After celebrating an early Christmas in Columbus, our next stop was at granddaughter Kaitlynn’s apartment in Atlanta, where she is working on her master’s in communication, specifically video production and related areas.  She has connected her hobby of geocaching to her studies with a YouTube site chronicling her adventures at home and abroad.

Then it was on to Cherokee Harrah’s in North Carolina’s Smoky Mountains, one of our favorite casinos, where Kaitlynn (now over 21 and can enjoy casinos), daughter Angela, and son-in-law Steve helped us use up $500 worth of comps that came with this freebie Harrah’s Seven Stars trip. Although the weather was cold and rainy, the 3 of them were intrepid, doing some major hiking in this beautiful area that they love.  (A park ranger gave them advice on hiking trails, avoiding those affected by the recent Gatlinburg fires.)

Brad and I stayed in the warm hotel and casino, enjoying the nice heated indoor pool and unlimited free movies in our mini-suite.  (Perhaps the only Harrah’s casino that still gives this unlimited benefit for Seven Stars?)

All of us enjoy the food options at this casino.  Although we could have chosen the two upscale restaurants, we prefer more casual dining:  grabbing quick breakfast options at Starbucks; grazing in the food court on the casino floor; or, visiting the Diamond Lounge where major meal options are available during dinner time and extra selections in the room reserved for Seven Stars.  We especially liked the breakfast/brunch buffet in the Selu Garden Café.  And the main buffet we consider one of our favorites among all the casino buffets we have every visited, wide selection of high-quality food choices and no mysteries – every item was labeled!

And of course we all gambled.  Brad and I played $5 single-line NSUD since anything at lower levels had schedules with much lower EVs.  When we arrived on a Thursday, I saw signs promoting a mystery-multiplier for all Thursdays in December.  Checking at a kiosk, Brad found he had a 2x, but I snagged 3x so we played on my card that day, saving his play for the next one.

Angela likes to play VP but since there were no good games at a lower denomination, she joined Kaitlynn and Steve who love the penny slots.   I am always amazed at how long they can play on a small bankroll.  Yes, they will lose unless they hit a big jackpot but they do get a lot of entertainment at a small cost by bouncing around from one machine to another, betting minimum amounts per hand.  In fact the last evening we joined them and had a ball – hooting and hollering whenever one of us on the bank had a bonus round.  When we quit for the night,  I  surprised myself by winning $10 for the session!  Kaitlynn was especially proud of herself.  She had won $75 on her first day of play.  She said she ought to quit then – that was a big amount for her.  But then I told her that she could look at it as a way to “pay” for further entertainment and so she played on that for the next two days.  She finally lost the last of it that last night and she decided to quit.

“Look, I had fun for 3 days in a casino and it didn’t cost me anything,” she beamed.

She is now a proud member of our Frugal Gambler club:  Breaking even is a wonderful thing!

Your success rate has been much, much higher than that of the vast majority of players (myself included) over the past couple of decades, and as a result, you can afford to dump in the massive amounts of coin-in needed to get anything more than a complimentary doughnut.  I assume that since XXX casinos have absolutely no good video poker anywhere across the breadth and length of this great land, that you have figured out a way to make it profitable to play there nonetheless. One of these days, you’ll have to detail for us just how you’ve managed to make that work. The absolute best game you’ll ever find at a XXX property is 9/6 JOB (at very high stakes), and I’m truly curious as to how you squeeze a full 1/2 percent in extras out to make the play worthwhile.

Other people have raised some of the same issues as the poster above so I think they deserve a discussion.

First, Brad and I have had a higher success rate down through the years than many other knowledgeable players because we have always looked for a bigger advantage than many require.  A play with a .1-.2% advantage is a positive play but one might not live long enough to get to the long term and achieve that positive result.  That is the reason we don’t play as much as we used to.  We can’t find many plays with a bigger advantage.  We do some small lower-denomination plays with a lower edge than we would have done in the past – and that shows up in our records:  more losing streaks and lower profits. 

