Category: Video Poker

Posted on by — 1 Comment

Betting in Opposition

Bob Dancer

Today’s article involves sports betting rather than video poker. It’s still “advantage gambling,” so I believe it’s a worthy topic for me to discuss, but I know some of my readers are not interested in any gambling other than video poker. If that describes you, perhaps you should skip this week’s article.

A friend of mine, “Pete,” recently attained Diamond status in the Caesars Rewards system. He now qualifies for a monthly $75 “free bet” (after betting $100 with “real money.”) Since I have Seven Stars status in the same system, I get a monthly $150 in free bets. I’ve mentioned this several times in my writings. Since Pete generally reads my articles, he was aware of this.

Pete wrote to me and asked if I was interested in “opposition betting” with him so as to minimize the risk.

I told him I wasn’t interested — for a lot of reasons.

He didn’t define “opposition betting,” but generally it means betting both sides of a proposition so as to reduce variance. And there are two bets we’re talking about here. The “qualifying” bet of $100 that must be made to qualify for the free bet, and the free bet itself.

Insofar as the free bet goes, you do not get your original bet back, so it’s most profitable to bet underdogs. Betting favorites on free bets is NEVER a good idea, so I’m going to assume he wasn’t talking about these.

So for the qualifying bet, $100 per month, let’s assume he’s interested in betting one side of a game and me betting the other. Let’s say we’re doing it in football. On a given week, say the Kansas City Chiefs were favored by three points over the San Diego Chargers. He’d bet KC, giving up three points, at 11/10 odds against him I’d bet SD, receiving three points, also at 11/10 against me. (Paying eleven to win ten is written as -110 in sports books.) Since we’re each betting $100, usually one of us would lose and the other would win $191 (round numbers) and would pay the other guy $45.50. This reduces variance. (We’ll ignore the case where the game ends with KC winning by exactly three points. It doesn’t affect the point I’m trying to make today.)

This bet costs him $5.50 to get a $75 (or in my case $150) free bet. The thing is, a bet chosen at random, without me on the other side, is also going to cost him about $5.50. What he’s getting is the certainty of the loss of $5.50 on this $100 bet versus the expectation of the loss of $5.50.

He’s making these bets monthly — indefinitely. Over time, the expectation will be pretty close to reality. 

I generally do not make -110 bets. I’m not a sports betting expert and have become convinced that betting when I’m a 2-to-1 favorite (odds -200 in sports-book-speak) is a smarter way to go on these qualifying bets. Opposition betting wouldn’t work so well on these bets.

Another reason I would not want to bet in opposition with Pete is Bonnie and I both have accounts at Caesars Sports Book. Since Bonnie and I are often in the same room with each other, and Pete lives 2,000 miles away, it would be far easier to opposition bet with Bonnie (if I wanted to, which I don’t) than it would be with Pete. 

The odds of KC minus three points might very well last all week — but it could also shift around quite a bit. If we wanted to guarantee our bets were in opposition, we’d need to do it at the same time. And when he’s ready, I might not be, and vice versa. One or both of us might not even be in a state where we have a Caesars Sportsbook account. Or we might be gambling at a casino with poor Internet connection. Or we might be in the middle of something else and not want to drop that “right now.”

And this rigamarole, to my mind, would be for no gain. I’m betting millions of dollars a month in video poker and slots where my decisions are based on expectation. Locking up a guaranteed loss of $5.50 over an expected loss of the same size strikes me as really pointless. 

Finally, to me, it appears that the reason Pete wants to bet in opposition is that he really hates to lose. A $100 loss to him is much more painful to him than it is to me. While he still bets as an AP, he’ll sometimes give up a bit of EV if it will increase his chances for a positive score. I’m looking for the highest EV I can get and I know that means I’ll have some losing sessions.

Pete is one of those APs who is relatively risk adverse. Seems strange for a successful gambler to be this way, but that’s the way he is.

Posted on by — 1 Comment

Helping a Friend

Bob Dancer

I received a phone call from a very good friend — who isn’t a video poker expert. He’s the kind of person I’m willing to help basically an unlimited amount for free. 

He asked about using the “user defined games” section of WinPoker to add Deuces Bonus Poker (DWB). He didn’t see any way to enter a game with wild cards using that feature.

“Well,” I told him, “You’re correct that you can’t enter such a game using user defined games, but fortunately the game is already included. If you’re looking for “Deuces Bonus” you won’t find it, but if you’re looking for “Bonus Deuces,” you will.” 

Sure enough, he found it easily, and was embarrassed he couldn’t find it before he called me.

I asked him if he could share where he found a playable DWB game. I knew he wouldn’t be playing for small stakes, and he wouldn’t be playing if he didn’t think he had the advantage. 

Sometimes players aren’t willing to share such information, figuring that more skilled players who know about a particular play will kill the game. Still, we do favors back and forth so maybe he’d share with me this time. (And maybe not. He’d still be my friend if he felt he couldn’t share this particular game.)

