Thursday, October 31, 2013

Video Poker Primer

            It was just over 10 years ago that I started writing for Gaming Today.  I have to be honest, that really blows me away.  That means I've written roughly 500 columns when I take into account off weeks and the fact that for the first 6 or 9 months, my column was bi-weekly.  I remember when I wrote my first few columns, I would wax poetic about how my father (Lenny Frome) had written nearly 1000 columns for a variety of different publications.  I remember when I hit column number 100, I remarked how far behind I was.  Now, my total count is probably about 600-700 columns and I can almost see myself someday surpassing my dad's total.  That said, I definitely don't plan on taking steroids or PEDs to get me there.

            Part of what is so amazing about having written 500+ articles is that I have somehow managed to come up with that many things to write about.  I'm not really sure that there are 500 unique subjects to write about.  I have to remember that if I borrow a subject from 2005 that there is a strong likelihood that if someone reads it today, they didn't read that article from 8 years ago.  So, in that spirit, I'm going to start back at the beginning today and discuss some basics about video poker.

            Video poker is truly a unique game in the casino.   Far too often it is lumped together with Slots, but there is little in common except for the technology.  I don't think of a video blackjack machine as a slot machine and the same is true for video poker.   As the world starts turning more to online gambling, the separation will no longer be about the technology.  Instead it should be about the essence of the game.  Video Poker is a game that is based more on skill than almost any other game in the casino.  This doesn't mean that luck doesn't play a part, especially in the short run.  But, if I were to challenge a random Player to a slot competition, there would be no way to gain an advantage.  If I were to challenge a random Player to a video poker competition, I'd like to believe that I would have a distinct advantage.  The longer the competition runs, the more strategy and skill will rule the day and the less that luck will impact the results.

            How is video poker a game of skill?  Because the Player must make a decision that will clearly impact his results.  This decision is frequently NOT of the 'no-brainer' variety.  Technically, in the game of Casino War, the Player must make a decision to - whether or not to go to War when the Player and Dealer tie.  But, the proper decision is the same all the time - to go to War.  So, while technically, there is 'strategy', I doubt very many people get this one wrong.  In Three Card Poker, there is one strategy decision - to Play or Fold.  The decision is also relatively simple.  If the Player has Q-6-4 or better, he should Play.  As simple as this sounds, many Players don't follow this rule (and I don't mean that they go with Q-6 or Q or better), and as a result, they give up a larger portion of their bankroll to the casino than they need to.

            Video Poker strategy is far more complex than this.  First of all, the decision is not one of Fold or Play, but rather which cards to Discard.  There are 32 ways that a Player can make each of these decisions, ranging from keeping them all to discarding them all.  Granted many of these possibilities will fall into the brainless category.  If you are dealt Three of a Kind and two off-suit kickers, which cards to discard is pretty obvious.  If you are dealt a Straight, then you don't have to discard at all.  Oh wait, what if it is also a 4-card Straight Flush or a 4-Card Royal, then what is the proper play?

            If you are dealt the following:

4♦        4♠        5♠        6♠        7♣

the decisions get a bit more complex.  You might keep the Pair of 4's, or the 4-Card Straight or maybe the 3-Card Straight Flush.  This is 3 of the 32 ways the hand can be played.  The other 29 are quickly discarded, so there isn't a need to go through 32 possible decisions for each hand.  Obviously, you're not going to keep the off-suit 4-7 in this case.

            Unlike table poker (which involves even a higher level of skill), the strategy in video poker is based strictly on math.  You don't play hunches and you're not trying to beat another Player.  You don't have to worry that you might pull your Straight and he might come up with a Flush.  All that matters is the likelihood (aka probability) of each final hand and how much that hand pays.  But, I'll leave that for next week.  For now, I'll be happy if I've convinced you just a little bit that video poker is not slots.


Thursday, October 24, 2013

Buy More Tickets

(*Note: this column was written on the 3rd day of the recently completed government shutdown)

            As we finish Day 3 of the government shutdown, it is hard to find a news story that is about anything else.  I was pleasantly surprised (initially) when my eye caught a story on Yahoo's main news page that dealt with lotteries.  Apparently, they were revealing the secret of how to win the Powerball Lotto.  Who doesn't want to win Powerball?  I read the article, which was all of about two paragraphs. 

            It began by talking about last month's sole winner, who won $400 million.  He 'beat the odds' by hitting the lottery which is a 1 in 175 million chance (I'll take their word for this).  Per the article, the odds of getting struck by lightning is a mere 1 in 10,000 (again, I'll take their word for this).  Finally, the article gets to the important question "How can you increase your chances of winning the lottery?"  Then they apparently provide the way.  A statistician in Louisiana has discovered that certain numbers come up more often than others!

