Category: Advanced Strategy

Posted on by — 10 Comments

Video Poker’s Participation Awards   

A ‘participation award’ is one you get just for being there — whether you win or lose. There are people who believe that when raising children, winning and losing isn’t so important, but participation is. With that in mind, there are some sports leagues for children where every player gets a trophy at the end of the year.

I’m not here to argue the merits of such a program and I’m not here to tell you how to raise your kids or grandkids.

What I want to talk about today are video poker’s participation awards. It’s possible you didn’t know there are any such things. But there are!

They are called jackpots!

A royal flush, which is the top award in most video poker games, is really a participation award. Show me a player who has hit 20 royal flushes in the past two months and I’ll show you someone who has played a LOT. Show me someone who hasn’t ever hit a royal flush, and I’ll show you someone who hasn’t played very much at all.

If you want to change the discussion to four aces, or maybe four deuces depending on the game, or dealt quads, or some other hand that pays well, be my guest. If you play long enough, you’re going to get these hands. If you don’t, you won’t.

But, do I hear you say, in the sports league for children that awards trophies to everybody, your skill level doesn’t matter. Surely, it’s different in video poker where you need to make skillful choices.

Well, yeah, sort of. On a hand like K♦ K♠ Q♠ J♠ 4♦, there are games where you should hold the kings and others where you should hold the spades. If you hold the spades, rightly or wrongly, on average you’re going to end up with a royal flush once every 1,081 of these hands. If you hold the kings, you’re never going to get a royal flush on this hand.

So, if the computer says to hold the kings on this hand but you actually held the spades and the 1,080-to-1 shot came in, would you consider that skillful? If you take a picture of the royal flush and show it to your friends, do they ever ask what cards you threw away? Or what game you were playing? Doubtful. Mostly they congratulate you on your good fortune and wonder what it’s like to be such a winner as you!

I participate on several Internet forums related to gambling. On some forums, you’ll see players posting pictures of dealt royals when they’re playing 8/5 Double Double Bonus, which is a game that returns less than 97%. There are other games shown in the pictures as well, yielding approximately the same thing.

Other posters on the forum line up and immediately congratulate the poster on the good fortune. My personal feeling is that anyone who plays a 97% game is clueless about the winning process. Clearly this is a losing player who got a participation award to briefly provide them with some ammunition to play more. To me, posting jackpots on such a bad game announces to the world that you are not a knowledgeable player. Why not keep this secret?

If I actually post such a comment, I get my head handed to me. People want to celebrate their participation awards. People want to be praised for how good they are. They tell me (correctly!) that it’s okay to be a recreational player and rejoice in their successes when they come.

So, I generally don’t comment on these jackpot pictures anymore. But I take note of who posted them. When that person enters into a later debate on some matter on the forum, I’ll understand going in that their opinion does not carry the same weight with me as the people who are actually knowledgeable players.

In my own case, I’ve hit more than 500 jackpots of $20,000 and larger. Are they all participation awards? Absolutely! Every last one of them! The only thing that number of jackpots tell you is that I’ve been playing a long time for higher stakes than many others play. It doesn’t tell you anything about how good a player I am.

Until you know why a player was playing a particular machine on a given day, what slot club benefits and promotions were available, and the accuracy of the strategy used, you have no idea how good that player is. You cannot say with confidence that someone who has hit 200 royal flushes is a better player than one who has hit four — although you CAN say the former has participated a lot more than the latter.

Posted on by — 13 Comments

If You Weren’t Such a Hypocrite . . .

Periodically I receive a version of the following email:

Mr. Dancer:

I have read your books and practiced on Video Poker for Winners. I’m a really good player. I live in Las Vegas and can see there are good games to play — except I simply do not have the bankroll to play at the stakes necessary to succeed.

But you do! So why don’t you bankroll me? I’ll share the results with you 50-50 of course and we can both do well!