“It’s actually an Ultimate X (UX) game. I’m trying to run coin-in at a casino in case I can’t find enough slot plays there. It’s not a positive play by itself, but enough coin-in gets you good mailers. Playing that game exclusively would be too expensive of a way to earn the mailers, but if it only averaged 20% or so of your play (with the rest being slots), it would be a good filler.

“I know UX games are played differently than regular video poker,” he continued, “but I don’t know the DWB game at all and wanted to get a feeling for it.”

I told him he was going about it wrong. The strategy for UX DWB is much different from regular DWB — primarily because when you get a straight flush in UX DWB, you get a 12x multiplier on the next hand. So you play for straight flushes MUCH more often in the UX game than you do in the regular game.

I do not have a UX DWB strategy. If I felt I needed to play that game, I’d have to buy the strategy from somebody else — and I currently don’t have anyone I know who can make one — or use the VP PRO strategy analyzer on videopoker.com to figure it out. 

The VP PRO strategy analyzer requires a monthly or annual fee to use. It allows you to get correction on several games that WinPoker doesn’t — and one of those games is UX. 

You can play the game, get correction when you are wrong, and ask it the correct play for any hand with any “sum of multipliers (SOM).” It’s a lot of work to create a strategy using this tool, but it’s the best way to do it for those of us without access to advanced programming skills.

The difficulty with UX for any game is that the strategy changes for different SOMs. Consider the Triple Play version. Multipliers can range from 1x to 12x for each hand — meaning the SOM can range from 3x to 36x. There are hands you play the same for all SOM levels (like a dealt straight flush, for example) and there are hands that you play differently at low SOMs and high SOMs. 

To cover all possibilities, you need to create 30+ strategies. Which is not a trivial feat. Five Play SOMs range from 5x to 60x, so that means 50+ strategies. For Ten Play you need a different approach because VP PRO doesn’t cover that game. It’s far too complicated.

When I played UX, I used a simplified strategy for each game — created by someone who I’m not in touch with anymore. It was complicated, but manageable. I don’t play the game anymore because the games I have the strategy for (like 9/6 Double Double Bonus UX Ten Play) do not exist anywhere that I know about.

I’m not sure my message was welcome news to my friend, but it kept him from wasting his time practicing something that wasn’t going to do him any good.

Posted on by — 7 Comments

Further Look at Changing Strategy

Bob Dancer

A few weeks ago, I discussed a long-gone game where getting all 13 quads yielded a 500-coin bonus. In the article, a lady, “Joyce,” asked me about a situation where you just needed four kings to complete the cycle and you were dealt KK443 in 9/6 Bonus Poker Deluxe.

I said you should hold two pair — and Joyce said that whatever I said she was just going to hold the kings because it made more sense to her.

One of my readers, John, wanted a better clarification because holding the kings made sense to him as well.

Another reader, Mike, suggested he read the Wizard of Odds discussion of Power Quads — which describes a very similar situation. In that discussion, Michael Shackleford analyzed the game under a “use a constant strategy for the entire cycle” strategy — but suggested at the end that the return might be higher with strategy deviations — but the reader would have to figure out those adjustments for himself. If you’re going to be making adjustments, presumably, at the minimum, you’d hold the kings from KK443 if kings were the last quad you needed to get your bonus.

With a great deal of nervousness, I suggest Shackleford is wrong! I believe a constant strategy is best. 

By the time you see this, you can be sure that Shackleford has been forwarded the original article and my statement that I think his line in the Power Quads article is incorrect — and if he chooses to respond, I will publish here what he says. 

Shackleford is an extremely proficient mathematician, specializing in analyzing games, and my skills in this area pale in comparison. Comparatively speaking, I might be a smart high school student and he would be an award-winning college professor. Not in the same league at all!

I did reach out to Shackleford. He said he stands by what he wrote in his original article, and from the hand in question, he would just hold the kings. He went over the math of the value of holding the kings — for this one hand only — and the value of holding two pair — and holding the kings was clearly superior.

I’m not disputing that. But I’m looking at maximizing the value of getting all 13 quads, again and again, not getting kings once. I didn’t continue the discussion with Shackleford. He’s largely retired now from analyzing games and living in the state of Washington.

There was another promotion years ago that leads me to my belief that a single strategy might be best.

Perhaps 25-30 years ago, the Orleans casino in Las Vegas had a promotion where connecting on two royal flushes in the same denomination within a certain time period (perhaps it was one week — perhaps it was one month — I don’t remember) would lead to the second royal being paid double.

They had a dozen or so dollar Triple Play machines with a number of games on them including both 9/6 Jacks or Better (99.54% — royal cycle 40,391) and 10/7 Double Bonus Poker (100.17% — royal cycle 48,048). (Those were the days!)

