Category: Advice for Players

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Understanding a Flow Chart in Super Double Bonus

Super Double Bonus is a version of Double Bonus where four jacks, queens, and kings earn 600 coins instead of 250 and the straight flush returns 400 instead of 250. The best-paying version, which returns 45 for the full house and 25 for the flush, returns 99.695% when played well. When combined with a decent slot club and/or set of promotions, this can be a profitable game to play when you find it.

One of the trickiest parts of the strategy is when you are dealt an ace of one suit and a “JT” of another. Depending on the other two cards, sometimes you hold the “JT”, sometimes you hold the ace by itself, and sometimes you hold AJ.

For me to learn this, I created a flow chart which I believe is 100% accurate in this area of the strategy chart — although it presumes you know that a 4-card open-ended straight and a 3-card straight flush with one high card and two insides are both more valuable than the options presented in the flow chart. It follows relatively simple logic — but even relatively simple logic requires more concentration and study than some of my readers wish to endure.

What I thought I’d do is to present my flow chart, give you some sample hands to play, and let you see how you do. Afterwards, I’ll go through the flow chart more slowly and maybe it will be easier to understand.

And if you’re not in the mood for the logic of 9-5 SDB, it’s okay with me if you always play “JT” when you come to these hands. You won’t be giving up a whole lot. For some folks, making these kinds of distinctions cause their heads to hurt. If that’s you, take this column off and come back next week.

A versus “JT”:

 

Is there a flush penalty to the “JT”?

If no, play “JT”  — end

If yes, continue

 

Is the flush penalty to the “JT” a 2-6 and the fifth card suited with the A?

If yes, is it an 8 or 9?

If yes, play AJ — end

If no, play “JT” — end

If no, continue

 

Is the flush penalty to the ”JT” a 2-5 and the fifth card an 8 or 9?

If yes, play A — end

If no, play “JT” — end

 

Is the flush penalty to the ”JT” a 6 and the fifth card a 7, 8 or 9?

If yes, play A — end

If no, play “JT” — end

 

Using the above logic, play these hands:

  1. A♠ J♥ T♥ 2♠ 5♠
  2. A♠ J♥ T♥ 9♠ 7♦
  3. A♠ J♥ T♥ 9♠ 8♥
  4. A♠ J♥ T♥ 3♣ 7♥
  5. A♠ J♥ T♥ 9♣ 5♥
  6. A♠ J♥ T♥ 7♣ 6♥
  7. A♠ J♥ T♥ 7♣ 5♥
  8. A♠ J♥ T♥ 8♣ 2♥
  9. A♠ J♥ T♥ 8♠ 2♥
  10. A♠ J♥ T♥ 7♠ 6♥

Here are the answers. If you easily got them all correct, you don’t need to read any further:

  1. A♠ 2♠ 5♠
  2. J♥ T♥
  3. J♥ T♥ 9♠ 8♥
  4. J♥ T♥ 7♥
  5. A♠
  6. A♠
  7. J♥ T♥
  8. A♠
  9. A♠ J♥
  10. J♥ T♥

If you missed one or more of the above problems, the following explanations may help:

 

Is there a flush penalty to the “JT”?

If no, play “JT”  — end

If yes, continue

This rule is the easiest. Just look for a card suited with the “JT”. If you don’t find one, then “JT” is the play — unless, of course, some higher-ranking combination is in the hand.

 

Is the flush penalty to the “JT” a 2-6 and the fifth card suited with the A?

If yes, is it an 8 or 9?

If yes, play AJ — end

If no, play “JT” — end

If no, continue

We only get to this rule if there is a flush penalty to the “JT” and also a flush penalty to the A. Also, this is the only time we can hold AJ.  Notice that the flush penalty to the J cannot be a 7 or higher as that would make it a higher-ranking 3-card straight flush or 3-card royal flush. Also note that this says that if there is a flush penalty to the A, but it is not an 8 or 9, we hold the “JT”.

 

Is the flush penalty to the ”JT” a 2-5 and the fifth card an 8 or 9?

If yes, play A — end

If no, play “JT” — end

By the time we get here, there is no flush penalty to the ace.

 

Is the flush penalty to the ”JT” a 6 and the fifth card a 7, 8 or 9?