If you weren’t such a hypocrite, you’d see the wisdom of this! This is a chance for you to put your money where your mouth is. If what you’re writing is just a bunch of lies in order to sell books, I could see why you’d pass this up. But you’re not doing that at all, are you?

So, when can we start?

Eve

 

Dear Eve:

I’m not interested. For a lot of reasons.

First, even if you are a player with the same (or better) abilities that I have, playing 100% honestly, you’re asking me to receive half of the wins and bear 100% of the losses — on a game where only a tiny advantage is possible. That would not be an intelligent gamble on my part.

Second, Eve, I don’t know you from Adam. Even if you tested out really well when I was watching, who’s to say what you will do when I’m not around watching you?  I’m not saying you’re a cheater. What I AM saying, though, is that some people do cheat and I’m not proficient at detecting beforehand who’s going to cheat me and who’s not. Since I’m not very good at this, I believe it is better for me is to stay away from it.

Third, this is not my business model. I have no desire to form some type of insurance company. Maybe somebody else can see the opportunity here and prosper at this sort of thing, but I’m 70 years old now and that’s not how I want to spend the rest of my life.

Fourth, there’s a big difference between investing in myself and investing in somebody else. Those are very different mindsets. Those involve very different risks.

Lastly, I don’t respond well to “If you’re not a hypocrite then you’ll do what I want you to do” types of arguments. It’s reminiscent of grade school challenges like, “I double dare you to jump off of that building!” No thanks. Go try and manipulate somebody else!

I have bankrolled two players in the past. One went pretty much as expected and I won a bit. The other player lost at a very high rate — possible, but unlikely. It’s been more than 20 years and I still think I was cheated — but I couldn’t prove it at the time and certainly can’t prove it now. I promised myself “never again” at the time and see no reason to break that promise to myself now.

Posted on by — 13 Comments

Is There a Different Strategy and How Can I Be Sure? — Part I of II

One of the casinos I play at is Dotty’s, which is a chain of more than 100 15-machine outlets all across Nevada, plus a few larger ones. There are perhaps 10 of them within 10 miles of my home.

One of the promotions that attracts me relates to W2Gs. Every week, 10% of the W2Gs earned company-wide earn a 10% bonus. That is, if you receive a $4,000 royal flush, 10% of the time you receive an additional $400 in cash. I estimate the value of that by assuming I’ll get an extra $40 for every such jackpot. (in other words, $40 every time adds up to the same number as $400 10% of the time.)  I’ll end up with the same EV, although I’ll be underestimating the variance a little.

My game of choice currently is 9/5 Super Double Bonus. If I play that game for at least $25 per hand, I’ll get W2Gs for all quads as well as for each straight flush and royal flush.

I’ve known the strategy for that game for some time and I’ve written about it periodically. The question I’m looking at today and next week is: Does the strategy change with the Dotty’s promotion? And if so, what are those changes? Further, assume that I’m not a computer programmer and I don’t have access to computer software that you don’t. So how do I go about this?

I wish to learn to play the game perfectly. I understand that this may not be your goal. Still, learning how to do it is what this week’s and next week’s columns are all about. Someday there may well be a promotion that you wish to figure out.

The software I’m going to use for this analysis is the Wizard of Odds (WOO) Video Poker Strategy Calculator. It will give you a perfect strategy and it’s available for free online. Although I’m not a huge fan of the notation used on that product, it’s hard to complain too loudly when it’s free and completely accurate.

For the base game, the pay schedule is 800, 80, 160, 120, 80, 50, 9, 5, 4, 3, 1, 1   Adding 1% to each of the top six figures will make the return on one of them 50.5. Although the WOO software does accept decimal points, I prefer to multiply all of the amounts by 10. That is 8000, 800, 1600, etc. Since the strategy is calculated using relative values, multiplying all pay schedule categories by a fixed amount has no effect whatsoever on the strategy.