At the time, Triple Play was relatively new and they didn’t have any version with more lines than three. Still, if you’re playing a promotion where you get paid double on the second royal within a given time period, playing the same pay schedule on Triple Play rather than single line is a no-brainer you had sufficient bankroll. Royals come about much more frequently on Triple Play than they do on single line games. I think I decided to play JoB because the royal cycle was shorter.

The question then became: What strategy should I use? Although there are many possible strategies, I decided to look at two.

  1. For the first royal, use regular 4,000-coin royal strategy. After I got that one, if I still had time to play, use an 8,000-coin royal strategy until I hit the second one.
  1. Use a 6,000-coin royal strategy and keep going until I hit two royals. 

I’m not going to reproduce my analysis here, but I remember it came out using the single 6,000-coin strategy until I hit two royals was more profitable than using the 4,000-coin strategy until I hit the first one and then use the 8,000-coin strategy. 

The differences between the two promotions are numerous. Still, I’m guessing (hoping, really) that the one strategy rule applies in both cases.

I still believe that the one strategy approach is better — even though Shackleford seems to believe otherwise. I have a ton of respect for him. But this time I think my approach is better.

Posted on by — 10 Comments

Annie’s Rule

Bob Dancer

A few weeks ago, I published a colorful chart (originally created by Jimmy Jazz) about how to hold the 4-card straight hands W567-WQJT in NSU Deuces Wild. The chart I created in Word didn’t translate to the program used for the column, but the information on the chart was correct.

Strangely, holding the 4-card straight every time is worth exactly $5 to the five-coin dollar player. Of the 47 possible draws, 9 give you your money back exactly, 19 give you a straight worth $10, and 19 give you five cards that do not return anything.

If you just hold the deuce, the hand is worth between about $4.97 and $5.03, depending on the rank and suit of the 47 remaining cards. 

A now-deceased friend of mine, Annie Fried (sometimes she used Annie Lefton, or Annie Fried Lefton), decided she didn’t like memorizing the rather complicated rules and always held the deuce in these hands. She justified this in numerous ways:

  1. The rule was complicated. Memorizing it used mental band with and was subject to errors. 
  2. Always holding the solitary deuce in these hands is much faster to play.
  3. It’s only worth a few pennies if it’s wrong.
  4. Sometimes she connects on a nice hand (say 5-of-a-kind, dirty royal, or four deuces), which are a lot more fun than just a straight.
  5. She inherited a lot of money, increased it through employment and shrewd investing, and was really gambling for entertainment — not profit. If her play reduced the total EV of the game from 99.728% down to 99.726%, what difference did that make to a multi-millionaire?

I understood her logic, but I always tried to play the strategy exactly correctly. I was using video poker for my livelihood, and my rule of thumb was to play as accurately as possible. 

There was a casino we played at where the best two games (for considerably higher stakes than dollars) were 8/5 Bonus Poker (99.16%) and 9/6 Double Double Bonus (98.98%). I played BP because it was higher EV. Annie played DDB because the bigger jackpots were more fun for her.

So far as I was concerned, the two decisions were consistent with each other. I was a “nit” looking for every little edge and Annie was looking for fun as she gambled. We understood the position of the other, talked about it some, but didn’t dwell on the subject repeatedly.

The reason I bring this up now, is that in the chat following my column on categorizing hands, a poster named Bradley Davis said he always held the deuce on these hands. His “reasons” were very close to some of Annie’s. He took some flack for presenting this opinion from somebody who didn’t understand the point he was making — welcome to my world!

Turns out I know Bradley Davis and we’re friends. Some 35 years ago he wrote a book called “Mastering Joker Wild Video Poker.” The strategies in the book were much more accurate than those published by other video poker writers of the day — most prominently Dan Paymar and Lenny Frome.

I met him in the mid-nineties at an Atlantic City function sponsored by Casino Player magazine. A bunch of gambling writers from around the country were invited to speak. It might have been my first teaching gig. At the time, I had three self-published booklets on video poker I was peddling for $10 apiece.

Davis used a laser pointer in his presentation. I had not seen one before, commented on it, and he gave his to me! We’ve kept in touch over the years and sometimes meet up when he comes to Vegas.

Anyway, while I continue to play as a nit, I’m not critical of those who play for fun. I don’t know Davis’s exact bankroll by any means, but I believe he’s a senior citizen with enough money to last him “for the duration.”

Posted on by — 15 Comments

You Need the Right Tools

Bob Dancer

I was playing $5 NSU at Harrah’s Cherokee sometime last year. A man I didn’t know, who said his name was Archie, sat down next to me and started playing the $1 version of deuces wild on the same bank of machines.

He was dealt WWQJ3, where the W indicates a wild card (i.e., a deuce) and the bold italics indicate that all the cards were suited with each other. He looked at me and asked if he should hold all five cards (a flush) or maybe throw away the 3 and go for the wild royal flush. I told him I didn’t know for sure. I had never played that game before.

“Anybody who plays $5 deuces wild can play $1 deuces wild,” was his reply.