If yes, play A — end

If no, play “JT” — end

By the time we get here, there is no flush penalty to the ace. The only difference in the last two rules is when the fifth card is a 7. If the flush penalty to the J is a 6 (meaning it is not a straight penalty to the A), we hold the A by itself. If the flush penalty to the J is a 2-5 (which are all straight penalties to the A), we hold the J.

 

Do the notes in green help you any? If so, welcome to them.

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Be Careful What You Wish For  

Say you’re playing 9/6 Jacks or Better and are dealt a hand like A♦ K♣ J♦ T♦ 3♦. The best play, of course, is AJT3. Many players hold the inferior AJT. As I see it, players make the lesser play for one of two reasons:

  1. They simply do not know that AJT3 is worth 3.7¢ more than AJT for the 5-coin dollar player — given that the fifth card dealt was an off-suit king. Holding the flush kicker is a rather advanced play and many players aren’t students of the game. Or maybe they go back and forth between games without understanding the differences between them and make more-or-less the same plays for all games.

 

  1. They know AJT3 is better and they just don’t care. They really love to get royals and 3.7¢ isn’t that big of a cost for a chance to get such an exciting hand.

 

Today I want to address that second group of players, namely the ones who are willing to pay an extra premium in order to get the royal flush. My position is that for most players, this is a costlier move than they realize.

When I spoke of that 3.7¢ difference in value between the two plays, the math included a 1-in-1,081 chance of getting a $4,000 royal flush. The trouble is that the $4,000 royal flush for most people isn’t worth $4,000.

First of all, there’s tipping. When they bring you your money, they usually provide you with 39 $100 bills and five twenties. You’re not required to tip, but many players give away one or more of their twenties to the casino staff. If you’re generous enough to give away all five twenties, you have increased the difference between holding AJT and AJT3 from 3.7¢ to 12.9¢. If you got the best hand available holding AJT3, namely a $30 flush, no casino employee would be there holding his/her hand out expecting a share of it.

Second, and far more importantly, there’s a W2G that comes along with that $4,000. If you’re playing in Mississippi, the state takes away $120 — with no chance of getting it back. Louisiana takes $240, and you can get some or all of that back by filing a Louisiana state income tax form. If you fill out the form yourself, it takes an hour or more and you may not do it correctly. If you hire a tax professional to do it, it can cost more than the $240 you’re hoping to get back. There are a few other states with similar policies. If you shrug off that extra $240 every 1-in-1081 times it occurs when you draw two cards to AJT, that increases the difference in EV between the two plays by an extra 22.2¢.

Possibly different from the state where you’re playing, the state where you reside has tax rules too. Some states let you deduct your gambling losses from your gambling winnings. Some don’t. Some states have a state income tax on gambling winnings. Some don’t. Professional gamblers have different rules than non-professionals. If you itemize your W2Gs, it reduces other benefits you can claim.

I’m not a tax expert by any means, but I can safely say that there are significant costs to getting a $4,000 royal flush for many players.

The third reason royal flushes can be “bad news” is that casinos get excited if you get too many of them. Not so much for $4,000 royals perhaps, but if you play for larger stakes, $20,000 or higher royal flushes end up with you being discussed by casino management. Although exactly how many royals you hit is largely luck, being lucky can get you kicked out. Nobody has everbbeen kicked out for hitting too many flushes.

If players correctly understood the factors discussed today, even on a hand like A♣ 6♥ J♣ T♣ 3♣, where AJT is superior to AJT3 by 5.1¢, these players would intentionally and intelligently go for the flush — simply because ending up with the royal has so many additional costs.

(I understand that the two hands presented today look virtually the same to many players and they cannot see why the correct play is different. That’s a discussion for another day.)

Playing for quarters or less makes you immune from these considerations at most casinos. Some casinos, however, do make a $1,000 jackpot a hand-pay situation. If that’s the case where you play, some of your immunity disappears.

Taking slightly the worst of it to go for a jackpot that creates a financial burden strikes me as similar to paying money to buy heroin. Heroin ends up destroying an individual and to pay money to do this boggles the mind. Most healthy people are disciplined enough to stay away from heroin. Few gamblers are disciplined enough to be willing to pay a small premium in order to stay away from royal flushes.

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How Important is Having Fun?

I like my life. And my life includes (currently) maybe 40 hours a month playing video poker. In the good old days, there were long periods where I averaged 200+ hours of video poker each month.

That said, while video poker is not unpleasant at all to me, I do not do it because it’s fun. I do not consider it a hobby. I consider it a profession. It’s how I support myself and family.

