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 finishes the fifth
After four days of fun in the hot desert sun, experiencing the faux opulence of Las Vegas, it was good to be back in the upfront honesty of the Anaheim Club, particularly in our favorite haunt, a dim booth of the coffee shop. Aunt Sophie was still grilling me on seven-card stud high-low, familiarly known as 7/8. Sara relaxed in the corner, quietly perusing the only notable novel with a one-letter title, Andy Warhol’s a, for her night class in contemporary trompe l’oeil literature.
“Let me elaborate a bit,” I began, “on my earlier comments on fifth street. I said that, just as in all stud games, fifth street is the most important in 7/8. If you have followed the guidelines so far, your hand falls into one of the following five categories:
- “You’ve made a two-way hand on fifth street. This doesn’t happen often.
- “You’ve made a one-way hand on fifth street with a draw to scoop.
- “You’ve got a one-card draw in both directions.
- “You’ve got a one-card draw in either direction.
- “You’ve started with a premium draw, but bricked out on both fourth and fifth street.”
“But you could be there,” Aunt Sophie supplied, “because on fourth street there wasn’t much betting, it looked like you had the best hand, and everyone else appeared to have bricked.”
“Right,” I responded, “and we’ll get into what to do when you also get a bad card on fifth street in a moment. But first, that first category is what we dream of: completing a sweep hand, preferably in a multiway pot with several bets (and several players) in it. Examples of these hands include:
- “A low straight (seven-, six-, or five-high).
- “A low flush (a smooth eight or better).
- “A full house or quads with all other hands looking high-only.”
The coffee shop waitress, that requisite nameless minor character who perennially provides expository relief in the form of fresh coffee and sometimes pastries, slices of fruit pie, and cheese cake, appeared with caffeinic replenishment for Sophie and me, plus English PG Tips for Sara.
“When,” I went on, “you’re fortunate enough to have a made hand like this by fifth street, get as much money into the pot as you can. Ordinary table logic applies here: If somehow the hand still has several players in and there’s a bet and raise coming from your right, you might want to consider just calling to collect double bets from one or more players on your left whom you might force out with a reraise. But don’t try to get too fancy here — if it’s checked to you, put in the first bet unless you’re quite sure that someone to your left will bet the hand for you. If there’s a single bet behind you, whether to call or raise will depend on too many factors to get into here, but, in general, I prefer to raise.”
I paused for a bite of the heretofore alluded to saskatoon berry pie. Sara glanced up for a moment. “Did you know,” she offered, “that the saskatoon berry, which comes from a Cree word, is also known as serviceberry, which is also the name of the tree from which the berry comes, while the tree itself is also known as Juneberry, shadblow, and shadbush?”
“This it says,” Aunt Sophie demanded, astonished, “in this a-book?,” but Sara vouchsafed no reply, having receded back into her haven. So ensconced, she would provide no further diversion.
Draw to scoop
“The second category of hand,” I resumed, “you might have on fifth street, a made one-way hand with a draw to scoop, is still very desirable. You’re an odds-on favorite for half the pot with (essentially) a freeroll for the other half. This can take the form of having a monster low that is very unlikely to be beaten by someone with a straight or flush draw, or having a monster high with the possibility that no one will make their low. When you hold a hand like this, you still want to get lots of money into the pot, but now you have to be sensitive to how the other players are going to respond to any pressure you put on the pot. If, for example, you’re showing a board of 6-4-A of mixed suits, and have a 2-3 in the hole, you don’t want to drive out all the other low draws, only to be left heads-up against a mediocre (but winning) high hand. You might be able to drive out one high hand, not all, but you’re still unlikely to sweep unless you improve your hand for high, with either a five or another ace. Since you’re unlikely to improve, you’ll be getting half the pot, and your goal should be to make that half-pot as big as you can. This goal might very well be accomplished by only smooth-calling bets that originate on your right. The worst thing to do when you have a lock for half the pot is to drive out players who are drawing dead against you, and leaving yourself against one opponent who is likely to split the pot with you. There is an exception to this. If you’re in a game in which you frequently find yourself playing against someone who’s fond of high-only hands, pound on him with your made lows. You’ll win more money on those hands when you do sweep, and you’ll force him to consider folding some of the time if his high really is mediocre.”
“Using,” she said, “as you said, the principle of selective aggression.”
“Right,” I agreed. “The third category, in which you have a one-card draw in both directions, is possibly the trickiest situation in 7/8. The most important consideration is your chances of making a hand that wins in at least one direction. For example, if you started with four low spades (seven and under), and caught a red jack on fifth street, the most important factor is how many ‘good’ cards are left. A good card can be defined here as one making your seven-high, a flush, or both. Twelve cards can make your seven (the three missing numbers from your hand times four suits) and six higher spades (eight through king).”
