Giving Thanks

            I apologize to those of you who have been looking for my column the past couple of weeks and couldn't find it.  As some of you may have heard by now, my mother (and wife of Lenny Frome), passed away two weeks ago.  After the funeral, my brother recounted a story to me that I had never heard before.

            When my father passed away in 1998, my brother was the first one who headed out to Las Vegas to be with our mom.  It took a day or two before all the arrangements were made for them to come back East for my dad's funeral.  Yet, of course, they still had to eat.  My brother asked my mom where she wanted to go to dinner and she responded with Hugo's Cellar at the Four Queens.  My family had already made that a regular dinner spot when anyone came to town - and it is a tradition that carries through until today. 

            As they walked through the casino from the parking garage to the restaurant, they passed by two women playing video poker.  They were each holding a copy of one of my dad's books.  My brother said he could not have staged it any better if he tried.  This was clearly a sign.  My father's impact to the industry would continue long after he was gone.

            My father was informally called "the Godfather of Video Poker" by many in the industry.  To be sure, he played NO part in the invention of the game.  At the same time, no one can deny the impact he had on popularizing it.  Even if you are not a video poker expert or even a regular, I can't help but imagine that your play isn't just a tiny bit better from having read his articles - or any of the numerous writers who came after him - including me!  Would video poker have had the staying power if there wasn't someone telling the early Players how to play it?  Would video poker have eaten up as large a percentage of the casino floor as it does today?

            Of course, my father could just have easily been called "the Godfather of Proprietary Table Games".  He had a hand in the development of Let It Ride, Three Card Poker, Spanish 21 and Caribbean Stud Poker.  At their respective peaks, there must have been a combined 2500-3000 of these tables.  As I consider myself an extension of my father's work, we can add on Ultimate Texas Hold'em, Mississippi Stud and a host of smaller games to the total.  This brings the total to perhaps as high as 4000 proprietary tables that my father directly or indirectly had a hand in.  Imagine the casino floor without any of these games.

            While my father was the public face of everything that went on, everyone that knew them (both personally and professionally) knew that my parents were always together.  My dad brought my mom to business meetings to size up the potential client.  My mother was the proofreader for all of my dad's books and booklets.  She was responsible for shipping orders and for the accounting.  In fact, it was my mother who was always listed as the "President" of their company. 

            With the help of Catherine Jaeger, the editor of Midwest Gaming and Travel, we have launched a campaign to get my father into the American Gaming Association's (AGA) Gaming Hall of Fame in 2012.  No disrespect to Blue Man Group (one of the inductees for this past year), but I truly believe Lenny Frome's impact on the industry has been far greater.  To this end, we are asking people to write to the AGA and urge them to induct my father into the Hall of Fame in 2012.

            There are a number of ways to make your voice heard.  You can copy the sentence below or use your own experience to explain why you believe the time has come for Lenny Frome to be inducted into the Gaming Hall of Fame. "Because of his many significant contributions to casino gaming, I respectfully request your consideration of Lenny Frome for induction into the Gaming Hall of Fame."

Mail it to:
American Gaming Association
Frank J. Fahrenkopf, Jr., President/CEO
1299 Pennsylvania Avenue, NW, Suite 1175
Washington, DC 20004

Online:
E-mail to:
Brian Lehman/Communications Manager-AGA
blehman@americangaming.org
Facebook: www.facebook.com/AmericanGaming

            Over this Thanksgiving weekend, my family and I one again dined at Hugo's Cellar.  This time, for the first time we toasted the memory of both my father and my mother.  My dad may have been the "Godfather of Video Poker", but most importantly, they were the "Father/Mother and Grandfather/Grandmother of the Frome family."  Once again, they are "always together."

Beating the Casino

            

            A couple of weeks ago, I discussed how a blogger lamented how the last good table game invented was blackjack because none of the games invented since gave the Player a chance to beat it.  I would argue that blackjack is hardly 'beatable'.  It requires an incredible amount of discipline and knowledge of card-counting schemes in order to eke out even the slightest edge.  With the continuous shufflers and regrettably 6 to 5 payouts on blackjack, even with the most sophisticated counting scheme, beating the game is almost impossible.