There are many things I put up with:  sore back after long hours, sometimes smoky environments (although I’ve cut out playing at casinos where this is really bad, no matter how high the EV), distance in time and energy to get there, security issues, needing to be present according to “their schedule” rather than mine in order to get the right play, forced interactions with certain people with whom I’d rather not interact, my wife insisting I pick up the latest “casino crap” even though we have absolutely no use for whatever it is, eating at restaurants because they are “free” rather than because we enjoy them, etc.

I put up with these things because, overall, the profession is lucrative and the lifestyle it provides is pleasant. But my idea of “fun” would not include these things.

I call my writing career interesting. I call my radio career fun. I call the “big fish in a small pond” aspect to my life usually enjoyable (although it does make me a target for many). We enjoy cruising. We enjoy dancing at fancy dinner parties. We take advantage of going to shows. Some casino locations (Lake Tahoe, New Orleans, and Cherokee come to mind) are a lot of fun to visit after I’ve done my playing in the casino. At times, we have access to better restaurants than we would frequent if we had to pay retail. These goodies are a direct benefit from playing video poker.

Hosts and other casino employees are trained to say, “It’s not whether you win or lose but rather whether or not you have fun,” and it makes sense for them to be doing this. Most players are not successful at the game and if the casinos can convince players that gambling is fun and losing is all right, then the casinos will prosper more.

Many people buy the slogan in the preceding paragraph, and it actually makes sense that they do. People need to justify to themselves that what they spend their time and money on is “okay.” So, they convince themselves that playing is fun. And if that’s the way it is for you, that’s fine.

When I lived in a location without machines, I moved to Las Vegas. There are some casino locations where there isn’t anything playable if your choice is between playing and winning or not playing. (There are not nearly as many of these locations as people believe. There are MANY ways to win in a casino if you have the skills and do the scouting.) But if I couldn’t find games to beat, I simply wouldn’t go into a casino.

On cruise ships, I “never” visit the casino. (Well, there have been promotions where I got $100 in cash or $125 in slot machine play if I ran it through once, so I took the slot play and ran it through once on 7-5 Bonus or worse. But after I played the minimum to qualify for the bonus, I was out of there.)

I’m in casinos looking for profit, not fun. I see gambling as a means to support myself. I understand the swings, and I certainly don’t win every time (or even every year), but if the overall result over a period of three or four years is negative, I’ll quit. I’ll do something else. It just makes no sense for me to throw good money after bad.

Even though I don’t go to a casino specifically because it’s fun, while I’m there I try to enjoy myself. I joke or chat with friends and casino employees. I look to find humor and pleasantness in the things I’m doing — whether it is in the casino or not.

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What Should I Say?

There was a news story recently that 11 years ago, a college professor had told Julian Edelman (currently a New England Patriot wide receiver with two Super Bowl rings) that his goal of playing football professional was unrealistic and he should try something else. The teacher recently sent Edelman an apology for doubting his passion — Good for her! — and Edelman tweeted, “Set your goals high. Do whatever it takes to achieve them. #motivation.”

It turns out that Edelman went far beyond what this teacher thought he could do. But it also might be true that if this same teacher discouraged 25 other men from trying out for the NFL, she may well have been correct the other 25 times. Edelman is an exception — an undersized guy who made it through with a lot of grit and determination — and clearly there was some luck involved. (Not having a debilitating injury has to be a mixture of skill and luck.)

The reason I bring this us is that I also am a teacher. During the first session of my most recent semester of free video poker classes, one young man — I’m guessing 30 years old — “Charlie” — wasn’t very impressive in class. My class is interactive and I ask each student a question in turn. It’s pretty obvious to me if somebody has a knack for the game or not. By listening to how they answer the questions, how fast they grasp concepts, and the questions they ask, it’s not that hard for me to make some sort of an evaluation.

Still, it’s just my opinion. It’s at least possible that someone whom I think has no chance of becoming a decent player ends up being a successful one — in whatever way you wish to define that. It is, however, an educated opinion. I’ve been around successful gamblers for more than 40 years and there are recognizable patterns. Every successful gambler is different from all the others, but things such as apparent intelligence, a curiosity about how things work, and the ability to grasp concepts are pretty common.

Anyway, after the class, Charlie came up and told me he had recently received a settlement. He had $40,000 total, supplemented his living driving for Uber, and wanted to become rich playing video poker. What should I say?