“It has nothing to do with denomination,” I told him. “At this casino, the $1 deuces wild pays 100 coins for wild royals and 60 coins for 5-of-a-kinds. The $5 deuces wild pays 125 coins and 80 coins for those same two pay schedule categories. The $1 version is more than 2% tighter and many hands are played differently between the two games. 

“The return on 5-of-a-kind isn’t a factor on this hand, but the return on the wild royal definitely is. 

“I’d need to study the $1 game to know how to play each hand,” I continued, “and since the game pays so little, I know I’m never going to play it in a casino. Why should I bother to study a game I’m not going to play?”

“But I don’t know how to play this hand,” Archie continued.

“Not my problem,” I told him. “I’m here to play my own game. I didn’t come to the casino today to help you play a terrible game.”

Five minutes later, he asked me about another hand. And then another a few minutes after that. After telling him twice more that I wasn’t there to help him, I didn’t even acknowledge his further questions. I cashed out and went to play on the opposite side of the bank of machines. If he followed, there were other $5 NSU machines elsewhere in the casino.

Later that day, Archie came back near me, but this time he had a couple of buddies with him. One of them had obtained a deuces wild strategy card and they were using that card to tell them how to play the hands. This was fine with me. They were not asking for my assistance.

The thing was, the deuces wild strategy card they were using must have been for a game called full pay deuces wild. This is a game where the pay schedule categories, from wild royals to flushes, pay 25, 15, 9, 5, 3, and 2. The machine they were on paid 20, 12, 10, 4, 4, and 3 for the same pay schedule categories. Nothing matched up! I’m guessing more than 20% of the hands were played differently between the two games. I didn’t actually see the card they were using. It might have been one they bought from me!

In addition, they had trouble figuring out how to read the card. The right number of gaps with straight flush draws takes some time to get correctly. These guys were trying to figure it out on the fly — and their results were predictable.

Using the wrong strategy card turned a 97.6% game into one that might have paid 96%, although this was probably better than not having the card and guessing all of the time. Plus using the card for every hand slowed them down so they weren’t playing many hands — which meant they weren’t losing quite so fast.

I didn’t say a thing to them. I could have told them they were using the wrong card, but from earlier experience with Archie I believed that saying anything would give him permission to start asking a lot of questions again. And I didn’t want that.

I don’t know how much they lost — but it’s certain that they did lose. Even with good pay schedules of deuces wild played well, if you don’t hit four deuces or a royal today, you’re going to have a losing session. And with only 100 coins for a wild royal and 60 coins for 5-of-a-kind, your score is going to be even worse. A royal would have locked the machine up and these guys would have whooped and hollered if they connected on four deuces. They didn’t.

The lessons were clear — at least to me. Play better games, use the correct strategy, and practice before you get to the casino. Still, if they guys were once-every-two-years players, and the money lost was small change for them, perhaps they went about it the right way. Studying might have ruined the fun for them, and studying makes more sense if you’re a more frequent player.

Posted on by — 6 Comments

I Didn’t Mean to Upset Him

Bob Dancer

Years ago, Sam’s Town in Las Vegas had one $5 8/5 Bonus Poker progressive machine slightly to the right of the cashier on the main floor. On Thursdays they had a “Young at Heart” day where seniors would get benefits. I don’t remember what all was involved. Maybe a point multiplier and half-price meals, but I’m sure there was a senior drawing in the afternoon where your play on that day earned you drawing tickets. Ten seniors earned $500 apiece in the drawing.

Playing on a $5 machine for two or three hours usually meant I would be called in the drawing. The vast majority of seniors played for smaller stakes — including quarter Full Pay Deuces Wild — and few seniors earned nearly as many drawing tickets as I did. On occasion, one of the other seniors would come up to me and tell me in no uncertain terms that it was unfair of me to play the $5 machine on Thursdays. “The rest of us can’t compete with that. Go back to the Strip where you belong!” 

I didn’t argue with these players. I just listened to what they had to say. I understood the point, and there was the possibility that these same complainers would talk to casino management about my “unfair” presence. Since I was a winning player there, enough complaints and the casino might be motivated to “fix the problem” by removing the machine or removing my welcome. Neither of these solutions appealed to me. So, whenever I was drawn, I would skip playing for the next week or two. There’s a big difference between winning semi-regularly and winning all the time.

But it wasn’t these players who led to the title of today’s blog.

Next to the $5 8/5 Bonus Poker progressive machine was a $5 8/5 Double Double Bonus machine. Many times when I was playing on Thursdays, the same guy was playing the DDB machine. This is a 96.8% game when played well — which this guy didn’t. How much he ended up losing, I don’t know, but it must have been a lot. He was always glum — and totally untalkative. His silence may have been due to the fact that he was losing — or he might have just been a quiet guy.

One day I ended up hitting AAAA4 on my machine. On my machine, where kickers don’t matter, it was worth $2,000. On his machine, it would have been worth $10,000. I was pleased with the result, of course, but gloating would have been insensitive. He was probably losing that day and “needed” such a hand to catch up. 