For the Dotty’s version, I enter the payout amounts as 8080, 808, 1616, 1212, 808, 505, 90, 50, 40, 30, 10, 10. The lowest six pay schedule categories don’t receive the 1% increase because they don’t result in W2Gs. If I wanted to bet $134 or more per single-line hand, I could get W2Gs on full houses as well. For today we can ignore that refinement.

In the chart below, the numbers in red indicate numbers for the base 9/5 SDB game. The numbers in green represent the numbers for the Dotty’s version.

The actual chart created by the WOO software has several more columns to it that I’ve omitted here. If you duplicate either the red or green Payoff numbers in the WOO Video Poker Strategy Calculator, you’ll see the omitted columns. Those columns include useful information, but not information we’re using today. If you don’t duplicate this information yourself, how do you know if you can do it? It’s not difficult, but “practice makes perfect.” If you don’t know how to use a tool, it’s the same as not having the tool at all.

In the red section of the chart, find the number 490,732,320. That’s the number of occurrences for royal flushes out of 19,933,230,517,200. (In a recent Gambling with an Edge episode, Michael Shackleford explained where this number comes from.) In the green section, the corresponding number is 491,575,464.

That means that when you change strategies to take advantage of these W2G bonuses, you get more royals. You should be able to see you also get more straight flushes, more aces, more 2s-4s, and more 5s-Ts. For some reason I’ll explain next week, you get fewer Js-Ks.

Okay. Now I know there are strategy changes. This is the first part of what I wanted to know. I now need to find out what these changes are.

I’m going to tell you what those changes are — next week. I’m going to use the WOO Video Poker Strategy Calculator to do this. What I strongly recommend is that you work this out yourself. All the information you need is in the software which is online and free. As I said before, if you don’t know how to use a tool, it’s the same as not having the tool at all.

Posted on by — 9 Comments

You’re Upsetting Our Players

In 1999, I started communicating with “Richard,” the marketing director of the Laughlin Flamingo hotel. (Today the same property is called the Aquarius, and it may change names again because the parent company is in the process of changing owners.) Richard knew my name because I wrote columns for Strictly Slots and Casino Player, both of which were distributed for free in that casino.

He wanted to use my “fame,” such as it was, to draw in customers, but he didn’t really want me to teach his players how to beat him. Was there any middle ground?

I suggested he hold a video poker tournament, giving away whatever amount he wanted, and I could teach a class on “How to Succeed in a Video Poker Tournament.” His players would get real value because tournament play definitely has some skill elements to it (in addition to a considerable amount of luck) and most of the lessons for tournament play don’t translate into regular casino play. We reached a deal for me to host two events over the next year.

The only tournament software they had was for Jacks or Better.  An unusual choice for a video poker tournament, but I could adjust my class accordingly.

One of the major points in tournament strategy is that on the last hand, if you aren’t “in the money,” you should go for broke. If a tournament had 250 entrants and paid out 50 places, then being in 51st place was tied with 250th place. Zero is zero. This is very different from casino play, where 51st place might represent a profit of $100 and 250th place might be a loss of $500. These aren’t the same at all.

Players are used to the concept that a higher score is better than a lower score, but this is only true in tournaments if you’re above the “bubble.” If you’re below the bubble, all scores are equal.

Since it was a Jacks or Better tournament, the example hand I used was being dealt AAAAT on the last hand where you weren’t already in the money. Assuming 125 coins (the payout for four aces in this game) wouldn’t be enough to move you into pay dirt, you should throw away three of the aces and just hold the suited AT. Your only chance was to get a royal flush. You didn’t have a big chance — actually 1-in-16,215, but a small chance was better than no chance at all.

If this were the more standard Double Double Bonus tournament, I would have picked a different hand. Four aces pay at least 800 credits, maybe 2,000, and just that score would usually be enough to move you into the money.