Another reason for our success is that we never used gambling profits for “living expenses” – we either had a job or, in later years, retirement savings.  We have always lived quite frugally so when we hit a jackpot we didn’t think about how we could “spend” the money for some luxury item.  We kept plowing our profits back into our bankroll and this allowed us to go up in denomination where the profits would be even bigger.

Second, people are always talking about “no good games in that casino.”  We don’t waste our time looking for 100% EV games; there are few anywhere.  We are looking for good plays.   That means looking for not-quite-so-good games and then piling on the extras – players club benefits, promotions, bounce-back, and anything that will add value to the EV of the game.  And how do we find some of those almost-good games so it isn’t so hard to bump up the value with the extras?  We scour the information in vpFREE2.   Have you ever studied it casino by casino?  You might find some of the hidden gems we play.

Third, I have written three books and more articles than I can number – thousands? – “detail(ing) for us just how you’ve managed to make that work.” I can’t reveal every specific detail at every casino where I have played because some extras depend on long-term relationships with casino employees, play levels higher than for the average player, extra knowledge learned by many years of experience, and the personality, circumstances, and goals that differ for each player.  However, I really don’t have that many video poker “secrets.”  It’s mostly spelled out pretty clearly in my writings – and in much detail – for anyone to study and use. It’s up to you how far you want to run with this information.

Download Casino Coupons to Your ANDROID Phone or Tablet, with the New Updated 2.0 Version of the FREE American Casino Guide App  All Coupons are FREE through October 31, 2015. – New coupons are being added all the time. Be sure to check back frequently. – Uses GPS to show you which casinos near you have Instant Coupons offers. – Ability to search instant coupon offers by type. For example: buffet, room, show, etc. Users can also search by casino name, city, state or zip code.

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For more information, go to  the Google Play Store and search “American Casino Guide.”

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2. For VP Players – A major upgrade to Dunbar’s Risk Analyzer for Video Poker. 

Here are some of the new features in v2.0:

· You can now do bankroll risk calculations on 46 multi-line video poker games.

· You can now include progressive jackpots.

· You can now include a jackpot bonus.

· You can now see how stopping when you hit a royal flush affects your bankroll.

· You can now see what happens to your overall results if you plan to stop when you reach a specified “Goal”.

As before, DRA-VP 2.0 can answer questions like these:

·How much money do I need to bring with me to have just a 1% chance of going broke in 10 hours of play? What if I want to play 20 hours?

·What is my long term chance of going broke if I start with $2,000?

·What is the chance I will be $3,000 ahead at some point during a 20-hour trip?

·How does cashback affect my bankroll requirements? What about tipping?

·What is the effect of occasional play errors on my risk of ruin?

·How does state tax withholding affect my bankroll requirements?

·What is the chance I will end my trip with at least a 20% gain in bankroll? A 40% gain?

·What is the chance I will have lost more than 60% of my bankroll at the end of a trip?

·What is the chance I will bust out before I’ve played 16 hours of a planned 20 hours?

·How long do I have to play this game to have about a 5/6 chance of being ahead?

DRA-VP 2.0 comes pre-loaded with 54 video poker pay schedules (46 are also 3-, 5-, 10-line) and room for another 50 custom games. It’s easy to use and runs on any PC with Excel 2002 or later. (Sorry, it will not run on a Mac) The price at ShopLVA.com is $19.95. It’s available on CD, or can also be ordered as a download. If you  already own DRA-VP 1.0 or 1.5, you can upgrade for $12.00.

Go to  his site for a rich source of his ideas for frugal gambling, accommodations, food, and entertainment.  He is a big fan of bus transportation to get around town and shares those money-saving experiences here.

Here are some of the Websites and Internet forums he and others use to keep up on the ever-changing casinos in a city that is constantly reinventing itself:

https://www.lasvegasadvisor.com/resort-fee-hotels/

ACG forum

Vegas Message Board

A number of LVA forums on various gambling subjects, some free and some for LVA subscribers only.