            The most frequent powerball number is 20.  The most common white ball numbers are 42, 16, 35, 26 and 19.  There you have it.  The winning numbers!  So, to increase your changes all you need to do is play these 5 numbers with the number 20 and you can start spending your millions!   I didn't actually look up the historical winning numbers, but I'm going to take a strong guess that this particular combination has NEVER come up before, but undoubtedly they are on their way.

            Now, nothing in this article gives the actual frequencies of these numbers.  Nothing shows that they show up an abnormally high amount of times.  Let's assume that Powerball has been drawing twice a week for 20 years.  That is 2000 total draws.  That is 10000 numbers drawn (white balls) and 2000 red balls drawn.  There are 59 white numbers and 35 red balls.  On average each white number should be drawn 169.4915 times.  So, for all we know the 5 numbers he cited showed up 170 or 171 times while the rest of the numbers showed up 169 times.  Clearly a massive statistical edge!   On the red balls, the average is 57.14.  So, 20 may have shown up a couple more times that all the others.  Again, a clear statistical advantage!

            I've always been strong at math.  I realize not everyone is.  I don't expect everyone to be.  But, bad math packaged as an article on the front page of Yahoo news really drives me absolutely nuts.  To add insult to injury, the article went on to suggest you should buy your ticket in Pennsylvania because that's where the largest number of winning Powerball tickets have been sold.  It doesn't even take into account the possibility that more tickets have been SOLD in that state than many others! 

            I've often said (semi-jokingly) that the world's largest casino is the stock market.  But, there is one critical way that the stock market greatly differs from gambling.  With stocks, past performance CAN BE used to determine the likelihood of future performance.  While there are no guarantees, there are likelihoods.  A stock that has paid a dividend for the past 100 years is not likely to stop paying it next year (barring any specific news being known).  Stocks have their ups and downs, but you are NOT really dealing with random events.

            The same cannot be said for what happens in a casino (or a lottery).  The last 3 numbers on the roulette wheel could've been red and the likelihood of the next number being red will still be 18/37 (or 38).  The last 10 numbers could've been red and the probability will STILL be 18/37 (or 38).  The last 5 hands of video poker could've contained the 2 of diamonds in the initial deal and the probability of it showing in the next hand's deal will still be in 5 in 52.   Nothing changes when we are talking about the lottery.  It does not matter if one number has appeared more often than others.  Next week's numbers are completely random and each number has the same probability of being drawn as the next. 

            Okay, I'll admit it.  Maybe I'm just jealous that after a decade of writing for Gaming Today, Yahoo has not covered a single one of my columns, but some guy writes a complete nonsensical piece of useless information and that makes their front page.  The sad part will be how many thousands of people will read that article and actually run out to play those numbers.  There is only ONE way to increase the likelihood of winning the lottery - buy more tickets. 

Thursday, October 17, 2013

Imitation is the Sincerest Form of Flattery

            A couple of weeks ago, I two days walking the halls of the Sands Expo at the Global Gaming Expo.  If I had to pick one word to describe the event, it would definitely be "SLOTS".  Like last year, I think they dominated the show.  For those who have been reading me for years, you know my thoughts on Slots from a Player's perspective.  But, I do give the slot manufacturer's a lot of credit for creativity.  This year, they kept it up, not only in the games that are being developed, but in terms of the marketing.  There were zombies everywhere.  I'm not sure if there was only one manufacturer who had a zombie themed game or if there was more than one.  But there were a lot of zombies in some really good make-up all over the halls.

            As much as I write about video poker in my column, my real love is table games and that's what I'm at the show to really see.   This year, brought a particular trend to its apex (or perhaps more appropriate, its nadir).  Besides the three big table game companies (SHFL, Galaxy and DEQ), there were virtually no new table games.  I did see a couple of other new games, but they were almost afterthoughts from gaming companies involved in other aspects.  I saw exactly ZERO small independent game inventors showing any new games.  I recognize that the cost of a booth at the G2E is not cheap and could easily wipe out the budget of a small inventor, but I always found it fun to talk to someone new about their game.  I didn't get a chance this year.

