**Note: **Not at the old Poker1 site. A version of this entry was first published in Pan Player+. This entry in the "Aunt Sophie" series covers pan (or panguingue), which is a multi-player form of rummy, often played for money.

**Aunt Sophie forsakes the deuces**

“Which is better,” asked a familiar voice, as a familiar presence eased into the aisle seat next to me, “a straight eight, or should I maybe add four deuces?”

“My God, Aunt Sophie!” I blurted, whipping my gaze away from the Thai Airlines jet at the next telescoping umbilical tunnel into the terminal. “How could you possibly have known I was on this flight?”

“I didn’t, Dollink,” she beamed, “it’s all a happy coincidental. But when I saw you among the first boarding group I asked the ticket agent if I could change my seat assignment, and the one next to you was empty.”

“That explains,” I responded, “how you could get the seat next to mine, but not what you’re doing on this flight.”

**Las Vegas**

“*Nu, tsatskeleh*,” she went on, “you think you’re the only high-and-mighty roller who goes to Las Vegas?”

“Of course not,” I retorted. “I’m going for the lowball event at the Hilton’s Summer Poker Festival. And what are *you* going up for?”

“A little R&R, Dollink,” Aunt Sophie replied, “rest and recreation. I’ve had enough of pan for a while. I think I’ll play keno, where I can win some big money.”

“I think that’s `rest and rotation,’” I remarked, “although probably some people think it’s `rest and relaxation.’”

“Never mind the grammar lesson,” she snapped, “what I want is a keno lesson. You know all about probabilities. Should I play the straight eight ticket, or add the four deuces like I see a lot of players doing?”

“Now that depends,” I procrastinated, “on what your aim in playing keno is. If you plan to last a long time, and not lose a lot of money, you should not play any kind of way ticket. You should play the ticket that gives you the best compromise between bad odds and high payoff, and play it for the minimum investment.”

The plane began to back away from the terminal, pushed by a small, powerful truck whose only job all day long it was to push planes out to runways.

“I want to win the $50,000!” she exclaimed.

**Keno**

“That’s the ticket,” I concurred. “A lot of keno players seem to deliberately handicap themselves. They play tickets on which the most they can win is a few hundred dollars. If that’s all they’re after, they should play craps or roulette, any game with a lower house take. The average house edge on keno is 30%, although a smart player can sometimes find lower. The lowest I’ve ever seen is a few special promotions down around the 10% range, although I’ve heard David Sklansky say he’s seen a couple of promotions in which the player actually had the edge. The point is that you’re going to lose money most of the time at keno. Since you want to make big money, you really shouldn’t play any ticket lower than an eight-spot. You’ll have to shop around a bit, but there are a few casinos that pay $50,000 for eight out of eight on a two-dollar ticket. It’s about 230,000 to one against hitting eight out of eight, mind you, but that’s at least within the realm of possibility. When you start talking about nine out of nine, that’s over a million and a quarter to one. Seven out of seven doesn’t really pay enough, $20,000 at most for $2. Now I realize $20,000 is a fine win, but you said you’re shooting for $50,000, and the smallest ticket that will pay you that for a $2 investment is the eight. You can’t win any more for nine out of nine, so why make your odds that much worse?”

“What about progressive keno?” demanded Aunt Sophie.

“Yes,” I assented, “you can win more than $50,000 on a progressive keno ticket, but you also have to invest more, usually $3 per game. But that’s another topic that we’ll get into another time. Let’s just talk about the `regular’ tickets with respect to your question about adding the deuces. You can pay $2 for a chance at $50,000 on a 230,000 to one shot, or you can pay $2 for a chance at $50,000 on a 1,300,000 to one shot. Which do you think makes more sense?”

“The easier way, of course,” returned Aunt Sophie. “I’m not stupid, you know, *bubeleh*.”

“I didn’t think you were, my dear,” I continued. “That was just a rhetorical question. Okay, so I agree with your decision to play the eight-spot ticket. That gives you a chance if you’re lucky to win $50,000. You could also win two or three thousand, depending on the casino, for seven out of eight. That’s the kind of win you want. But how about those deuces? You circle off your eight numbers into four groups of two, and add an extra dollar to pay four twenty-five-cent twos. In most casinos, two out of two pays $3 for a quarter investment. A lot of keno writers tout this as `insurance.’ All you have to do, they say, is catch two numbers, and your ticket is free.”

“Sure,” Aunt Sophie interjected, “that’s just why I wanted to play that way. I’ve heard both keno writers and other players call it insurance. But, you know, you’ve told me how bad a bet insurance is in blackjack, and so I was wondering about how it is in keno.”

The captain came on the intercom to announce that we were at the runway awaiting takeoff clearance. He stated that there were twenty planes ahead of us.