            There is only one game on the casino floor (barring the occasional game that accidentally makes it to the floor) that is readily beatable.  That is video poker.  There are games all are over Las Vegas with paybacks of over 100%.  If you learn the proper strategy you can earn these paybacks.  I will not, however, promise that you will become filthy rich off them.  Unlike card-counting schemes which would allow you to bet $5 when the count is against you and perhaps $5000 or more when it is in your favor, video poker machines essentially have a constant wager and there are no known counts for you to track.  Each hand is completely random and no matter how many hands you have won or lost in a row, the next hand is still random.

            Over the years the casinos have caught on to this idea and this is why many are still willing to put machines on their floor with paybacks over 100%.  They simply don't put them on the floor with high denominations.   If you are willing to play video poker 40 hours per week (like a job), are able to play 700 hands per hour, you would play 1,456,000 hands per year (approximately).  If you played a quarter machine, you would wager the staggering sum of $1.82 Million per year.  If you can play the entire time on a full-pay Deuces Wild machine paying 100.76%, you'll earn about $13,800 per year.  This doesn't account for any taxes and doesn't account for any cash back and/or comps.  

            Of course, some of you will just suggest playing a higher denomination.  Even playing dollars, the annual 'salary' will get to only $55,000 or so.  This is certainly not a bad income.  Of course, this most certainly doesn't mean you can count on any sort of regular 'paycheck'.  There are going to be weeks you lose and there are going to be weeks you win far more than average.  And, as I said earlier - the casinos have caught on to this.  According to my research, there are no $1 machines playing full-pay Deuces Wild in the Las Vegas area.  So, the casinos are willing to let the resourceful Player make some money, but not enough to really entice large numbers of Players to do them harm. 

            This is also further proof that video poker machines are not slot machines.  Casinos would NEVER allow banks of 100+% slot machines to exist.  Slot machines require no strategy.  Thus, as long as the slot machine were to be played for 40 hours per week the casino would be paying out the $13,800.  To the casino it doesn't matter if this is one person, 10 people, 100 people or 1000 people who wind up winning this money.

            Video poker requires that the Player learn the proper strategy to earn this money.  So, if 52 people took turns playing for 1 week and played using Expert Strategy, then the casino would still be paying out the $13,800.  But the casinos know this is highly unlikely.  Despite strategies for virtually every imaginable game being available for 10-20 years, the overwhelming percent of Players simply choose to ignore the proper strategy.  The reality is that 50% of the Players probably know of no real strategy and just muddle along - playing a Deuces Wild game at no better than a 95% payback.  Perhaps another 25% play using some rudimentary strategy that they learned somewhere and play at 97%.  Another 15-20% have made real attempts to learn strategy but haven't really mastered it and can play at 99%.  The final 5-10% have learned the proper strategy and make a significant attempt to play properly.  Perhaps half of this group truly attains a payback of 100.5% or better.

            The result for the casino is that their machine probably pays out at no more than 96.5% in total.  A number that they can definitely live with.  However, just as the casino doesn't care if it is 1 or 1000 Players that win the $13,800, you do not have to be concerned with how any other Players do.  The casino is very happy with that machine that pays back 96.5% and will net them more than $65000 per year - EVEN if it means one of the Players made a few hundred or thousand over the course of the year.

            But, if you want to be this Player, you have to learn how to play video poker using the proper strategy.  To help you along the way, we're offering up our two full-length books for just $5 each (which includes postage and handling).  Winning Strategies for Video Poker includes strategy tables for 61 of the most common games found anywhere.  America's National Game of Chance: Video Poker is 200 pages of Lenny Frome's best articles, stories and quizzes and is an excellent way to learn how to play video poker in an easy to understand way.

            Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133 and you'll be on your way to becoming an Expert Video Poker Player.