It’s always a guess as to how much to encourage somebody. I really don’t want to give anybody false hope. Yes, I would earn a few extra dollars for each of my books and software that he purchased, but truly that’s small change. Telling somebody they have a great chance to succeed when I believe the opposite is true is not what I’m about.

At the same time, telling him flatly, “You have no chance at all,” isn’t what I’m about either. He might have been having an off day and he might be much smarter and more dedicated than I originally surmised. Although I was pretty sure I was correct in my judgment about him, I’ve been wrong before about many things.

So I told him that percentagewise, very few video poker players can support themselves just by gambling. It’s tough to succeed and a lot of players are competing with each other to do this. There is simply not enough room for everybody to make money at this. When this occasionally happens, casinos tighten up and then all the players struggle to find the next great opportunity.

I told him that the successful ones have some aptitude and work very hard perfecting their craft. And luck plays a role as well. You will likely hit “about” the right number of royals over time, but if you’re playing both quarter and dollars, it makes a big difference whether the royals you hit are quarter royals or dollar royals.

I also told him that while $40,000 sounded like a lot of money, money goes pretty fast when you’re paying rent, automobile expenses, whatever. If you’re using that money for both living and gambling, going through that in a year or two is very possible — even with some extra money coming in from driving. And then what?

Finally, I recommended he practice on the computer rather than in the casino. In-casino practice is very expensive. Playing on the nickel machines to save money isn’t usually a good option because those pay schedules are typically very bad. Even I would be a loser on most nickel pay schedules.

Anyway, that’s what I told him. I tried to balance being realistic with being reasonably supportive. What would you have said?

(Author’s note: After the first class and after this blog was written, Julian Edelman suffered a tear in the ACL of his right knee and will out all season. My reference early in this blog to Edelman being lucky to avoid debilitating injury now seems awkward in light of more recent events. I left the reference in unchanged — as the story was about Charlie, not Edelman. Writing blogs a month in advance means I’m not under big deadline pressure, but also sometimes current events change what I have written.)

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I’m Glad I Didn’t Hit It — Revisited

The Undoing Project is a recent book by Michael Lewis (author of Moneyball, Liar’s Poker, and The Blind Side, among others). It follows the careers of two Israeli psychologists, Daniel Kahneman and Amos Tversky, as they break new ground and basically invent the field of Behavioral Economics. I’ve written about these guys before and one man they greatly inspired — Dan Ariely.

Today I want to talk about the Undoing Project itself and the psychology of regret. Had I understood these concepts better many years ago, I would have never written a particular article that I now intend to revise.

When somebody wants to “undo” something, they usually think about relatively easy ways it could be accomplished. For example, Andy is driving and reaches an intersection just at the point where it’s a very close call whether to speed up and go through the intersection when the signal is orange or slow to a stop and wait for the next green. Andy’s decision may be the same or different from yours, but all drivers have occasionally experienced this sort of thing.

Regardless of whether Andy sped up or slowed down, let’s assume that at the next intersection, his car was sideswiped by another car which caused considerable damage, although thankfully Andy came out okay.

If Andy wanted to think about how this could have been undone, his mind would naturally go back to the speed-up-or-slow-down decision he had just made and conclude that if he had done the opposite, he would never have been sideswiped. He would not, typically, think that if the other driver had been killed the week before in a drive by shooting, then Andy would have avoided the accident. People just don’t think that way — but frankly, either “solution” would have kept Andy’s car from being crumpled.

When I read about this, I thought back to an article I had written perhaps 20 years ago. Seems like I was playing $1 10-7 Double Bonus at the Orleans and a woman sitting nearby commented, “I’m glad I didn’t hit it.” She was playing only four coins and had been dealt A♠ K♠ Q♠ J♠ 7♦. She threw the 7 away and ended up with a worthless 6♥.

I commented that if she had hit the royal, it would have been worth $1,000 rather than the nothing she received. I thought she was basically an idiot for preferring $0 to $1,000.

The thing is, though, that if she had hit the royal, she would have felt terrible that she hadn’t been playing max coins at that time. She would have seen it as a $3,000 loss rather than a $1,000 gain. The pain of losing $3,000 (even though it’s all in her mind) was bigger than the pleasure of actually winning $1,000.

Since I had studied economics before Kahneman and Tversky came along, I “knew” that having $1,000 was better than having $0. There was just no other way to look at it insofar as I was concerned. This woman was being very foolish.