“Wait, tsatskeleh,” Sophie interrupted. The flush cards I see, but the low cards can you elaborate?”
“Of course,” I assented. “Let’s say you have 7-6-3-2, you can make your low with any five, four, or ace, of which 12 remain in the deck if you haven’t seen any elsewhere. Now, two chances at 18 cards is pretty good, but it’s essential to consider how live these cards are. This can make a major difference in determining whether to go on or not. Here’s where a good memory can be a stud player’s best friend.”
“Oh my,” Sophie sighed, “a memory course now I’ll need.”
“Let’s say, to continue the example,” I continued, “that in addition to your five cards, you’ve seen 13 cards exposed in other players’ hands, and of those 13, nine were cards that would have helped you. The number of helping cards left in the deck has been cut in two, from 18 to nine. In this situation, you’ve gone from roughly a 4-to-1 favorite to complete your hand in at least one direction, to a slight underdog. This is an enormous difference, especially since only three of the 18 ‘good’ cards are sweep cards for you, and the rest are only going to give you half the pot, with a final-card draw for the other half.
“Dollink,” Aunt Sophie cut in, “I hate again to interrupt, but the numbers I don’t see. Would you please so kind be to supply the math.”
“Certainly,” I consented. Let’s say five players, including you, remain on fifth street. This means you’re looking at 15 upcards, plus three more were folded on third street. That makes 18 cards, to which you add your two downcards, making 20 you know. This leaves 32 cards you can catch, and two tries in which to catch one you need. Of course, the cards you need may be among the other players’ downcards, and you have no way of knowing that, so you can ignore them in your calculations. The actual situation may be somewhat worse than you calculate, or somewhat better. Okay, to figure the chances of catching at least one of your needed cards, you figure the chances of catching two cards you don’t want, and subtract that number from 1. When there are 18 good cards, there are also 14 bad cards. The chance of your first card being bad is 14/32. If the first card is bad, 13 bad cards now remain, and you’re drawing from a deck of 31. That’s 13/31. Multiply the two numbers together to get the chance of catching two bad cards, and subtract from 1 to find the chance of catching at least one good card. One minus 14/32 times 13/31 equals about 0.81; 81-to-19 is a bit better than 4-to-1 in your favor. But now go down to only nine good cards available. This leaves 23 bad cards, so the chance of your first card being bad is 23/32. If the first card is bad, 22 bad cards now remain, and you’re drawing from a deck of 31. That’s 22/31. As before, multiply the two numbers together to get the chance of catching two bad cards, and subtract from 1 to find the chance of catching at least one good card. One minus 23/32 times 22/31 equals about 0.49, a bit less than 50-50. That’s the math.”
“Ah,” Aunt Sophie breathed, her enlightenment enhanced by having scribbled figures on a napkin.
“If the pot remained small through fourth street, and you’re faced with multiple bets here (or even the prospect of multiple bets), it’s probably prudent, albeit admittedly difficult, to muck your hand. Your opponents will find these kinds of hands almost impossible to get away from here, and your ability to do so, when it’s correct, will be a major advantage of your strategy over theirs.”
“If even a strategy they have,” Aunt Sophie laughed.
“Here’s a final consideration for these hands,” I mentioned. “When counting your outs, be very careful to include only cards that are likely to make you a winner. If a hard rock showing good low cards is pounding the pot, and you’re drawing to a six-high flush, you may not want to consider a seven as a ‘good’ card for you, and adjust your mental calculations accordingly. You certainly don’t want to be drawing dead. For the same reason, you might want to give up on a draw to a seven.”
“How you assess the situation,” Sophie observed, “depends on the situation.”
“Um, yes,” I replied, “excellent analysis. The fourth category, wherein you have a one-way draw, is thankfully considerably simpler to assess. You’re now fighting for half the pot, and this usually isn’t a good idea. It may be correct to draw for half the pot if:
- “the pot has gotten big,
- “the action is still multiway,
- “your cards are very live, and
- “you’re drawing to a hand that is very likely to be a winner.
“Otherwise, you’re probably not getting pot odds to continue here.”
“Ah hah,” Aunt Sophie nodded with comprehension.
“The fifth category,” I concluded, “where you catch bad on fourth and fifth street, really shouldn’t need much discussion. You’re not here to play five-card stud against opponents who are playing seven-card stud. I don’t care how good a draw you started with, playing on here will undo possibly hours of your patient mucking on third street. So one final word about playing on here: don’t!”
Lest readers think the author incapable of original thought, he hesitates to acknowledge continued indebtedness to Mike Zimmers for input on this 7/8 series. Nonetheless, credit must go where it is due.