The Godfather of Video Poker

The November issue of Midwest Gaming and Travel is a tribute to my father, Lenny Frome.

I'd like to thank Catherine Jaeger (the editor) for coming up with this idea and using it as a means of launching a campaign to have my father inducted into the American Gaming Association's Gaming Hall of Fame.  Here is a little bit more about this campaign - Make 2012 Lenny's year!

My father changed the landscape of every casino in the world by helping to make video poker as popular as it is.  He also provided the original analysis for games like Let It Ride, Three Card Poker, Caribbean Stud Poker and Spanish 21.  Imagine the casino floor without any of these games.

Below is a link to the article I wrote for Midwest Gaming and Travel about my dad.

The Godfather of Video Poker

Video Poker Progressives

            A couple of weeks ago, I described in detail how the math behind Progressives work.  In that column, I mentioned how video poker progressives works just a little different.  There are still two paybacks to be concerned with - the long term theoretical that the casino is concerned with and the specific payback at any point in time that should be the attention of the Player.  The majority of the calculation is still the same in that we multiply the payout of a winning hands by the frequency of the winning hands  and sum up these values.

            What is different about video poker is that the frequencies of the different winning hands can vary as the amount on the meter changes.  For those of you who are video poker Players, this should be no surprise.  For years, I've been telling you that a single unit change in the payout of a hand not only changes the payback but can change the strategy.  Each time you change the strategy you potentially increase the frequency of some hands at the expense of others.

            As a very simple example of this, imagine how the strategy changes as we go from a standard full-pay jacks or better machine to a Double Double Bonus machine.   Because the payout for Four Aces is so high, we actually find that the Player should discard Two Pair in favor of a single Pair of Aces.  This will obviously reduce greatly the frequency of Two Pairs and Full Houses and increase the frequency of Three of a Kinds and Four of a Kinds. 

            So, it should be no surprise that as the jackpot for a Royal increases above 800 that the strategy will begin to shift.  Hands with the potential to be a Royal will have their expected values increase.  This will lead to more Straights, Flushes and of course Royals and the expense of Pairs, Trips and Quads.  Of course, we will also throw away a variety of partial Straights or Flushes to go for the Royal, so this will work against the Straights and Flushes and might increase the number of High Pairs. 

            Thus, pinpointing the exact frequencies can be a bit tricky.  Fortunately, the far easier of the paybacks to determine is the payback at any point in time.  This is because at any point in time, we can know the exact amount of the Progressive jackpot and use this number to determine the exact strategy and in turn the exact frequency of each hand.

            The most common video poker Progressive is an 8-5 machine, meaning it pays about 97.3% when the jackpot is reset to 800 (per unit wagered).  At this level, the frequency of the Royal is about 1 in 40,200 hands.  If the jackpot were to climb to 1600 (per unit wagered) then the payback of the game will go up to about 99.5% and the frequency of the Royal goes up to 1 in 32,700 hands.

            Of course it is rather unlikely that you're going to see a Progressive for a Royal get this high.  With only 1% of the amount wagered (at most) going to the meter, the average amount that will be added to the Progressive Jackpot is somewhere between $327 and $402 (1% of the previously mentioned frequencies).  Of course, something that can occur 1 in 40,000 hands or so can easily occur every 10,000 hand or 80,000 hands.  So, it is not impossible to see the progressive meter go to 1600.  It would have to go to about 1800 for the game to become positive (payback over 100%).  This is not impossible, but not very likely.

            As the payback goes up, the strategy changes and the frequency of the Royal increases, making it harder and harder for the jackpot to keep increasing as the likelihood that it gets hit goes up.  Because of this, it is a bit harder to calculate easily the long term theoretical payback.  It is reasonable, however to approximate it using the same process used for regular progressives.

            In this case, I would take the frequency of each hand using the reset value of the jackpot and multiply each by the payout of the hand and sum these up.  Lastly we would add the percent of each wager going to the jackpot to the total.  This means that the long term theoretical payback of a Royal paying 8-5 with an 800 unit reset amount is about 98.3%.