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Another frugal resource, from The American Casino Guide:

Travelers looking for savings at U.S. casinos can now get the FREE American Casino Guide app that allows them to instantly download casino coupons directly to their iPhone or iPad. [Available for Android planned for the near future] The app was developed by the publishers of the American Casino Guide, which has been published annually for the past 24 years and is the #1 bestselling book in the U.S. on the subject of casino gambling and travel. A special new feature of the app is its “Instant Coupon” section which allows users to download coupons for FREE, or on a paid basis, for only 99 cents. However, as an introductory 90-day offer, all coupons can be downloaded for FREE, until October 31, 2015.

CHOICE OF GAME

When Brad and I started playing VP, we mostly played Full Pay Deuces Wild (FPDW) because it had the highest EV of any game we knew about at the time.  We would sometimes play 9/6 Jacks or Better when we found it with a promotion that made it as good a play or better than our trusty FPDW.  We had to fly from Indiana to Reno or Las Vegas to find these plays.

Okay, can you find one of those same situations today?  In Las Vegas and Reno, for sure.    Perhaps also, if you live near the Gulf Coast or Atlantic City or an Indian casino.  However, if you want to play FPDW today, you will have to travel, as we did, to Las Vegas or Reno.   I know many players today are doing the same type of plays we did twenty-five years ago, and some still play nothing but FPDW.

After several years of sticking with our two basic games, we added new games to our stable, i.e., 10/7 Double Bonus ( DB), and Not-so-Ugly-Deuces (NSUD – 99.7%).  Students of VP today will need to learn new games too.

DENOMINATION/BANKROLL

When we started out, we played only quarters – and we stayed at that level for four years.   For awhile we had only a $3000 bankroll and we didn’t come close to losing it all.  However, a few years in we hit a long losing streak and were close to the bottom of that barrel – and right about the time “48 Hours” was filming us and we were showing them how to be successful low-roller gamblers.  Fortunately, we gave the show a happy ending by winning a car at the Stardust and when we sold the car back to the dealer we replenished our bankroll.  However, we decided that $3000 was cutting it too close and from then on we always had at least $5000 at our disposal to play quarters.  We never like being very near the bottom of the barrel.

Today you might not be quite as “safe” with $5000 to play FPDW because you may be playing with fewer extra benefits than we did.  It takes $5800 to have only a 5% ROR (risk of ruin).  To be super safe and have only a 1% chance of going broke you may be surprised that you need $8800.  (There is never a zero chance of going broke.)

EXTRAS

The reason we never really absolutely needed more than a $3000 bankroll while we were playing only quarters was that we never played VP without some extras outside the EV of the game.  From the very beginning – and, in fact, to this very day – I have chased extra benefits like a woman possessed.  Why?  I have always run a little scared gambling.  The fear of going broke is a strong motivating factor for me – and I think a little fear of this kind is a valuable safeguard for all gamblers.

The kinds of extras available for video poker players have varied over the years.  At first it was same-day cashback, and then it gradually changed to free-play bounce-back.   But some extras have lasted, albeit in various forms down through the years:  free tournaments; promotions for various VP hands, i.e., card-of-the-day, and other slot club benefits; check-cashing bonuses; and drawings.   And the quarter player still can find extra value today, mining in the promotion fields, with some powerful extras we didn’t have back when we started, i.e., multiple-point days.

AN ASSIGNMENT

I have more advice – don’t I always – even when you don’t ask for it?     But before I write Part 4, I want to stop a minute here and give you an assignment.  Before you complain about not being able to find good games or good plays, go to vpFREE2 and do a thorough exploration under the heading of “Games and Machines.”  Choose a game you want to play (or learn to play), one with the desired paytable.  Choose your comfortable denomination and # of lines.  Choose the format, whether simple Standard or an exotic like Spin Poker or Ultimate X.   Finally choose the section of the country where you want to play.   Click on “Search.”  Do that for each “good” game with a strategy you know or could learn.

When you have found some possible “good” games, click on the “Slot Club” information for each casino where they are found to see what slot benefits you can add to those games.

Now you will be prepared for Part 4.

It is true that the gambling world is a much different place these days.  But I started thinking about this subject and wondering if someone who wanted to be an advantage video poker player could start out today like we did. Although we started coming to Las Vegas in 1984, we spent the first years card-counting at blackjack.  We never made much profit, but the comps were great, with private casino jets, overseas trips, and a very glamorous lifestyle.  However table comps were decreasing while machine comps were the new emphasis in casinos, so in 1991 we switched from BJ to video poker.