He groaned audibly. Seeing the hand he needed on the machine next door doesn’t affect the odds on his machine, of course, but he seemed devastated. He probably figured that my hand had “used up” the aces with a kicker quota for the day because he cashed out and left the machine, and probably left the casino, before I was even paid. Usually he stayed for the drawing — where he was called with regularity but $500 didn’t come close to what earning the tickets cost him. 

He skipped the drawing that day, I think. At least, I didn’t see him. He must have been pretty upset. As was often the case when I played there. I got called that week at the drawing. I got enough evil eyes from some of the quarter players — but none from my fellow $5 player who wasn’t around.

Although I was glad I hit four aces — with or without a meaningless-to-me kicker — I didn’t draw that hand on purpose. As if I could. If I had the power to make aces with a kicker show up on my machine whenever I wanted, I assure you I’d be playing a different game for much higher stakes. But I can’t. Nor can any of us.

When I saw him again three weeks later, we were both playing our usual games. We didn’t discuss what happened “last time.” Or anything else for that matter. He was just his normal sullen self while I quietly played to earn drawing tickets.

Posted on by — 4 Comments

Bobby Vegas — So I Like Numbers

Bobby Vegas: Friends Don’t Let Friends Play Triple-Zero Roulette

Trigger warning: about to toot my own horn.

And a caveat. I screw up. I make mistakes. I’ve gone bankrupt once, been broke twice. I’m not now. What’s important is not the mistakes, it’s the lessons learned.

Paying for groceries, I’m adding the numbers upside down using my own approximation technique faster than checkout employee can scan. I say, “That’s … $39.60 … or thereabouts.” When the total comes to $39.69, the checkout girl looks at me like I’m from Mars. “How’d you do that?!”

I shrug. “I like numbers.”

My ex and I loved going on bookstore dates. She read autobiographies. Me? Math history, Feynman, Edward Thorp, maybe brush up on some probability theory. She just shook her head.

In business tech specs, efficiency ratios, wholesale volume discounts, I easily stated, “That’ll save you 20% or $2,300 a month and the ROI is 19 months.” Again: “How’d you do that?” For me, the numbers are just … there. Multiplication, division, percentages, they’re all just OBVIOUS, in some cases instantaneous.

When I became obsessed with roulette, spending 18 months in the NC State fifth-floor math library absorbing everything on nonlinear dynamics, recurrence and chaos theory, I just loved it. The daily lean into the right headspace often took 30 minutes, but it felt so good! Was it weird, composing a 45-page heuristic paper on Nonlinear Dynamic Short-Term Recurrence Theory applied to roulette, when I barely made it out of high school alive?

Every time I searched out someone to talk with, like folks working on weather prediction, they got real uncomfortable. “I have a Master’s and you left me behind 20 minutes ago.”

When I found my people, like Laurence Scott (roulette prediction) and Chuck Webber (recurrence theory), I was finally no longer the fishnerd looking for water. But it’s okay. Ask me about applying the birthday paradox to double wheel roulette and see me light up.

I like math. It’s clean, clear, concise. I like video poker for those reasons. I find the decision tree very relaxing. It massages my brain.

But when faced with craps, I freeze up. Too many chaotic variables, like the yahoo rolling, for starters. Craps is a good game; I’m just not made for that particular decision tree. Card counters are memory geeks, too. But again, I’m just not wired up for live action. I’m way too transparent to have to bluff and lie.

I believe my most valuable skill is recognizing opportunity before others, way before. Like energy-efficient lighting in the ’80s, LEDs in the ’90s, or specific Vegas-value plays. And applying them in creative ways.

When Mrs. Luttenton, my seventh-grade advanced math teacher, crammed trigonometry down our throats, we hated her. She was mean, demanding, and ugly. Apologies Mrs Luttenton, wherever you are. But thank you for being such a math drill sergeant.

And kids? Put away the phone and think.

Yes, I find math relaxing.

So sue me.

Posted on by — 9 Comments

Do You Change the Strategy?

Bob Dancer

The promotion I’m going to talk about today happened several years ago and I may be off on some of the details. For the sake of this column, assume the details are as I present them. The purpose of this column is to explain how to evaluate and play a promotion that might come up in the future, rather than describe exactly one that has come and gone a while back.

The promotion was at a casino in California, and the best game for dollars at this casino was 9/6 Bonus Poker Deluxe (although many players played Double Double Bonus or some other game.) The BPD game is like Jacks or Better, except all quads pay 400 and two pair just gives you your money back. This game returns 99.64%, the slot club paid 0.25%, and there were mailers of $200 four times a month (almost weekly, but not quite) if you played at least $300,000 coin-in over the previous three months. Players who played this much also received free rooms and meals. On occasion there were other promotions as well — in addition to multiple other casinos relatively nearby.

  If the player played exactly $100,000 in a month, the mailers were worth 0.8%. If you played twice that much, the mailers were worth 0.4%.