**Way ticket**

“How it is,” I went on, “is how you view way tickets. A way ticket is merely a convenient means of combining several tickets on one piece of paper. When you play an eight and four two-spots, you’ve essentially playing five different tickets. Each is independent of the other. Your chances of catching two out of two are independent of your chances of getting five or more out of eight. Let’s consider the two-spot tickets separately. You choose two numbers, say one and two. The house picks twenty numbers out of eighty. You’ve got twenty chances out of eighty for one of your numbers to be picked. You don’t win on a two-spot unless both are picked. So, if one of your numbers is chosen, which, remember, is twenty out of eighty, your other number could be among the other nineteen the house chooses. The house, after picking one of your numbers, is no longer choosing among eighty numbers; it’s choosing from seventy-nine. They don’t put a ball back again after it’s chosen; otherwise the same number could conceivably come up more than once on the same game. Removing each ball as it’s chosen is what mathematicians call `sampling without replacement.’ To figure the chances of hitting two numbers, you multiply the two fractions together.”

“What two fractions?” queried she.

“Oh,” I answered. “Twenty chances out of eighty, that is, 20/80, times nineteen chances out of seventy-nine, that is 19/79. When you multiply 20/80 times 19/79 you get, let me see…” I pushed a few buttons on my calculator watch. “You get 0.0601265. If you take the inverse of that fraction, that is, divide it into 1, you get 16.631601. Subtract 1 from that, and you get the odds against hitting two out of two, or about 15.6 to 1. The ticket pays off at 11 to 1. For $1 you get $12. Now don’t confuse this with 12 *for* 1. Anyway, you’re playing quarter two-spot tickets. One time in 16.631601 you should catch both. When it does, you get back $3. During that time you spent 16.631601 times 25 cents, or $4.1578945, that is, approximately $4.16. The house profited by $1.16. Their edge is that $1.16 divided into the amount you spent, 1.1578945 divided by 4.1578945, which equals 0.2784809, or approximately 27.8%. That’s how much they keep out of each wager you make. On a quarter ticket, then, they keep 25 cents times 0.278, or about 7 cents. On four quarter tickets, which is what you’re playing on that ticket, they keep about 28 cents. Are you with me so far?”

“Yah,” she offered.

While we waited on the runway to take off, the head stewardess came on with announcements about safety equipment, demonstrated to us by the stewardess in our section.

**Eight-spot**

“Okay,” I added, “and on the eight-spot ticket the house edge is around 30%. That means that out of every dollar you wager, the house keeps about 30 cents. Now, you’re going to have to take my word for the rest of these figures. They’re something I wrote a program for a number of years back, and then analyzed a bunch of keno tickets. Of the 70 cents or so that you get back on eight-spot tickets, about 40 cents is in the form of catches of five and six numbers. About 30 cents is in the form of catches of seven or eight. In a typical keno session you won’t catch seven or eight. This means that you’re going to get back only about 40 cents for every dollar you wager. If you play the $2 eight-spot, you will get back about 80 cents for every dollar. That is, it will cost you $1.20 per game to play the ticket. But let’s say you add those deuces, that `insurance’ the keno writers are so hot for you to play. (Incidentally, most of them don’t understand anything of the math of the game. They truly believe that because every once in a while you pay for a ticket that it’s a good bet.) If you hit a deuce about once in three games, you’d break even on the proposition. In fact, though, you get one of your four deuces on the average about once every four games. That’s the house edge, not paying as much as the odds against an event. Most people can’t figure this, though, and don’t see it. They think, just as the keno writers and their friends tell them, `Yeah, it pays the freight now and then, so once in a while I get a free game.’ It’s just like the reasoning in pan on a `sucker’s pat.’ `If I put this down, it’ll pay the freight.’ Of course, if the pan hand shouldn’t be played, they lose money on the proposition. You lose by playing the deuce primarily because it doesn’t pay much. You don’t expect to be ahead thousands of dollars at the end of an evening by playing two-bit deuces, do you? It’s `insurance,’ remember, just pays the cost of a ticket now and then. In fact, what you expect is to be out 28 cents on every dollar you bet. Okay. Still with me?”

“Of course, Dollink,” murmured Aunt Sophie.

“Good,” I said. “So, without the deuces, you lose about $1.20 per game on the $2 ticket. With the deuces, you still lose that $1.20 per game on the eight-spot portion of the ticket, and another 28 cents on the deuces. That is, if you just play the straight eight, it costs you $1.20 per game; if you add the deuces, it costs about $1.48 per game. When you play keno, what you’re doing is just playing the minimum, killing a bit of time, maybe, hoping that lightning might strike, you might lucky, and maybe hit the big one. So better to cost yourself $1.20 per game than $1.48. If you look at it as five different tickets, then you’ll see that the only smart one—that is, if you *must* play keno—is the eight. I mean, would you sit around all evening just playing one or more two-spot tickets per game? Of course not; that would be stupid. So why play them when you’re also playing an eight-spot? Don’t believe that nonsense about `insurance.’ Just use your head, and give yourself a shot, at minimum investment, of winning a bundle.”

“But that would be so boring!” she exclaimed.

“Of course,” I agreed. “That’s why keno should not be your main game for the evening. Play at a casino that has pan. While you’re playing pan, play keno with a keno runner to pick up your tickets. That way you’ll have something fun to do until you hit your $50,000. And if you play pan the way I’ve been trying to show you, maybe you’ll get lucky and pay for your keno tickets.”