Although it is still possible to play BJ with an advantage, this discussion will be about starting to play advantage video poker since that has been our concentration for about 22 years.  First I want to say that starting – or continuing – on this path is not for everyone.  I’ve talked a lot in the past about the various goals gamblers have.  Not everyone has the desire, the time, the conditions, or even the temperament to be an advantage player – and no one has the right to judge someone else negatively if their goals are different from your own.

But for those who may be thinking about becoming an advantage video poker player, I want to share our experiences when we embarked on this journey and how much has not changed.

DESIRE

First, let’s talk about “desire.”  After our first trip to Las Vegas, we both decided we wanted to go back many more times.  We had fallen in love with casino life.  However, we looked at our financial situation and knew we couldn’t afford frequent trips like this first one.  But our desire was so strong that we made this our first priority: We had to find more money and/or discover a way not to have this life cost us so much.  And this meant dropping some of our other entertainment choices and life interests.  We zeroed in on this desire with all our attention.

GOALS

Desire led us to setting our goal, which you might be surprised to learn was NOT to make money gambling.  I have never encouraged anyone to take up any form of gambling to expect a profit. Our goal from the very beginning was just to break even moneywise and enjoy an abundance of comps as “gravy.”  If you have a copy of The Frugal Gambler, you will notice that the last chapter is titled “Breaking Even is a Terrific Thing.”  Here is an excerpt from that chapter:

If someone told you that you could take the kind of vacations that I’ve described in this book and you could do it all for free, would you also insist that you had to make some money while you were at it? Take home a profit from a free trip to paradise? Maybe, but that sounds a little greedy to us.

Yes –  and much to our surprise I must say –  eventually we did make money – actually gobs of it – but it was not our original goal.  And, in fact, it is STILL not our goal – and if VP conditions continue to deteriorate, we will be quite happy to merely break even and continue to enjoy whatever comps the casinos choose to give us.

BANKROLL

Now comes the sticky issue for most gamblers who want to be advantage players.  You need to have “starter money.”  I will talk more about specific dollar amounts in a later blog when I discuss how game choice and denomination determine bankroll needs.  But now I want to emphasize that this gambling bankroll should be money on top of your assets and/or income that provide living expenses.  We have never “needed” to make money gambling to cover the necessities.  Therefore it has always been a relaxing stress-free activity for us.

There are those who have taken the big risk to earn their living by gambling, and a few hard-working persons have been successful.  I admire them – they work SO hard.  Most, however, have found this path just too rocky and been forced to choose another.  Even the most successful would say that it is not a relaxing and stress-free career.

Therefore, I would advise anyone who wants to become an advantage video poker player to – at least at first – look at it as a fun hobby, one that will need some start-up capital but might turn into a no-cost adventure that brings much enjoyment.

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Stay tuned and in a few days I will continue on this subject.

So here are some personal stories that people have e-mailed me privately or shared on the vpFREE forum.  Maybe they will give you some good ideas you can use!

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From Anonymous, an example of discipline – and patience – being an important need for a gambler:

At our casino the promotional drawings are on the weekends when there are usually no point multipliers in place.  The drawings usually cover a 10- to 12-hour period.   Without the multipliers in place the games are less than 100% but you have to be present to win. We take our iPads and read while the drawings take place but it takes a good deal of discipline to enter a casino and not play for that length of  time. (I confess that at times we cannot resist the temptation but that is the exception as opposed to the rule).  We have been pretty successful in these drawings but only because we do not lose at the machines while waiting for our names to be called.

[Some might argue that you could use this waiting time to better advantage, but this is a personal choice that works for you – so I won’t criticize it, especially when I don’t know all the details, i.e., how much can you win, are there other gambling activities in your area that would be more valuable, how much pleasure you get from this vs. non-gambling activities.]  

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Here’s one from a Forum contributor who chimes in about “playing for comps.”