The following year I received a call from “Cheryl” who was Richard’s assistant. She said Richard was busy, but she was asked to call and see if they could get me to Laughlin again for two more events. But there would have to be a few changes in the contract.

First, they wanted to lower my fee by $100 each time. Since I had already prepared my notes, it would be easier on me and that should be reflected in the price. I told Cheryl that I wasn’t crazy about this change. At that same time, there was a casino in Las Vegas that was giving away the store (I didn’t tell her this was the MGM Grand).  To induce me to come down to Laughlin for two days at a time would take more money, not less. But what was the other change you were talking about? Maybe that would offset the money.

She told me there were complaints from some of the seniors that I was telling them to throw away four aces! They didn’t get such a good hand very often and they just KNEW this couldn’t be right. Since the complaints went through her, it would be making her life easier if I never told them to throw away four aces.

I asked her if she understood the context behind sometimes throwing away the aces. She didn’t. She didn’t care. She never gambled anyway so she paid no attention to somebody else’s silly ideas about gambling. She really only cared about getting fewer complaints from the players.

I asked her if Richard knew about the changes she was requesting. She said no, but she was sure he would be proud of her for reducing the costs and not making the players angry.

I told her “No thanks,” but if they wished to increase my fee and allow me to teach the class as I saw fit, she knew how to get in touch with me. She never did.

I never taught there again, but as I recall things worked out pretty well for me at the MGM Grand.

 

Author’s Note:  The next semester of classes at the South Point will begin Tuesday January 9. The original schedule of classes on bobdancer.com accidentally said Sunday January 7. The schedule has been repaired, but I want to make sure everybody has gotten the word.

Should anyone be worried about the classes upsetting them, I promise that this semester I will never tell you to throw away four aces!

Posted on by — 7 Comments

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.

Posted on by — 24 Comments

The Las Vegas Massacre and Me

Many of us are sick and tired of discussing the terrible events of October 1 and the speculation afterwards of what made this unhinged man do what he did. If that’s where you are and you want to skip this article, I won’t blame you.

Once it was discovered that Stephen Paddock played video poker, I started getting calls from a variety of news outlets. Although I didn’t get nearly as many calls as Anthony Curtis did, when something related to video poker makes the news, my name comes up as someone who might be able to offer some insight.

For each telephone interview, I started it off with the fact that I didn’t know the guy and had never heard his name until after he was dead. I don’t know if he was a winning player or not, but I have my doubts. And in my opinion, there is nothing inherent in the game of video poker that will create such a monster. So, with that said, how can I help you?

Some reporters wanted to know the difference between video poker and regular poker, or video poker and blackjack, and those were easy for me to answer. Some wanted to know why the game was so popular. To my mind it’s because the game is beatable, and even casual players can get relatively inexpensive casino vacations out of the game.

From there, the questions usually evolved to what other casino games were beatable. Years ago, I would have said blackjack, poker, and sports betting and that would have been the end of my list. But since I’ve been hosting the Gambling with an Edge podcast I’ve become aware that there are LOTS of different avenues for profiting in a casino other than just these games.

Some wanted to know how many winning players there are, and I had to say that any number I came up with would be a wild-assed guess.  I don’t know how much any other player nets, let alone how many of the tens of thousands of players (most of whom I have never met) had net scores greater than zero.

One question from the Associated Press was one that I didn’t want to address. The reporter argued that this attack exhibited a great deal of planning and would a successful video poker player have the ability to do such planning? I didn’t want to answer this question because the answer is “Yes!”

What I said was that a successful lawyer would have those planning skills, as would a successful architect, as would a successful chef, as would a successful political advisor, as would a successful reporter, as would basically a successful anything. So yes, you can add successful gambler of any stripe onto that list, but the list is very long.

One reporter told me that CNN reported Paddock was ahead more than $5 million in a recent year. Was this possible? I told them it was very possible that a high-stakes player had more than $5 million in W2G jackpots, but that’s an entirely different matter than being ahead that much. Or even ahead at all! Getting the total of W2Gs from the IRS might be obtainable by the police. But knowing whether he was ahead or behind was a totally different matter.