            I have to admit, if I were designing a paytable for a video poker progressive, I would probably make the likelihood of the game going over 100% a bit more common.  I think it would be a lot of fun to the frenzy that would/should occur each time the payback at any point in time goes over 100%.

            

Vintage Lenny Frome - A's and 8's

When I have time I'm going to try and post up some of my father's (Lenny Frome) articles here as well.  The following article is about a rarely found (but I'm told there are still a few 50-cent machines at Circus Circus) version of video poker - Aces and Eights.  Its payback is about 100.25%.  This article is probably 15-20 years old, so some of the information may be dated:

Aces and 8's--From Green Felt to Video  

             Long, long ago before the world played Video Poker, the story of Aces and Eights, the dead man's hand was abroad in the land. It always conjured up a mental image of evil-- a hand that brought fear into the hearts of men, even the roughest, who made a living with the pasteboards and reckless gun slinging.

             Leave it to the enterprising folks at CircusCircus to capitalize on this theme and then carry it out in high-tech fashion under their big top. They have come up with a sure winner in Aces and Eights, a 100% payback machine featuring four progressive Jackpots as added attractions which will frequently push the payback into positive territory.

            The pay schedule  is very straight-forward for a multi-progressive (or is it just that we are getting adjusted to the new regimen in such lengthy tables?)  It is an 8/5 schedule Jacks or Better with these four bonuses to offset the 2.3% shortfall vis-a-vis full-pay 9/6ers:

·         Four 7's pay 50 for 1 on 1 to 5 coin-play non-progressive.

·         Four 8's or Four Aces pay on a single progressive which resets at 80 for 1 (5-coin play only).                

·         A Royal Flush pays on an 800 for 1 minimum progressive jackpot.

·         Sequential Royals (either way) pay on a 10,000 for 1  minimum progressive

Looking at the payback situation, these bonuses work into the picture this way:

            Four of a Kinds in any one specified suit occur on average only  once in 5,500 hands; a regular Royal once in 40,000 and in either    sequence once in 2,400,000 hands.  The extra 25 on the 7's adds .47%. The extra 55 on the 8's adds a  minimum of 1% as does the extra 55 on Aces. The Sequential Royal gives us an extra 9,200 which is worth .38%. As the meters climb  upward the value of these jackpots further increases the payback. Together, these bonuses,  take the payback up from 97.3% to 100.15%. With some minor changes in strategy, we can pick up a little bit more.

            The first time we saw this machine, the Sequential was posting $13,204, the Royal  $1,030 and the Four Aces or Eights a whopping $154. The game was close to 102% payback. While watching it, the jackpot was hit on 8's by one of the players seated at about 50 machines on the floor.  The Aces/Eights progressive had gone an unusually long time since the last hit. We cannot expect many such generous jackpots. Frankly, we were genuinely surprised when the meter reset at $100, since that is more than three times the 25 for 1 normally paid on quads.

            Even with this liberal machine we need all the savvy we can muster to play the game expertly. The extra value of Aces and 8's dictates these modifications in the ranking order of 8-pairs: Even at minimum meter value of $100 on a quarter game (80 for 1), the pair of 8's is better than a 4-low-card flush and at $120 beats those 4-card flushes with two high cards.

            Incidentally, the player who hit the $154 would have been right in breaking up 8's full to go for the quads. I'm happy to report that it wasn't necessary to wrestle with that problem--but if it were you, what would you have done?

 

Don't Be Foolish!

            It was almost a year ago that I launched this blog (gambatria.blogspot.com).  I was very nervous about launching it.  If there is one thing I've learned about the internet over the years is that pretty much any idiot can have a blog - and quite frankly, I didn't want to be 'any idiot.'  I'd like to think that the name "Frome" is the gold standard in the industry where math analysis is concerned.  To our credit, we have Three Card Poker, Let It Ride, Caribbean Stud Poker, Spanish 21, Ultimate Texas Hold'em, Mississippi Stud, Imperial Pai Gow and countless sidebets.  That's a lot of the casino floor whose math was done by Leonard Frome or Elliot Frome. 