Another thing to consider is some players knowingly play under-100% games for the comps.  I don’t live in Las Vegas, so I need a hotel room.  I also need to eat. I consider free rooms, food, drinks and entertainment to be part of my return.  I know that I’m not an advantage player under these conditions, but they are items I would have to pay for if I didn’t play.

At the Hard Rock Hotel in LV, I’m willing to lose money to get a free room, free meal at Mr. Lucky’s, free cocktails and water, and free Motley Crue tickets.  My expected loss will always be less than if I had to pay for all these items at full price.

UNDERSTANDING VARIANCE

By Henry Tamburin

Astute video poker players know that the best games to play are those that have an ER (Expected theoretical return) close to, or slightly over, 100%, using perfect playing strategy. However, there is another characteristic of video poker games that is not so well known but just as important and that’s volatility.

A game that is volatile means your bankroll will experience some nasty up and down swings, and if you are not properly bankrolled, you can easily tap out. We can quantify volatility, and the term most frequently used in video poker circles to do this is variance per coin wagered. Simply put, the higher the variance, the more volatile the game.

Another way to look at variance is this: In the short term, a game that has a high variance means your expected results will more than likely be greater or lesser than the theoretical or expected results. This means a game that has a high variance will most likely result in bigger bankroll swings (both positive and negative); therefore, you’ll need more bankroll to play a volatile game to avoid going broke. (Thus, players with small bankrolls should not be playing video poker games that are highly volatile.)

What makes one video poker game more volatile than another is the amount of the payoff  for winning hands at the top of the pay schedule (the rarely hit hands) vs. the payoff for the hands at the bottom of the pay schedule (the more frequently hit hands). A game that is more volatile (i.e., has a high variance) generally pays more for hands at the top of the pay schedule whereas a game with a low volatility, pays more for hands located at the bottom of the pay schedule.

For example, look at the per coin pay table below for 9/6 Jacks or Better (low volatility) and 10/6 Double Double Bonus (high volatility). I’ve also listed the contribution each hand makes to the overall ER of the game (column labeled % Return). Notice that the variance of 9/6 Jacks or Better (JOB) is 19.51 whereas for 10/6 Double Double Bonus (DDB), its 42.18 (meaning it’s more volatile). The reason the latter is more volatile is that it pays more for 4-of-a-Kind hands (or quads) than JOB. If you get quads in JOB, you are paid 25 coins per coin wagered. With 10/6 DDB, you’ll get paid more, from a high of 400 coins if you get four Aces with a 2, 3, or 4 kicker to a low of 50 coins for 4 5s through Kings (see pay schedule for the payouts for all the quads). More importantly look at the contribution the quads make toward the overall ER for each game. In JOB, quads contribute 5.91% toward the overall 99.54% ER for the game, whereas in 10/6 DDB, the quads contribute 23.51%. The latter is a classic example of a highly volatile game. (Greater payouts in the less frequently hit hands at the top of the pay table). Moreover, look at the return for the more frequently hit two pairs at the bottom of the pay table. In 9/6 JOB, you get paid 2 for 1 for two pairs (contributing 25.86% return) whereas in 10/6 DDB, two pair pays only even money (with a corresponding 12.31% return). This is another reason why 9/6 JOB has low volatility and 10/6 DDB has high volatility.

 9/6 Jacks or Better

* Assuming max coin wagered.

10/6 Double Double Bonus

* Assuming max coins wagered.

Here’s a dollar-and-cents example of why you need more bankroll if you play a video poker game with a higher volatility. Suppose you want to play two hours (1000 hands) on a quarter-denomination video poker machine with a $200 bankroll. By using the Bankroll Function in Video Poker for Winners software, you can calculate what the chance is that you will lose your $200 bankroll (i.e., your risk of ruin) if were to play the more volatile 10/6 DDB vs. the less volatile 9/6 JOB.

The table below summarizes your risk of ruin, or the percent of the time you will go broke in two hours, playing both games. You have only slightly more than a 1% chance of tapping out if you play the low-volatile 9/6 JOB but a whopping 25% of going broke when you play the more volatile 10/6 DDB. (That a sobering statistic … 1 out of every 4 two-hour sessions you will lose your $200 bankroll on average, even though the ER for 10/6 DDB is slightly over 100 percent when you play every hand perfectly.)