The promotion required you to get all 13 quads, and when you did, you received an extra $500. And then you could immediately start on your next 13 quads. To find out how much this is worth percentage-wise requires a bit of calculation. As a first approximation, I’m going to assume all quads are equally likely to occur — at a rate of one quad per 428 hands. Using this approximation, let’s see how many hands it takes to get each of the 13 quads.

I used Excel. I figured it would take 428 hands to get the first quad. The second one would be 428*13/12 = 464 because only 12 of the ranks would count towards getting all 13. The third one would be 428*13/11 = 506 because now there are only 11 “new” quads. When we get down to the 13th quad, the formula becomes 428*13/1 = 5,464 — which is how many hands on average it’s going to take to get the last one. We add these all up and we get 17,694 hands. If this takes you 20 hours, this is a $25 per hour addition to an already positive game ($500/20 hours = $25 per hour).

  At $5 per hand, 17,694 hands will cost you $88,470 coin-in during which time you should have hit 41 quads (most of which duplicated a quad you have already claimed). Since 41 quads are worth an extra $500, this means that each quad, on average is worth 400 + 500/41 = $412 (approximately). Putting this into WinPoker or some other video poker program will tell you the game is worth 100.2% — plus the slot club, plus the mailers, plus whatever other promos they decided to run at the same time. You can figure it out more precisely, if you like, but this was close enough for me to understand what was going on.

This was a nice promotion. It takes 5+ hours each way to drive there from Las Vegas. I was told about it at the time and decided I didn’t want to drive that far at least twice a month. It might be worth more than $30 per hour when I’m there, but it kills more than ten hours round trip each time I go and there are car expenses to consider.

One lady, “Joyce,” who regularly made the trip posed the following question to me: Let’s say I had all of the quads completed except kings. I was dealt KK443. How do I play the hand?

In normal 9/6 BPD, the correct play is to hold both pairs. In the way Joyce set up the problem, when you collect four kings, you get $900 instead of the normal $400. If you always collected $900 instead of $400 for a quad, the correct play would be just to hold the kings. So, this time, what do I do? A group of friends were there, including “Dave,” who is probably more knowledgeable about video poker than I am. He traveled from Las Vegas to Southern California because he was no longer welcome as a player in most-or-all Las Vegas casinos.

Before I reveal my answer, what would you do? Would you just hold the kings, or would you hold both pairs?

I told her that I would hold both pairs. And from KKK44, I’d hold all five cards.

“Yes!” exclaimed Dave. “That’s what I told you! Now that he tells you the same thing, Joyce, how will you play that hand?” 

“I’ll just hold the kings, whether from two pair or full house. Whatever you two so-called experts say, holding the kings makes more sense to me.”

It’s a $0.72 error to try for the kings from two pair (where you have about a 1/360 chance to connect) and more than $11 when you hold KKK rather than a full house (where you have 2/47 chances to connect). The 100.20% figure assumes you are going to use the same strategy all the way through. 

Joyce seems to be confusing getting the 13 quads more quickly rather than making the most money.

It was a lucrative enough promotion that Joyce was still a favorite even with these “misplays” (depending on how well she played the rest of the hands). But it was a more lucrative play for Dave, who didn’t make these unforced errors.

Posted on by — 9 Comments

Categorizing Hands

Bob Dancer

A friend and I were discussing 4-card straights with one deuce in NSU. The ones that are ever held are in the range of W567 – WTJQ. Each of the six possible ranges (i.e., W567, W678, W789, W89T, W9TJ, WTJQ) have different rules on which fifth cards require you to hold the deuce by itself, and which ones require you to hold the straight. Usually just the rank of the fifth card matters, but there are two separate cases where it matters whether that fifth card is suited with one of the other cards in the hand.

As an example, with W567, if the fifth card is an A, K, or Q, you hold the bare deuce. If it’s a J or a T, you hold W567. If it’s a 9, 8, 4, 3, you hold the 5-card straight. If it’s a 5, 6, or 7, you hold the 3-of-a-kind. And if it’s another deuce, you simply hold both deuces and discard the other three cards.

The exact rules for these hands are found in the Dancer/Daily NSU strategy card and Winner’s Guide. I’m not planning on going over all of the rules today — but the chart at the bottom, courtesy of Jimmy Jazz, covers the subject well.

My friend asked me how I practiced these hands using WinPoker. 

I use the fixed card feature in the advanced hand section. I put the program in “Show” mode, so I’m just hitting the enter button and it’s either dealing me five new cards or telling me how to play the cards that were previously dealt. I key in, perhaps, 2♠ 5♠ 6♦ 7♣ and let the computer randomly select the fifth card for me. While I’m going to be dealt lots of 3-of-a-kinds and 5-card straights, I’m going to get several where the fifth card is a T, J, Q, K, or A — and in this last set of cards, it won’t take me long to notice that when the fifth card is a T or J, the computer holds the W567, and when the fifth card is an A, K, or Q, the computer just holds the deuce.