            So, I was quite surprised this past week when I came across a financial blog that was very unimpressed this year's G2E where table games were concerned.  Admittedly, I did write a column last year that called on more inventors to display their ideas at the G2E.  I recognize that the cost of even a small booth can be rather prohibitive for the individual inventor, but what a great opportunity to show your game to people in the industry.  I was pleasantly surprised to see at least two new inventors displaying their games and larger booths from some of the more established companies.

            What I found amazing about this financial blog, however, was not that the writer looked over every game and found none of them to his liking.  That would've been one thing.  Instead he essentially takes table game companies to task for "designing games that the gambler has no hope of beating, but they force the gambler to take the time to learn how to play them!"  This blew me away!  Does he truly expect the casino to introduce games that the Player can easily beat?  That's not going to happen.  The only game that has ever been put on the floor that can readily be beaten are certain variations of video poker. 

            Further, our blogger is annoyed that you have to take time to learn how to play them.  The only game which requires ZERO time to learn how to play them is perhaps slot machines.  As I've recounted in my column many times, I can't even figure out when I've won or lost anymore in today's video slots, but since all you need to do is press the 'spin' button and we can assume that the machine will properly tally your win or loss, I assume this meets the requirement of not needing to take time to learn how to play them.

            Thus, we can conclude from our blogger that what he is looking for is a slot machine with a 100%+ payback.  Perhaps he should've read my column from two weeks ago where I talked about a company that provides the payback information for their slot machines.  This WOULD necessitate learning how to use the smartphone 'app', so I don't know if this meets his strict criteria.

            A couple of days after this first column appeared, our blogger was back with more information for us.  First, he repeats some of his thoughts from the previous column, decrying the lack of innovation from table game companies and then stating, "how the gaming industry has not seen a blockbuster table game since blackjack, and how the industry may not see one until somebody steps up and creates a game that is theoretically beatable."

            That is quite a statement.  According to Wikipedia, blackjack's origins may be as much as 400 years old.  The game as it is played in most jurisdictions is hardly beatable - or at least not easily.  Yes, we're all aware of the MIT team that did it, but this took a rather significant effort on the part of a focused group of individuals. 

            In 1991, the table half of the casino floor consisted of nothing but blackjack, craps and roulette.  Twenty years later, it is estimated that as much as 15-20% of the tables in the U.S. market may be those that were invented AFTER blackjack.  Twenty years from now, I have little doubt that blackjack will make up an even smaller percent of that floor.   Let's not forget that a blackjack table is essentially FREE to the casino while they have to pay to put a proprietary table game on their floor.

            As a gaming analyst - and one that focuses mostly on table games - I am keenly aware of the math of the games.  Most of the newer games that are being introduced have paybacks in the higher 98% to low 99% range.  Yes, they do require that you 'learn' how to play them to achieve these paybacks.  No one, not myself, not the inventors nor the casinos will try and let you believe that the games are beatable in the long run.  That does NOT, however mean that you cannot have winning sessions in the short run and enjoy the entertainment value that they can provide.  Most table games are developed to have the Player win about 35-45% of the time over a 3-hour session - assuming you are willing to 'take the time to learn how to play them'

            Best of all, I won't "force" you to do this, but I'll give you the opportunity to!  There are now 7 books in the Expert Strategy series for table games (Let It Ride, Three Card Poker, Four Card Poker, Spanish 21, Caribbean Stud Poker, Mississippi Stud and Blackjack Switch) and for a limited time, you can order the entire set for $20 which includes postage and handling.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

            

Progressing

            Last week, I alluded to the seemingly complex math associated with games that offer progressive payouts (i.e. "progressives").  Progressives are games where the top pays are not fixed dollar amounts or odds payouts, but rather have variable payouts that increase as more wagers are made since the last time the prize was won.