            I did get introduced to a few inventors who did not have booths at the game who wanted to talk to me about their ideas.  I find that most ideas seem to fall into two categories.  The first is the rather 'far-fetched' category.  These are ideas that aren't necessarily bad, but I have to wonder about their odds of commercial success.  One inventor remarked to me about how all the casino games are poker-based.  He found this to be problematic.  I find this to be indicative of what is likely to be successful commercially.  It is NOT that games that are not poker based haven't been invented and tried, it is that none have ever had the staying power in the casino.  Some might be fun and social for a few hours, but they don't seem to have the ability to create repeat customers the way poker-based games do.

            The second common category of games are the copycats.  People look at a game like Three Card Poker, which is undeniably the most successful proprietary table game (both financially and in terms of number of tables) and try to emulate it in some way.  Now, many table games have some form of patent protection on them (many do not!).  But I am not talking about copying to the point of patent violation.  I'm simply saying that people look at Three Card Poker as some magic formula and try to replicate it.   You know this is happening when they begin describing their game with "It is just like Three Card Poker but......."

            For the past several years, the casinos have been going through a Texas Hold'em craze.  While I think it has peaked overall, it has still left a lasting impression.  Games that might have been developed as 7-card Stud games are being developed with 5 community cards in Texas Hold'em style.  After the dust settled, there are currently 2 very successful Texas Hold'em table games.  The first is Texas Hold'em Bonus Poker - developed by Mikohn/PGIC and purchased by SHFL Entertainment a few years ago, and Ultimate Texas Hold'em - developed directly by SHFL.  I did the original math on UTH for SHFL.  It was by far the most challenging game I had ever worked on to that point and perhaps since.  It was also one of the most rewarding because of the success it has become.  It is generally acknowledged as the 2nd most successful game of all-time with several hundred tables in the market place and is the only game on the horizon that has any chance to knock Three Card Poker out of the number 1 spot.

            Like Three Card Poker, one of the surest signs of the success of UTH is how many times I have heard the phrase in the past few years from an inventor, "It is just like Ultimate, but....."  There is an old saying that imitation is the sincerest form of flattery.  I guess if everyone is trying to create a game just like UTH, then UTH must be a pretty darn good game.   Is it possible to improve upon Three Card Poker or UTH?  I suppose it is possible.  But, 15-20 years after the invention of Three Card Poker, it is not a minor improvement to Three Card Poker that might take it out of the top spot.  It is a game that while still poker-based, introduce many new concepts.  It is a game that has more uniqueness to it than similarity to Three Card Poker.  I think if someone wants to knock UTH out of the number 2 spot, it won't happen because someone tweaks UTH, it will be happen because someone comes up with a new and better idea. 

            To all the inventors out there, don't think of new ways to flatter the existing games by imitating them.  Come up with new games with new ideas if you want to make your mark.

Saturday, October 12, 2013

What is the Allure of Progressives

            There is a theory in physics that goes for every action there is an equal and opposite reaction.  In gambling, there is a similar theory.  For every table game there will eventually be a sidebet.  And, for every sidebet there will be a Progressive version of the sidebet.  The math behind Progressives is probably the least understood math of any type of gambling.  It really isn't that hard once it is explained properly, but I've worked with a lot of inventors on a lot of Progressives, and it is fairly obvious to me that few people, even in the industry, understand how a Progressive works mathematically.

            Generally speaking there are 3 components of a sidebet - the fixed pays, the seed and the contribution rate.  Normally when we calculate the payback of a sidebet, we simply multiply the fixed pays by the frequency of each winning hand and sum up these values.  For a Progressive, we have to alter one step slightly and add one.  For the jackpot event, we use the seed amount as the equivalent of the fixed pay for that event.  Each time it is hit, the casino is on the hook to put that money back on the meter, so it is similar to a fixed pay in that regard.  We then need to add the contribution rate - which is the amount of each dollar wagered that goes on the meter - to the total payback calculated.    I'll save more details for another day, as this is not the point of today's column.  What is the point is to discuss how a Progressive differs from other wagers.

            While the top pay for most sidebets are pretty large, the amount they contribute to the overall payback is usually pretty small.  If you pay 1000 for a 1 in a million even, the contribution rate is a meager 0.1%.   In video poker the Royal Flush contributes only 2% to the payback of the game.  If we were to look at most table game sidebets, we'd probably find that most top pays contribute about 1-2% (or less) to the overall payback.  But, when we switch to a Progressive, we find that the top pay frequently contributes 15-20% to the payback when we take into account both the seed and contribution rate.  What does this mean for the Player?