Now, I realize that this woman isn’t alone in her thought processes. When she wished to “undo” the results of a “mere” $1,000 jackpot, she normally would think that, “I should have been playing five coins.” She “knew better” and now was being punished for only playing four coins. The pain she would feel would be very real to her.

I, of course, would have recommended she play one coin or five — depending on bankroll considerations, but never four. Still, that ship had sailed and she bet four coins. Although I still feel betting four coins per hand was foolish, I have more empathy for her “I’m glad I didn’t hit it” statement.

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A Matter of Perspective

If you’re a computer programmer working on a video poker game, the hand A♠ Q♥ T♥ 8♠ 3♥ is equivalent to A♦ Q♣ T♣ 8♦ 3♣, but both of those are different from A♣ Q♥ T♥ 8♠ 3♥. Can you see why?

The ranks of the cards are the same and in all three hands QT3 is suited. In the first two hands, the ace and eight are suited with each other. In the third hand, the ace and eight are unsuited.

To 99% of all players, 99% of the time, that distinction is irrelevant. It could possibly be important, for example, in a Double Bonus game where there is a progressive on four aces. At reset, you hold QT on this hand. If the progressive on four aces is high enough, you just hold the ace. How high the progressive has to be will be different if there are 12 cards still in the pack unsuited with the ace than if there are “only” 11.

With that kind of thinking in mind, assuming you are playing 9/6 Jacks or Better, do you see any difference between A♦ Q♣ T♣ 8♦ 3♣ and A♠ Q♥ T♥ 7♠ 3♥?

For anyone who would hold just the ace on either of these hands, you’re a hopeless Jacks or Better player. Holding the ace can be correct in certain other games, but not Jacks or Better.

The Basic Strategy play on both hands is to hold the QT. It’s the second-best play in both cases, but AQ is better. The fact that AQ is better than QT in these two hands is because the 3 is suited with the QT. This is known as a flush penalty and is generally only of concern to advanced players. Many players have enough trouble just learning the basic plays without dwelling on the fine points. What makes the hands different is that in the first hand, the 5-coin dollar player is making a nickel mistake versus a 2-cent mistake in the second.

The difference in the size of the mistakes is due to the 8 interfering with the straight possibilities of QT and the 7 not doing so. Why is this important? Well, it’s not if you’re playing the game with a 4,000-coin royal.  But if you’re playing a progressive, holding QT is correct in the first hand when the royal is at 4,685 and above, while in the second hand, holding QT is correct at 4,365 and above.

So, for whom is this kind of analysis important? Frankly, only to a pretty small self-selected group. Some pros learn these things — many don’t. A few recreational players become competent in these distinctions — although it may never be cost-effective for them.

Some of us just plain like studying things. This has been one of my “secrets to success.” The more I know about how and why things work the way they do, the easier it is for me to learn and memorize strategies.

If you think my secret is worthless to you, that’s your right. But in general, the more people study these things, the better their results turn out to be. Whether it makes sense dollars-and-cents-wise if you put a value on your time is debatable. But if it gives you pleasure to gain insight into these games, why the heck not do it?

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Dealing with Anguish

I received the following email recently: “I have been playing a few years and consider myself a pretty good player. I consider myself Bob Dancer-trained and try to play accordingly. I have given up at least six royals going for the high pair. My question is how you overcome the mental anguish of missing the royal. It takes me days to get over it. I am retired, play 10 to 20 hours a week of 9/6 Jacks or Better or 8/5 Bonus Poker. Help me, please. Anguished in Ann Arbor.”

I did some calculation and my best guess is that this has happened to me between 600 and 700 times. But it’s a guess, because I have no recollection of it EVER happening. This guess is based on how many million hands I’ve actually played, on which types of games, and how many were on single line compared to Triple Play through Hundred Play.

We’re talking about a hand such as K♦ Q♦ J♦ 5♦ K♠, where the correct play depends on the game and pay schedule. If you’re playing Jacks or Better or Bonus Poker, like Mr. Anguished is prone to do, you hold the kings. If you’re playing Deuces Wild, you hold the suited KQJ. If you’re playing Double Bonus where flushes return 7 for 1, you hold all four diamonds.

If you hold the kings (whether it’s the correct play or not), once in 1,081 times the first two cards out will be A♦ T♦. Also, once in 1,081 times the first two cards out will be the 7♥ 3♣. As far as I am concerned, these two situations are equally relevant.