Once I have these mastered, I change the 5♠ to perhaps an 8♥ and continue. This time I’m practicing W678 hands.

My friend nodded and said his brain didn’t work that way. In his mind, he saw 2♠ 5♠ 6♦ 7♣ K♠ as unique in terms of the suits of all the cards and the position all the cards were in. 

I was flabbergasted! Letting the deuce and the king be any suit, and the 5, 6, and 7 be different suits from one another (but possibly the same suit as the deuce and/or the king), we have 384 different combinations of these five cards. And since there are 120 different ways for these five cards to be displayed in the five positions, this means 46,080 permutations for ways to display this “one” hand. If my friend had to learn each of these 46,080 hands separately (instead of just once), then video poker is a much more difficult game for him than it is for me!

And further, I group W567 where the last card is an A, K, or Q as one thing to remember. Perhaps my friend has to remember all 138,240 permutations separately! I can’t believe this is the case for him — because, after all, W567 hands are only one of many hands to master. Of the 2.6 million possible hands (2,598,960, actually), that number doesn’t include the 120 different ways each of these hands can be displayed. Surely, he doesn’t attempt the task of memorizing what to do on each of the 311,875,200 cases for every 52-card game.

My advice to him was to learn to categorize. That combination is a 3-card royal, for example, and that one is a 4-card straight flush. In NSU, 3-card royals are all treated the same as each other — but that isn’t the case for many other games. Similarly, a consecutive 4-card straight flush is played the same as a 4-card straight flush with one gap, but that’s not always the case in other games. 

If all 4-card flushes are treated the same as each other in a particular game, that’s the way I learn them. If a 4-card flush with one high card is played differently than a 4-card flush with two high cards in another game (such as 9-7 Double Bonus), that’s the way I categorize them when I’m playing that game.

I only concentrate on penalty cards when they matter. In 9-6 Double Double Bonus, for example, KQJK9 is played differently than KQJKT, so when I’m playing that game, I pay attention to straight penalties to KQJ, but not to KQT, where they don’t matter strategically.

For each game, I’m trying to learn the fewest number of things I can that will let me play the game perfectly. If you want to know which categories I recommend, they are simply the ones used on the Dancer/Daily strategy cards and Winner’s Guides. 

Will this work for you? I’m not sure. It depends on the way your brain works. I’ve trained my brain to work efficiently at playing video poker well. Or perhaps I was born with a brain that allows me to play video poker well. Probably some sort of combination between the two. But whatever the type of brain you have going in, I’m confident that it can be trained to work better at individual tasks. And if playing video poker well is a task at which you wish to do well, then I’m pretty sure you can get better than you are now.

I know I can get better. Which is why, after being a player for more than 30 years, I still study before I make a major play.

I was discussing this article with Jimmy Jazz, and he showed me a chart he made when he was first studying 4-card straights with one deuce in this game. While the information in the chart is exactly the same as is found in the Dancer/Daily strategy card and Winners Guide for this game, the chart is prepared well. Possibly some of my readers will find Jimmy’s presentation easier to understand. So, I asked for permission to show this chart to you, and Jimmy graciously consented.

ST4 with one deuce in NSU

Each of the six rows represent individual hands.

Key:
Gray: unsuited cards dealt with one deuce

Light Blue: If this is fifth card, hold all five cards

Brownish/Orange: If this is fifth card, hold ST4

Yellow: If this is fifth card, hold deuce by itself

Violet: If this card is suited with one of the cards in gray boxes, hold deuce by itself. If this card is unsuited with the cards in gray box, hold deuce by itself

Gray – 3 cards dealt in addition to deuce

Orange –  ST4 is this is 5th card

Yellow – Deuce only if this is 5th card

Blue – Hold straight if this is 5th card

Purple – if 5th card is unsuited w/other 3 ST4, else deuce

Posted on by — 3 Comments

Reducing the Variance

Bob Dancer

Last week I wrote that I played ten-coin $5 9/7 Double Bonus Good Times Pay for a promotion at Caesars Atlantic City. This is a relatively rare game with multipliers, and if you’re not familiar with how the multipliers work you might want to read (or re-read) last week’s article before you tackle this one.

Over the first four days of play, including the play-up bonuses I received for every $150,000 worth of coin-in and the weekly free play for the week that ended Saturday and also for the week that began Sunday, I was ahead about $25,000 for the trip. This figure includes the 0.08% I earned in Next Day Bounceback. It’s not a large percentage, but I had played almost $1 million in coin-in so far and it adds up. The figure doesn’t include the Reward Credits I had earned (which I will redeem at Caesars Sportsbook) or the value of the Tier Credits (including one day with a 5x multiplier).