This is the reason that players who have modest bankrolls will most likely tap out when playing video poker games with a relatively high volatility. If you have a sufficient bankroll, then playing 10/6 DDB with a 100.07% ER is a great game. How much bankroll do you need? If you take the above example, to get the same risk of ruin as 9/6 JOB (1.28%), you would need a bankroll of $337 for your two-hour session (that’s 68% more bankroll compared to what you would need for the same risk as JOB). (This is what we mean when we say you need more bankroll when playing a game that is more volatile.)

The Table below lists the variance for a sampling of popular video poker games. As a guide, games that have a variance below 21 have low volatility, from 21-50 are medium volatility, and over 50 is a highly volatile game. (You can look up the variance for different video poker games in the book Video Poker for Winners by Bob Dancer, or by using either Video Poker for Winners or Optimum Video Poker software programs. The booklet The Frugal Video Poker Scouting Guide by Jean Scott and Viktor Nacht also summarizes the volatility of different video poker games. )

Summary

1. Video poker games have different volatility.
2. Games that have a high volatility have a high variance.
3. When you play a game with a high variance,  your bankroll will experience higher peeks and lower valleys in your profits  and losses.
4. You’ll need more money if you  play a game with a high variance to prevent going broke.
5. Check the pay table of the game.   If it has higher payouts for hands at the top of the pay table and smaller payouts at the bottom of the pay table, the game is most likely very volatile.

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Henry Tamburin is the editor of Blackjack Insider, a newsletter that focuses on the game of blackjack.  However,  he often included articles specifically on VP and also  on many general gambling subjects that would be of interest to all casino visitors.  Look here for a link to a special subscription sign-up bonus.

One part of that last blog entry that caught a bit of flak was my comment that you shouldn’t call yourself an “advantage player” if your plays are not always 100%+.  Actually I was careful to go on to explain that I was not dissing players who did not stick to positive plays, but I wanted you to be very honest with yourself.  I like the Suze Orman expression “standing in your truth.”   This money guru says you will never be financially stable unless you face all the monetary facts in your whole life.  The same holds true with your gambling life, whatever or wherever you play.  You must analyze every part of your play and KNOW what your edge or the casino’s edge is and whether your bankroll is sufficient for it.  Here just “kinda knowing” is extremely dangerous.

So this series on bankroll and related issues is an effort to help you “stand in your truth.”  Some of you may be casual gamblers who haven’t done much study on your “hobby.”  You may not realize how much information is out there to save you money in a casino.  You may be a beginning casino visitor who wants to learn more of the facts so you can eventually become more skilled.  And some of you may be former “advantage players” who are transitioning to “just recreational players” because you still want casinos to be a good vacation/leisure time option even when the VP offerings have gone south.

Everyone whose main goal is entertainment wants to find ways to stretch their bankroll and extend their “fun time.”  Those who are or aspire to be “advantage players” will want to find every piece of information they can to achieve their high goals.  We all can use help!  Let’s help each other.   I hope to see many “Comments.”

First, players are forgetting or straying away from the basic building block:  playing ONLY when you have an advantage.  You need to change your goals – and rename your hobby –  if you decide to play  – for whatever the reason –  when you do not have the advantage.  I’m not saying that is a bad thing IF you are doing this with your eyes wide open and you can afford purely recreational play.  But don’t try to fool yourself in thinking that you are still an advantage player. 

But even those who are sticking with that basic advantage-player premise, some seem to be forgetting another basic truth:  you must look at the LONG TERM and not be discouraged at the inevitable short-term losing streaks.  And I believe the cause for this anguish among even skilled VP players  is that the lower the edge you have on the casino, the longer the long-term will be AND the bigger the bankroll you will need to survive.

I’m going to talk about this subject more in future blog writings as there are many facets to these issues.  Today I want to share a good article on this subject that zeros in on the role of the royal flush and how it impacts your short-term results.  This was written by my good friend and fellow gaming writer, Henry Tamburin, the author of five books on casino gambling, featured blackjack writer for dozens of magazines and web sites, and editor of the Blackjack Insider Newsletter.   He is also an avid video poker player.