After I’ve held the kings and pressed the draw button, my “job” is over for this hand, and it’s time for me to start concentrating on the next hand. The best I can do is to play the hands perfectly. Going back and changing the past is not something I know how to do.

Although I prefer that I end up with four kings on this hand, I’m not too invested in that result. I know that I’ll get the 4-of-a-kind one time in 360 (more precisely three times in 1,081), full houses, 3-of-a-kinds, and two pair more frequently than that, but the hand will stay a single high pair more than seven times out of ten.

I have this type of draw numerous times every week. Sometimes I connect on the 4-of-a-kind and usually I don’t. Over the course of a year or two, it’ll average out pretty well, whether tonight is lucky or unlucky.

I suspect I’ve ended up with a 4-of-a-kind from this kind of position more tha 2000 times in my life. What this also means is that I’ve thrown away the royal more than 600 times from this same position. Drawing three cards to a high pair, you get any specific two cards (i.e. the cards that fill in the royal) one time out of 1,081 and you complete the 4-of-a-kind three times out of 1,081. Over the course of years, the numbers come out very close to this.

How many of this estimated 600 missed royals have I noticed? Exactly zero. Checking to see how the cards would play if I made an alternative, inferior, draw is a huge waste of time in my opinion. Doing this consistently would reduce my speed from 800 hands per hour to about 400. Why on earth would I want to waste that much time? Since I’m playing only when I have the advantage, this is slashing my dollars-per-hour win rate in half. It’s not only worthless information, but it’s expensive to gather. If you’re playing Fifty Play or Hundred Play, it could take several minutes at the end of each hand to work through all of this. Why bother?

Mr. Anguish seems to have the core belief that a missed royal is a tragic thing. He ignores the fact that trying for the royal every time (so that he can be assured of getting it when the cards are just right) would have cost him an extra 6,000 coins for every extra 4,000-coin royal received. He berates himself for not being clairvoyant enough to see the unforeseeable future.

The only reason Mr. Anguish takes the time to do this is to check whether he should feel really, really awful this time. One time in 1,081 he discovers that yes, indeed, feeling really, really awful this time is appropriate. The relief he feels the other 1,080 times is likely minimal.

To me, ignoring the specifics of a “what if” draw comes naturally. Perhaps Mr. Anguish is compelled to do this and can’t help himself. I don’t know. Offering useful advice on how you should deal with your compulsions is something I’m not good at. If this is something Mr. Anguish can learn NOT TO DO, I believe his life will work better.

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Does This Make Sense?

This is a column for “low intermediate” players and it involves 4-card inside straights in games where you get your money back for a pair of jacks or better, same payout for two pair, and 4-for-1 for straights. It also involves a paradox of sorts.

There are a lot of these games — Double Double Bonus, White Hot Aces, Triple Double Bonus, Triple Bonus Poker Plus, Super Aces Bonus, and others. What I’m talking about today does not work for games where you get double money for two pair (i.e. Jacks or Better or Bonus Poker), nor does it work for games where you receive 4-to-1 for straights (i.e. the best versions of Double Bonus.)

That last sentence should have caused many of you to do a double take. I said 4-to-1 rather than the more common 5-for-1. They are equivalent, but often players are a bit loose with their terminology. When a pay schedule lists numbers, the returns are always “for 1.”

Here’s the paradox:  Holding 4-card inside straights with no high cards (e.g. 4578 of mixed suits) is eligible to be held in these games.  (“Eligible” means better than throwing everything away. There may or not be higher paying options in the hand.) Assuming you’re playing dollar 9-6 Double Double Bonus, five coins at a time, holding this inside straight is worth $1.70. Holding 4-card inside straights with one high card (e.g. QT98 of mixed suits), worth $2.02 in the same game, is never held.

Both inside straight draws have four cards to fill them in. When there’s a high card involved, there are also three chances to pair up that high card. Of the 47 possible draws, three extra chances to get $5 (the payout in this game for a high pair), add 3 * $5 / 47 = 32¢, which is the difference between $2.02 and $1.70.

I call it a paradox because the greater of the two hands is never held and the lesser of the two hands is held sometimes (depending on the fifth card). So, what gives?

If you haven’t seen or heard this paradox before, I strongly urge you to see if you can figure it out for yourself before you read on. I’ll wait. No matter how many video poker paradoxes I write about, there are hundreds more that I will never get to. If you’re going to become a decent player, you’re going to have to learn to think for yourself.