I had hit four aces three times (with 1x, 2x, 3x multipliers for $4,000, $8,000, and $12,000 respectively), lots of quad 2s-4s, many with multipliers of 4x and higher, and six quad 5s-Ks with multipliers of 5x ($6,250), 6x ($7,500), or 7x ($8,750) — along with a slew of these lesser quads with lesser multipliers. I failed to hit a royal flush, with or without a multiplier. While not unexpected with the 20,000 hands I had played, a royal flush would have been welcome! Suffice it to say, I was enjoying this trip to Atlantic City — other than the fact that there was a blizzard going on outside and I had to stay an extra day and a half more than I originally planned. 

For my last day, I had $140,000 remaining to play to pick up Bonnie’s and my last two play-up bonuses — requiring perhaps four hours of play on the $50-per-hand game. On earlier trips I had sometimes lost a considerable amount on these same machines. I could play five coins per game, for $25 per hand, on the same machine, forgoing the multipliers and requiring eight hours of play. This had no effect on the 99.1% expected return on the game, but it greatly lowered the variance.

I decided to play the extra hours at the lower variance as a sort of money-management gambit. I had a very nice score going this trip and I wanted to “take it home.” I could have skipped playing the last day at all, guaranteeing I would take the money home, but I believed the extra play was an intelligent risk to take. Playing for the last bonuses on my card and Bonnie’s had an EV of more than $1,000 and I didn’t want to pass that up. So long as I was going to be at the casino anyway, it made sense to play.

At $25 per hand, you get “jackpots” of quads, straight flushes, or (I wish) royal flushes every 400 hands or so — meaning every $10,000 in coin-in. I put the word jackpot in quotation marks because quad 5s-Ks return “only” $1,250, which is lower than the W2-G threshold that has been in effect since January 1. In the $50-per-hand game, half the time these quads would be accompanied by a multiplier of 2x or larger, triggering a W2-G, but in the $25-per-hand game there are no multipliers. 

As a first approximation, the average of 14 “jackpots” would consist of no royal flush, one straight flush, and one quad in each of the 13 ranks. To be sure, it wouldn’t be impossible to connect on a royal flush, and straight flushes are about half as likely as any individual quad. Aces come about more frequently than other quads because from AA332, you just hold the aces, but from hands like KK447, it’s correct to hold KK44. Additionally, to it is proper to hold a single ace more often than any other specific high card. Quad jacks, queens, and kings come about more frequently than the remaining ranks because you’ll hold a single high card but not a single low card. Also, a pair of these high cards is more valuable than most 4-card flushes and all 4-card open-ended straights, but 22-TT are less valuable than any of these 4-card combinations. Finally, quad 22s-44s are each slightly more likely than quad 5s-Ts because when the same hand contains a suited QJ9 or JT9, you hold a pair of 2s-4s but not 5s-Ts.

That’s a lot of caveats, but as a first approximation, hitting no royal flush, one straight flush, and one each of the quads is about what figures to happen. 

Unfortunately, I ran very badly. While I did receive one straight flush and no royal flush just like my first approximation predicted, the quads were woefully short. I didn’t hit aces at all. I hit one quad (instead of three) in the 2-4 range, and four quads (instead of nine) in the 55-KK range. Even after collecting my bonuses and the NDB from the day before, I ended up losing about $17,500 on the day instead of winning the $1,000 my prediction said I “should” have won. No fun at all.

It’s tempting to conclude that my strategy of playing $25 per hand and forgoing the multipliers instead of $50 per hand was a failure. After all, sustaining a loss of the size I did can hardly be called a success.

I disagree with this conclusion — and the entire reason for this article is to explain why I believe my strategy worked well.

Had I played $50 per hand, there would only have been half as many hands played. Earning quads at the same rate as I actually did, I would have received three “jackpots” instead of six. While we will never know what the multipliers would have been on these three “jackpots,” an average of 2x would have resulted in a loss of at least $10,000 more than I actually had. 

That means my strategy was actually a success — even though a very expensive one. You have to make your decisions before you know the results — and live with those decisions. Just because the decision turned out badly this particular time doesn’t mean the decision itself was a mistake.

This is a concept many people just don’t get. Some people “learn” how to think by watching football and listening to the commentators. Football commentators, for example, often proclaim running the ball out of the end zone on a kickoff is a mistake if a kickoff is only returned to the 18-yard line rather than starting out at the 20- or 25-yard line that would have resulted from catching the ball in the end zone and staying there. That’s an easy comment to make — and wrong. The kick returner doesn’t know the result of his run before he runs. He needs to make his decision based on his read of what he sees is happening and what strategy his team is planning to use this particular time.

Running out of the end zone in a particular situation may or may not have been a mistake based on the information available to the decision maker before the run took place. Coaches can help kick returners make better decisions based on the hang time of the ball and other factors. But using where the receiver ended up being tackled as the sole criteria of whether it was a mistake or not is a foolish way to judge things. And it gives the kick returner no ability to make better decisions in the future.

However many of you criticize me for my decision to play $25 a hand rather than $50, I’m convinced it was the correct decision. To my detractors, I suggest you’re watching too much football on television and believing what the commentators say!