UNDERSTANDING ROYAL FLUSH CYCLES IN VIDEO POKER

by Henry Tamburin

 One of the most misunderstood concepts in video poker is “the royal flush cycle.” It’s important if you want to be successful at video poker that you understand what this is, and how it can affect your bankroll.

A royal flush cycle is the mathematically calculated average number of hands it takes to hit a royal flush using perfect strategy. The number of hands in a royal flush cycle varies slightly from game to game. For Jacks or Better, the royal flush cycle is 40,391 hands, whereas a Full Pay Deuces Wild game it’s 45,282 hands (See Table 1). Why is there a difference in the number of hands? Because in some games, the playing strategy calls for holding more two- or three-card royal flushes (than other games); therefore, you will get more royal flushes.

Table 1

Royal Flush Cycles

Most players expect to hit one royal flush after playing roughly 40,000 hands. That is not necessarily the case. The math says on average you will hit a royal flush once in every 40,000 hands, which means for a whole bunch of sets of 40,000 hands, you’ll average one royal. In other words, in any given one set of 40,000 hands, you could wind up with more than royal or, heaven forbid, possibly no royals. (Would you care to guess what the chances of the latter catastrophe occurring? Keep reading for the answer.)

There is a mathematical formula that you can use to calculate the probability of hitting any number of royal flushes in any number of cycles (the formula is called the Poisson Distribution after the French mathematician Simèon Poisson, who developed the formula in the 19^th century to calculate the probability of rare events). Don’t worry …you (or I) don’t have to take out our calculators because my friend and fellow video poker author Dan Paymar (creator of Optimum Video Poker software trainer) has done the work for us. The calculations yield the following results for one cycle of 40,000 hands (Jacks or Better):

Table 2

Probability of Hitting a
Royal in One Cycle

Wow! If you look at the data in Table 2, it says that you have the same 36.8% chance of getting one royal or no royals after playing one cycle of 40,000 hands. Since the royal flush contributes 1.98% toward the overall 99.5% ER for jacks-or-better, your return between royals is only 97.5% (meaning that your bankroll will more than likely head south from one royal flush to the next one). This, dear readers, is why you must have enough bankroll to play video poker … to cover those times when you play many hands without hitting a royal.

Have I ever played one cycle and not hit a royal? You bettcha and it was painful. I keep records of all my playing sessions and the worse streak I ever had was about 135,000 hands without a royal flush. Even though that was painful (for my bankroll and me), I have friends who play video poker that have gone way more than 135,000 hands between royals (ouch!).

However, let’s be optimistic and look at the other side of the curve. I recently played roughly 40,000 hands of 9/6 Jacks or Better (one cycle) in Las Vegas and I hit three royal flushes. Was I lucky? According to Table 2, the chance of hitting three royals in one cycle of Jacks or Better is a paltry 6.1%. So yes, I would consider myself very lucky to have hit three royal flushes during this trip.

The data in the above table also leads to this conclusion: You have about a 63% chance of hitting one or more royal flushes in one cycle and only a 36.8% chance of hitting no royals (does that make you feel any better?).

Do you think it’s impossible to play 200,000 hands of Jacks or Better (five cycles), which many video poker aficionados consider to be the “long term,” without hitting one measly royal flush? I hate to be the bearer of bad news but according to the data in Table 3, you have a 1 chance in 140 (0.7%) of not hitting a royal flush even after playing 200,000 hands (or roughly 400 hours of play).

Table 3

Probability of No Royals after X Cycles

The percentages in Table 3 are scary. You have a 5% chance of getting no royals after 120,000 hands (3 cycles), and 1.8% chance after 160,000 hands (5 cycles). Even though the chance of winding up without a single royal flush are slim, if it were to occur, it could be financially catastrophic (especially if you don’t have enough bankroll to weather this remote, but still possible, outcome).

The reality for video poker players is this: In any one royal flush cycle of roughly 40,000 hands, there are no guarantees that you will hit exactly one royal flush. If you are lucky, you could get more than one royal flush, and if unlucky, you could wind up without any royals (this is why having enough bankroll to play video poker is very important).