Four days after the shooting, Bonnie and I left for a long-scheduled two-week cruise from Boston to Quebec City and back again. While in Boston the night before the cruise, I checked my email and found one from Ryan Growney, the general manager of the South Point. He said that an FBI agent wanted to talk with me about the shooting and I should call him back right away to get that FBI agent’s phone numbers. Since I teach classes at the South Point and that casino sponsors the podcast, that casino was a reasonable place for the FBI to start looking for contact information.

Shit!

I’ve heard Bob Nersesian and other attorneys say you NEVER should talk to a police officer without having an attorney present. I figured that went double for talking to the FBI. Still, I was a couple thousand miles away from home and about to sail northwards soon. The $3.99 a minute charge for talking when the ship is actually at sea is relatively small change, of course, but I still didn’t want to pay it. I figured I could handle this, so I found out the number of the FBI special agent and called him.

The agent told me that my name was mentioned by several people when they asked, “Tell us the name of the most likely person you know who might have known Stephen Paddock.” Due to our “video poker connection” and the fact that I play what many would consider high stakes, it didn’t surprise me that my name had come up. When I said I had never heard of him, basically the interview was over.

Except, the agent wanted to fill out the form in front of him and he asked me if my name was Bob, or perhaps Robert? Another question I didn’t want to answer, but I told him that Bob Dancer was a pseudonym used for teaching and writing purposes.

This led to the next question of, “Would you mind telling me your real name?” The truthful (unspoken) answer was of course I minded, but I told him anyway, along with my address and phone number. That information could be easily obtained by the FBI anyway if they really wanted it, but I would prefer I wasn’t in their databases.

Oh well. I wasn’t going to lie to the FBI and making a big stand about something that wouldn’t be difficult for them to find out anyway would just make me look suspicious.

I said at the beginning of this article that I had my doubts that Stephen Paddock was a winning player. Why did I say that? Because articles said he’d been playing for high stakes for more than a decade and he was still allowed to play at a number of the biggest Las Vegas Strip casinos. From both personal experience and talking to many other successful players, I know that these places tend to restrict and/or remove players over whom they do not believe they have an advantage.

So, if he did have an actual advantage, he would have needed to fool several different casinos for more than a decade. And this, I believe, is unlikely. Even more unlikely is that the casinos would have allowed him to be $5 million ahead in one year.

Posted on by — 17 Comments

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.

Posted on by — 14 Comments

Is This Correct?

I get lots of emails from players asking about this or that. If the questions aren’t too frequent from the same player, I usually answer them. I recently got a question which I very much disliked from a player named Gary.

“Bob, I’ve been trying to figure something out that Linda Boyd said on YouTube. She said that when you were dealt the 4♠ 9♣ J♥ Q♥ K♠ that you would hold the J♥ Q♥. Is that true, because to me the 9♣ is a penalty card, not really sure what to think of all this, would you help me out?”

Here are my problems with this question:

  1. It is so easy to look up how to play a hand using software. Any player trying to learn should have one or more video poker software products. This level of information is also available for free online. Emailing me to ask how to play a hand is equivalent to asking me to add 432 to 743. Yes, I know how to do it, but I’m not interested in being a calculator for you. If you are unable or unwilling to look up how to play a hand, playing video poker well is beyond your capabilities.

 

  1. Gary didn’t tell me what game he was talking about. For some games, 9/6 Jacks or Better among them (which is the game most authors write about), J♥ Q♥ is the correct play. For other games, such as the versions of Double Bonus where you receive 5-for-1 for a straight, you play 9♣ J♥ Q♥ K♠. Somehow, I’m supposed to figure out the game that Gary is interested in.