The key to the paradox is using absolute values to deflect attention from relative values. The $1.70 and $2.02 numbers are absolute values — that is, what the position is worth on average if you play it out zillions of times.

What is important in video poker, however, are relative numbers. In the hand 4♠ 5♥ 7♣ 8♦ 2♠, we’ve already said the value of holding 4578 is $1.70. The important thing is that the value of throwing everything away is $1.62. Those are the best two choices, and the better of these two is to hold the 4-card inside straight.

From Q♥ T♥ 9♣ 8♦ 3♠, we’ve said the value of holding the 4-card inside straight is $2.02, but the value of holding the queen by itself is $2.12, and the value of holding the suited QT is $2.23. Relatively speaking, the value of $2.02 is less than the value of holding either the single high card or the high card with a suited ten.

Every time there is a 4-card inside straight with one high card, there is necessarily a high card by itself in the same hand — and sometimes a high card with a suited ten. So, we’re never going to hold this inside straight.

The fact that holding this inside straight is better than throwing everything away is interesting, perhaps, but irrelevant. We’re looking for the play with the highest EV, and throwing everything away isn’t going to qualify when there’s a high card in the hand.

Once you realize that we’re comparing one inside straight to throwing everything away, and the other inside straight to something else entirely, the paradox disappears.

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Which is the Better Place?

I received an email asking which of two casinos was the better choice for this player.

Casino A had 9/6 Jacks or Better with a 0.1% slot club with no multiple points ever. Casino B had 8/5 Bonus Poker with a 0.25% slot club, and he only played when there were triple points. He said the food comps at Casino A were better, but he wasn’t there for eating. He was there for making money.

He told me he played both games perfectly. This is extremely unlikely. Although 9/6 Jacks or Better is one of the easiest video poker games to memorize, 8/5 Bonus Poker isn’t. I would estimate fewer than one in a thousand 8/5 Bonus Poker players play the game perfectly. But letting that assumption slide, let’s see what we have, assuming perfect play.

 

Casino A:      9/6 Jacks                   99.54%

Slot Club                   00.10%

Total                           99.64%

 

Casino B:      8/5 Bonus                  99.17%

Slot Club                   00.75%

Total                           99.92%

 

The obvious answer, then, is that Casino B is considerably better. For a dollar player who plays 600 hands per hour, Casino A is $8.40 per hour more expensive than Casino B.

The obvious answer is incorrect, however. For this player, it is not the case that Casino B is better. Why not? Because his stated goal is to make money and that means that both casinos are TOTALLY unacceptable. Not less acceptable; TOTALLY unacceptable.

A return of 99.92% is not “close enough.” It’s impossible to end up a long-term winner when the casino has any advantage at all.

If the casinos had other promotions, however, that could change things. Perhaps one or both send periodic checks in the mail on the order of “come in during the first two weeks of the month and we’ll give you $50 just for showing up.” Or perhaps they have regular drawings and the player has a decent shot at winning something valuable. Either or both of these promotions could make the casinos potentially profitable. But without such promotions, the house has the edge.

For most players, this would not be an insurmountable problem. Few players demand that casinos be potentially profitable. (No slot player, for example, has any realistic expectation of being an overall winner. They hope to win THIS TIME, but they know that in the long run the casino will most likely win from them.)

Many players value the gambling experience and count the free meals and rooms as part of the deal. For players like that, both casinos offer an excellent gamble which is better for the player than can be found in many casinos. Which casino is better might well depend on how much better the food is at the casino with the lesser game and how important that is to the player. To some people having a quality meal is extremely important. Others don’t care that much.

Or perhaps how nice the rooms are. Or maybe how smoky the casino is. Or possibly “easier to get to.” All kinds of solid reasons exist for choosing one place over another.

What should this particular player do then? The choice is between either not playing, or lowering his expectations about whether or not this game will be profitable. It would not be terrible should he decide to play anyway because he really enjoys it. After all, people pay to do many pleasurable things. And if gambling is pleasurable, it’s okay to pay for that too. But I encourage you to be realistic about whether you are playing for profit or playing for pleasure.

In similar cases, I ALWAYS choose not to play. I’ve played video poker for close to 25 years and it’s isn’t a “special treat” to me. I enjoy it. But I can go without playing if the odds aren’t there.

