand stood up." Don't say anything. Just smile inwardly and know that you played the percentages.

Remember, just because you lose a bet most of the time you make it does not make the bet a bad investment – if you get paid off at higher odds than it costs to get into the pot. This is the same reasoning that hold'em players frequently use to correctly draw to inside straights when the pot gets large. But the interesting, and nice, thing about the lowball situation is that the pot doesn't have to get large to make the call correct. The call is often (not always) correct against one player, and almost always correct against two or more. (Standing pat on a 10 against one player has other complications.)

By the way, in the simulations, I pitted 10-9-8-7-2 against 7-6-5-3 and 8-5-4-A, each drawing one card, and 3-2-joker, drawing two. Those are typical draws.

And why did I reduce the 24 percent of the time a rough pat 10 wins against typical draws to account for there being a pat hand about 20 percent of the time by the first player only? What about the second or third? Yes, it's certainly possible that one of the other players is pat, but that doesn't happen very often in lowball games. Generally, if the second player in a pot has a hand that he's going to play pat, he raises. Even more so for the third. Yes, sometimes people slow-play pat monsters, hoping someone will raise behind so they can reraise. This is when it helps to know your players. Generally, however, players don't want to take a chance on no one raising, and they usually play their hands straightforwardly. And a pat monster comes up very seldom. Let's say that 0.5 percent of the time the first player has opened on a draw, the second player has a pat 7 or better and slow-plays it. Even if you reduce your win rate to 18.7 percent, you're still money ahead. (According to Super System, a pat 7 or better occurs about 1 percent of the time; I make the assumption that the hand would be slow-played no more than half the time.)

In fact, though, you don't need to reduce your win rate that much (by 20 percent). Often, your opponents do not include both the dealer and the small blind. When those two do not play, your $10 call is worth more than 7-to-1. If neither plays, it's 8-to-1. So, often, the figures for return cited here are conservative, and your actual return could be higher.

Sometimes, you get a 10-8 instead of a 10-9. What should you do then?

I compared 10-8-7-3-2 to the same three typical draws as before. If you stand pat on the 10-8, you win about 22.3 percent of the time. Reducing that by about a fifth, to account for the possibility of the first player being pat, the hand wins approximately 17.8 percent of the time. In 100 times the situation comes up, 82.2 times you lose $10, or $822; 17.8 times you win $70, or $1,246. Your overall profit is $424. Divide that by 100, and you get a nice $4.24 for that $10 investment.

What if you draw, instead? Then, it turns out, you win about 24.8 percent of the time. Plus, you don't have to reduce the win rate by as much. Of the approximately 20 percent of the time the opener is pat, he should have an 8-7 beat less than half the time. Your overall win rate probably drops only to maybe 23 percent. In 100 times, 77 times you lose $10, or $770; 23 times you win $70, or $1,610. Your overall profit is $840. Divide that by 100, and you get a phenomenal $8.40 for that $10 investment. And here you can't neglect the bet after the draw. This is a little harder to quantify, but you don't have to dump your hand almost every time there is a bet after the draw. In fact, sometimes you make the 8-7 and bet it. And you win more of the times there is a bet after the draw than you lose. So, you might be able to shade that $8.40 up as much as $1.60, giving you as much as a $10 return on your $10 investment. Clearly, the best play here is to draw a card.

I've done other comparisons, the details of which I won't bore you with, and they show that drawing one card to any 8-7 in this situation is better than standing pat on the corresponding 10-8-7.

I also compared better 10-9 hands than the 10-9-8-7 mentioned earlier. Let's take a hand like 10-9-7-3-2, again against the typical three draws. The hand wins about 22.7 percent of the time, which, again, should be adjusted to about 18.2 percent to account for the possibility of the first player being pat. You lose $10 81.8 times, or $818. You win $70 18.2 times, or $1,274. Your overall profit is $456. Divide that by 100, and you get a reasonable $4.56 for that $10 investment.

Might it be better to draw? If you draw, you must draw two cards. It is rarely better to draw one card to a 9 than it is to just stand on a 10. Part of the reason for this is that you never end up with a hand that you can feel good about betting. All you can do is check and call, which is not much better than the situation you were in with the pat 10.

When you draw two cards to 7-3-2, you win approximately 17.7 percent of the time. You don't need to adjust that at all, because you are hardly ever "drawing dead," even when one of the first two players is pat. That's only slightly worse than that adjusted 18.2 percent on the 10-9-7-3-2. In 100 contests, 82.3 times you lose $10, or $823; 17.7 times you win $70, or $1,239. Your overall profit is $416. Divide that by 100, and you get a nice $4.16 for that $10 investment. The slight difference is offset greatly by the money won after the draw. You'll win a lot more on the times you can either bet or call a bet than you will lose. Of the 17.7 times out of 100 that you win, maybe you bet or call 10 percent of the time, and you probably win two-thirds of those contests. So, seven times you win another $20, totaling $140, and three times you lose $20, totaling $60, for an additional net win of $80. This figure is a bit conservative, because some of the time you win more than one bet. That probably brings your overall profit up by maybe $1, to more than $5. This makes drawing two cards to the 7 here better than standing on the 10-9.

If you change the three low cards from 7-3-2 to 3-2-A, you improve to maybe 18.8 percent. I also would be much more inclined to draw two cards here, because I can sometimes make a hand that is worth multiple bets after the draw. Drawing to a 7 hardly ever makes a very strong hand, never one that can go three bets after the draw, and one that, in fact, usually loses if it bets and is raised, whereas the draw to 3-2-A can make a hand that can easily stand three and more bets after the draw. In the given matchup, if I make a wheel and bet, the 7-6 might raise, the 8-5 might call that bet, the two-card draw might make a 6 and put in another bet, and now I can reraise. This could never happen with a 7. Your overall profit by drawing two cards to 3-2-A vs. standing on 10-9-3-2-A goes from about $4.60 to as much as $6.

Both plays (standing pat on a 10-9 when you have the big blind, and drawing two cards) are clearly profitable, but the two-card draw is much better than standing on the very rough pat hand. This conclusion is not "intuitively obvious," and was probably not known to anyone before computers came along.

By the way, the figures I use in this article are only approximations, signposts pointing to the truth. Further, the figures are examples of specific situations. Adding $10 to the pot when it is your big blind, with three others in the pot, and you have a pat 10-9-8 does not have an exact expected profit of $5.36. That amount is only an average of what you might see in the long run over all situations. If, for example, the others are all drawing to wheels, you have by far the worst of it. You would be putting in $10 and taking out considerably less than $10 in the long run. Of course, if the second or third player didn't put in a raise, you shouldn't even be in that game. To balance that, though, if all three of your opponents draw two cards, or if one draws to a rough 8 and the others draw two, your overall expected profit would be greater than $5.36.