Note: Not at the old Poker1 site. A version of this entry was first published in Card Player. This entry in the "Aunt Sophie" series covers poker.
Aunt Sophie and the world-class lowball play
“Dollink,” said my Aunt Sophie, “can you tell me any world-class lowball plays?”
I signaled the waitress. “World-class?” I laughed. “You’re playing three and six limit and you want to know world-class plays?”
The lady in the black uniform approached the table silently, seeing that her customers were engaged in conversation. I pointed at our empty coffee cups, and she withdrew just as quietly.
“I want you to tell me,” she stubbornly persisted, “plays that I can make that are beyond the capabilities of the average winning players. Plays that properly only the best players make.”
“As it happens,” I picked up, “I do know of at least one play that seems quite straightforward to me, and yet I see even players who regularly win do incorrectly all the time.”
The waitress returned with the pot and refilled our cups. “I can’t stand it,” I sighed, “bring me another piece of cheese cake. Those blueberries are just irresistible.”
“And for me,” put in Aunt Sophie, “another piece chocolate cake I’ll have.”
Blind raps pat
“Okay,” I continued, “here’s the play. You’re in the deal position, and no one has come in yet. You have a very good one-card draw, maybe a seven or better with the joker. You open for a raise. The blind flat calls. This a fairly straightforward player, not particularly tight, but no gambling fool either. Comes time for the draw, and the blind raps pat.”
“Raps pat?” echoed Aunt Sophie. “But he didn’t raise.”
“Exactly,” I supplied. “Now what do you suppose this player has?”
“Hmm?” she mused. “A rough nine?”
“No,” I stated, “I said he was not particularly tight. When he’s on the blind, and the dealer is the only one in, he’s going to raise.”
“Well, then,” she queried somewhat puzzledly, “it must be a jack or a ten.”
“Not bad,” I responded, “although since I said he was no gambling fool, I would rule out the jack. If he had jack-ten-smooth, he would just draw two cards. If he had jack-nine or better, he would draw either one or two cards. If he had jack-ten-nine, he probably wouldn’t play. Remember, he’s straightforward. No, he has to have precisely ten-nine. And it’s likely not ten-nine-smooth, because then, if he didn’t raise, he would probably draw two cards. No the hand is almost surely ten-nine-eight.”
The desserts arrived, and the waitress again warmed up our coffees.
“Okay, okay,” agreed Aunt Sophie, “makes sense. So now when he stands pat and I draw a card, I know I got a lot of room to make my hand.”
“Uh, huh,” I ventured, “and that’s the mistake most topnotch players make. If you’re drawing one card to beat a rough ten, how often do you connect?”
“I don’t know,” Aunt Sophie hesitated, “but I would guess the drawing hand wins slightly more than half the time.”
“That’s a good guess,” I returned. “Of course it depends on the constitution of both hands. It ranges from a low of about 42%, to a high of about 60%. The low would be a hand like six-five-four-three discarding a ten against ten-nine-eight-seven-joker. The high would be something like ace-joker-two-three discarding a three to draw against ten-nine-three-two-ace. Let’s say it averages out to making the hand about 50% of the time. So how much is that worth?”
“How much?” she repeated. “I dunno. Lemme see if I can figure.”
Up for grabs
“That’s just a rhetorical question,” I explained. “I don’t expect you to figure it. I’m more or less thinking out loud here, and in the format of giving a lecture, so I will try to supply answers to questions I pose. How much it’s worth also depends on how you figure the worth of the pot. Let’s say you consider that at the point of making your decision, you consider the pot to belong to no one. It is in contention. Up for grabs for the winner of the pot. You each have $6 in the pot. Antes represent $4. Total of $16. You make the hand half the time, so your return is about $8 per hand.
“What you make after the draw, if anything, is somewhat difficult to pin down. If you decide to bet only if you make the hand, and the player calls you every time, half the time you’ll get $6, or $3 per time. In actual play, though, the other player would not call you every time, so your actual earnings would be something less than $3. On the other hand, you might bet some of the times you miss the hand. If the player still calls every time, you lose some of those bets. What most likely happens, though, is you bet every time you make the hand, and some of the times you don’t make it, and you get called randomly. If that randomness is close to what game theory recommends, your after-the-draw bets are supposed to be a wash. That is, you neither make money nor lose on them. For that reason, and because we can’t really predict how you will bet and how your opponent will call in this situation, we can ignore the bet after the draw. So drawing one card is worth about $8 of that $16 pot.
“Now, you put in $6 before the draw on this play. You average $8 per pot, for a net profit of $2 per play. To put it another way, you average winning half the antes. But there’s another way to play this hand, and this is where the ‘world-class,’ if you insist on calling it that, comes in. As I said, very few even excellent players make this play. How about if instead of drawing a card you stand pat on whatever hand you have? That is, as soon as the blind raps pat, you rap right behind him with your king-three-deuce-ace-joker, or whatever you have. The otherwise-good players don’t do this because they lack the imagination. They just can’t see having that joker-wheel to go for and not drawing. Nor, for that matter, can they stand pat with any good one-card draw that they know is live to the other hand. So they draw, and bust out half the time.”
“Aha!” exclaimed Sophie. “But if you just stand pat behind the other player no matter what you have, he checks after the draw, you bet, and he folds.”
“Exactly,” I beamed. “Not one player in a hundred with a rough ten would call in that situation. He’d just be glad he hadn’t got in trouble by raising with the hand, and can just ditch it for the two small bets before the draw. So instead of 50% of the pot, or $8 per time, this play is worth 100% of the $16. That is, a net profit of $16, instead of $2.
“Of course, you never show the hand when you aren’t called, or you can bet you won’t get away with that play again. Also, just in case it backfires and some suspicious player calls you anyway, give it up for a while. Don’t do that play again for a long time, or at least not with anyone from that group again. Also, sometimes some devious player doesn’t raise in that spot with an eight or even a seven. If it’s a seven, he bets, and you have to give it up. If it’s an eight, he passes, you bet, he calls, and you just muck the hand as fast as you can and hope no one asks to see it. Now that’s pretty rare, and of course I did specify a straightforward player. Don’t make the play against a good player, a player you don’t know, or a tricky player.
“You may well ask why some of your opponents even bother with this play, when it seems like they’re practically playing their cards face up. No reraise, stand pat, check after the draw, a player might as well be saying, ‘I have a pat ten-nine-eight; see if you can beat it. If you stand pat behind me, just bet and take it.’ They do it because most players don’t know how to properly respond to that play, and the pat hand wins close to half the time. Now you know how to play that situation.”
“A world-class player,” she concluded, “I’m on the way to becoming. And by standing pat on a king-four, yet.”
“World-class I doubt,” I ended. “This play works in the smaller games, but probably nothing above fifteen and thirty. Any higher, and you’ll never have an opponent standing pat against you in the blind without first having raised.”