 

  1. Gary mentioned a penalty card, although not in a way that indicates he knows what he’s talking about. Penalty cards are a consideration for advanced players — and many such players think they are more trouble than they’re worth. At the minimum, however, you need to know basic strategy cold before you start messing with penalty cards. And if Gary is asking about this particular hand, he clearly doesn’t have basic strategy mastered.

The fact that Gary is at the intermediate level is neither here nor there. Everybody starts at the beginning and each one of us is at a different point along the learning curve. I’ve had raw beginners in my classes as well as students who are professional video poker players. If Gary were to attend class or discuss private lessons, that would be fine.

But asking me questions that he could answer easily himself is abusing my generosity. I do answer questions via email for free, but not questions like this.

Posted on by — 26 Comments

How Often Do Things Happen?

Today’s paper is on simple video poker mathematics. Let’s assume you are playing a game where, on average, you hit a quad (i.e., a 4-of-a-kind) every 400 hands. Further, let’s assume you play for a total of 1,200 hands. I’ll arbitrarily say that it takes you two hours to complete the 1,200 hands. How many quads can you expect to end up with over that number of hands?

It appears obvious that the answer should be three, but this is the wrong answer. To get the correct answer, we need to look at the binomial distribution, the results of which appear here:

 

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

What this says is that 5% of the time you won’t hit any quad; 17% of the time you’ll hit four; 2% of the time you’ll hit seven; etc. These numbers don’t tell you WHICH quad you’ll hit. Just how many.

These numbers are accurate, but not really precise. For example, the chance to get exactly three quads could more precisely be written as 22.4322%, but that is far more precision than we need for today’s discussion. It looks like they only add up to 99%, but that’s rounding error and also not important for today.

One of the interesting features of this distribution is that the number of quads that we think we “should” get, namely three, actually occurs less than one time in four. Another typical feature of the distribution is that the probability of getting one fewer quad than typical is virtually the same — actually 22.4135%, which is slightly less.

We could, I suppose, refer to getting either zero or one quad as “bad luck”, getting two, three, or four as “typical luck”, and getting five or more as “good luck”. It doesn’t change anything by assigning terms dealing with luck to the results. When somebody asks me, “How much skill and how much luck was involved?” in describing whatever happened yesterday, my answer is often, “I have no idea.”

Let’s assume that on this particular day in question, we don’t hit any 4-of-a-kind. Definitely worse-than-average luck, but it happens about one day in twenty. Slightly rare, but not extraordinarily so. Now the question is, since you’ve just gone through worse-than-average luck, what will be the distribution of quads for your two-hour session tomorrow? For this, the following distribution will hold:

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

The distribution, of course, is the same as first given. Just because we had a bad day says absolutely nothing about what our score will be the next day. There is no tendency to either, “Once you start running bad you keep running bad because you’re an unlucky player,” or “You’ll get more quads the next day to make up for the shortfall.”

Let’s assume we change machines halfway through. Now the distribution of the quads expected over the 1,200 hands is:

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

Is this distribution beginning to look familiar? It should. Changing machines has nothing to do with changing the distribution.

In this discussion so far, we’ve said nothing about skill. We are assuming players are playing perfectly. If players play imperfectly, the distribution will change. For example, on a hand like K♥ K♠ 4♦ 4♣ 5♦, it is correct in almost every game to hold KK44, although many seat-of-the-pants players playing games where two pair only return even money incorrectly hold just the pair of kings. Making this kind of mistake systematically will IMPROVE your chances for hitting quads, but COST you overall. The increased number of quads you get by holding only one pair rarely compensates for the reduced number of full houses.

The numbers are for three “cycles.” If full houses normally come around every 90 hands on average, the numbers above apply to how many full houses you hit in 270 hands. If royals come about every 40,000 hands, the numbers above apply to how many royals you hit in 120,000 hands. In games where the royal cycle is 45,000 hands, the numbers apply to how many royals you hit in 135,000 hands.

Posted on by — 7 Comments

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?