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Comparing Two “Super” Games

Super Double Bonus (SDB) and Super Aces Bonus (SAB) are both variations of Double Bonus. In “regular” Double Bonus, four aces get paid 160 for 1, four 2s-4s get paid 80 for 1, and four 5s-Ks get paid 50 for one.

Each of the variations we’re looking at today keeps that basic structure for the quads, with one exception each. In SDB, four Js-Ks receive 120 for 1 rather than 50 for 1 (and you receive more for the straight flush as well). In SAB, four aces receive a gigantic 400 for 1. In both games, the amount for the full house and flush is adjusted downward until it gets into the “acceptable” range. This means the pay schedule returns enough to attract the players, but not so much that the casinos are afraid of it. The two pay schedules discussed in this article are the highest allowed for these particular games. In many casinos, you’ll find lower pay schedules than these, but that won’t affect the discussion that follows.

 

9/5 Super 8/5 Super
Double Bonus Aces Bonus
Royal Flush 800 800
Straight Flush 80 60
Four Aces 160 400
Four Js-Ks 120 50
Four 2s-4s 80 80
Four 5s-Ts 50 50
Full House 9 8
Flush 5 5
Straight 4 4
Three of a Kind 3 3
Two Pair 1 1
Jacks or Better 1 1
Return 99.69% 99.94%
Variance 38.0 63.4

 

The strategies for the two games are very similar. This is largely because they receive identical amounts for flushes, straights, and two pair — which are the three pay-schedule categories that matter most when it comes to strategy.

In today’s column, I’m going to present four hands that are played differently in the two games. Your job is to figure out both plays. Even if you have never played either game, you have two important clues to help you out:

  1. The plays are different. This is a HUGE clue.
  2. The plays are different because of the pay schedule.

 

  1. 5♣ 6♣ 7♣ 8♣ 9♥
  2. A♥ Q♠ J♦ 9♣ 3♠
  3. A♠ Q♥ 8♦ 4♣ 3♠
  4. K♥ T♥ 8♦ 7♣ 6♠

 

Where dollar and cent amounts are indicated, it assumes you are playing for dollars, five coins at a time.

 

  1. There are only two reasonable plays here. The “chickens” keep the straight and the “gamblers” go for the straight flush. The different returns for quads has no bearing when you hold at least four cards of different ranks, so the determining factor must be that SDB returns more for the straight flush. In SDB, ‘5678’ is better by $2.87, and in SAB, 56789 is better by $1.39. Obviously neither play is close.
  2. With three unsuited high cards including an ace, the “standard” play in both Jacks or Better and Double Bonus is to discard the ace and hold the other two high cards. That’s the correct play in SDB by 10.6¢. In SAB, the much greater return for four aces means that you go for them more. In SAB, holding the single ace is the better play by 20.6¢.
  3. This is very similar to the last hand. In SDB you hold AQ by 2.6¢. In SAB, you hold the solitary ace by 19.6¢. And the reason, again, for the difference is the large amount you receive for four aces in SAB.
  4. This last hand is intentionally tricky, in that there are more than two choices. Holding ‘KT’ is obvious. Holding the inside straight, T876, is also an eligible choice. It takes some experience to know that inside straights with no high cards are worth considerably less than either single high cards or a single high card with a suited ten. Perhaps the hardest option to see is holding the king by itself. Some players can’t bring themselves to break up royal combinations no matter what the pay schedule. Once you realize that the king by itself is a viable option, then since SDB pays more for four kings, holding the single king in that game is the better play by 2.8¢. In SAB, the “normal” play of ‘KT’ is better by 3.0¢.

 

So how did you do? As a test, this wasn’t too difficult. But as a learning experience, there were some important things to remember. First of all, each game has its own strategy and those of you who use more-or-less the same strategy for most games are taking the worst of it. Second, sometimes the reason for the differences in the strategies is obvious once you closely examine the idiosyncrasies of the pay schedule.

Finally, I want to leave you with a hand that’s played the same in both games, assuming you are playing with the best pay schedule. K♥ K♠ 9♥ 9♦ 3♣. Although many seat-of-the-pants players will just hold the kings, in SAB, holding KK99 is better by 79¢. In SDB it’s a closer play because four kings pay so much, but KK99 is still better in that game by 19¢. If you find yourself playing a version of SDB where the full house pays only 40 or less instead of 45, that’s enough to change the correct play to KK.