            Progressives have become very popular for table games sidebets.  They have long been used for some video poker machines for payouts on Royal Flushes.  Most commonly they are found on slot machines, which love to use a progressives ability to create a very large payout for a very rare occurrence.  As is always the case with a random event, the cycle between hits can frequently become far larger than 'average' and thus create an even larger than normal jackpot.

            As I described last week, Progressives essentially have two different paybacks.  The first is the long-term payback which is what concerns the casino.  The second is the payback of the wager at any point in time which is what should concern the Player.  Let's take a closer look at how these are calculated and why there are two different paybacks.

            Normally, to calculate payback, we take the frequency of a winning hand, multiply it by the payout of this hand which gives us the contribution rate for the hand.  We then sum up these contribution rates to arrive at the overall payback.  For most wagers, the frequency of a particular winning hand is fixed as it is unaffected by strategy.  So, if we are playing Caribbean Stud Poker, we don't have to worry about the strategy of Folding and Playing for the sidebet because you would never Fold a hand that is strong enough to earn a bonus.  Video Poker presents an additional challenge in that you can alter you strategy depending on the payouts and thus alter the frequency of winning hands.

            So, to calculate the payback of a Progressive at a particular point in time, we follow the calculation I just described.  For example, let's assume the following paytable at a particular point in time for a $1 wager:

Hand	Pays (For 1)
Royal Flush	$113,473
Straight Flush	250
Four of a Kind	50
Full House	10
Flush	7
Straight	5
Three of a Kind	3
Two Pair	2

           

            If we perform the calculation described, we get the following:

Hand	Frequency	Pays (For 1)	Contribution Rate
Royal Flush	0.00015%	$65,473	10.07680%
Straight Flush	0.00139%	2500	3.46292%
Four of a Kind	0.02401%	250	6.00240%
Full House	0.14406%	50	7.20288%
Flush	0.19654%	20	3.93080%
Straight	0.39246%	15	5.88697%
Three of a Kind	2.11285%	10	21.12845%
Two Pair	4.75390%	5	23.76951%
Total	7.62536%		81.46074%

            So, if you were to walk up to a table and see these payouts, the payback of the game at that very point in time is 81.46%

            But, the payback to the casino could be vastly different.  Let's assume that the Royal Flush is seeded at $50,000.  This means that every time someone wins the jackpot, the prize for the Royal Flush will be reset to $50,000.  Further, let's assume that for every $1 wager that is made, the Progressive increases by 10 cents (i.e. 10% of the wager).

            There are two changes that we must now make to calculate the payback for the casino.  The first is that we always use the seed amount as the payout for that hand.  Thus, we repeat the calculation shown above but we use $50,000 as the payout for the Royal Flush.  This is the amount that the casino itself directly paying out each time the jackpot is won.  When we do this, we find that the payback of this wager is 79.08%.

            However, we must now ADD to this payback the amount of each wager this added to the Progressive meter - in this case 10%.  Eventually this 10% will go back to a Player.  It might happen while the jackpot is at $50,000.10 or it might happen when it is at $120,000 or more.  From the casino's standpoint, it doesn't matter.  That 10% belongs to the players.  Essentially all the Players that don't win the jackpot are handing those dimes to the person who finally does.  So, when we add that 10% to the 79.08% we find that to the casino this wager really has an 89.09% theoretical payback.  Over time, the casino will keep 10.91% of every dollar wagered.

            So, if you were to play this wager while the Jackpot is $65,473, you would actually be playing it on the 'low side' of the average jackpot.  How big is the average jackpot?  To calculate that, we take the average number of hands between jackpots (in this case 649,740) and multiply it by that 10%.  On average the jackpot will grow by $64,974 before it is hit.  We add this to the seed amount and find that the average jackpot will be $114, 974.  At that point, the payback of the wager is the same as theoretical payback of the wager. 

            If the jackpot grows to be above $185,930 (which is very likely at times), then the payback of the wager at that point will actually be OVER 100%.  The only problem with this is that it will only be over 100% for the ONE person who actually wins the jackpot.  Everyone else will just be feeding dimes to the one person who wins.