            As I said, the Royal Flush accounts for 2% of the payback of video poker.  What this usually means is that until you hit one, you're only playing at about 97.5% which can be a bit rough.  When you hit one - and if you are a regular player, you WILL hit one, you bring the theoretical payback back to 99.5%.  Hit the Royal more frequently than 'normal' and you're likely up money as you will be above 100%.  With Progressives, it doesn't quite work the same way.  That top hand is either more rare or you'll be playing a game that deals much more slowly than video poker, meaning that there are no guarantees that you will EVER hit it.  So, even if the sidebet were paying 99.5% like video poker, ONE PLAYER is going to wind up winning 15-20% of that payback and everyone else will be playing at 77.5% - 82.5%. 

            When you consider the fact that many sidebets have paybacks far lower than 99.5%, you realize that the picture for those that don't hit the jackpot is even more bleak.  So, why do people play Progressives?  There are two main reasons.  One is a bit emotional and the other a bit more practical.

            First, Players have always been willing to accept low paybacks for a chance to win a life-changing amount of money.  The Lotto has made a lot of money for a lot of states.  Most states payout only 70% on their lotteries.  This is lower than the legal minimum of any casino game here in Nevada.  But, for the chance, however slim, of winning millions of dollars, Players are willing to throw a few dollars in for the hope of getting struck by lightning. 

            The second reason deals with the way Progressives work and makes far more mathematical sense.  To the casinos, the payback of a game is the long-term payback, which is calculated as I described earlier.  You'll note that what I described completely ignores the specific value on the meter at any point in time.   This money is merely an accumulation of the contribution rate over time.  It really doesn't matter to them (mathematically), if a jackpot that is supposed to hit about once a year, doesn't get hit for 3 years.  However, to the Player, the payback of ANY wager is dependent upon the specific payouts for each winning hand at the point in which you make the wager.  It doesn't really matter if the contribution rate is 10% of 20%.  If a Jackpot which is supposed to average $250,000, goes all the way up to $600,000 then the payback at that point in time is WELL above the theoretical payback. 

            It is possible that at a particular point in time that the payback of a wager could be over 100%.  At this point, it makes sense to play the game mathematically.  The problem is, however, that it will be one person that will benefit from this occurrence and it may not be you.  Then again, it might!

Friday, October 4, 2013

Why Play Max Coins?

            Generally speaking, I advise players to play max-coins when playing video poker.  For most versions, this means 5 coins.  The penny Player puts up 5 cents, the nickel player 25 cents, the quarter player puts up $1.25 and the dollar player has to put up $5 per hand.  This is done for one simple purpose.  On most video poker machines, the top payout - the Royal Flush - changes from 250 for 1 to 800 for 1 when that 5th coins is put in.  If you are playing a Progressive, the only way to win that jackpot is to play 5 coins.

            A payout of 800 for 1 on the Royal is worth approximately 2% of the total payback of the machine.  A payout of only 250 reduces this down to about 0.65%.  So, the Player is giving up more than 1.25% of payback if he plays below max-coin.  In similar fashion, if the machine is offering a Progressive, which should push the Royal payout to above 800, then the Player would be surrendering even more payback by playing below the max-coin level.

            The notion of playing max-coin does NOT mean you should wager 5 times the amount you feel comfortable wagering.  Instead it means you should consider lowering your denomination to the next lower level and then play 5 coins.  So, rather than playing 1 quarter, you should play 5 nickels.  This, of course, assumes that all things are otherwise equal.  It is certainly possible that when you go to a nickel machine (or change to the nickel option on a multi-denominational machine) that the paybacks may change as well and you may find that the payback on the nickel machine is well below that of the quarter.   This makes things a bit more complicated.  If the quarter machines pays 99.5% at max-coin, then it will be closer to 98% if you play 1 quarter.  If the nickel machines pays 98.5% at max-coin, then you'll still be better off playing max-coin nickels.

            There are a few times when you may want to play less than max-coin.  The first is when you are first leaning how to play.  As you are more apt to make mistakes at this point, you might be better off simply playing 1 nickel at a time.  Yes, you will be playing at a lower payback, but at this point, your goal is to become a better player while playing on a real machine.  Ideally, you'd spend most of your 'learning' time playing on your computer (or phone or tablet) at home for free ,but I realize that playing for free may be a lot less exciting than even playing for a single nickel.

            Another reason that you may not want to play max-coin is your bankroll.  If your bankroll is not large enough to support playing max-coin then you might be better off playing single-coin.   Once your bankroll is gone, you're done and you need to make sure you have enough money available to ride out the cold streaks.  Of course, one solution to this issue is again to simply drop down in denomination.  So, this advice really only applies if machines of a lower denomination are not available.  Since the advent of the multi-denominational machine, finding machines that play the denomination you want to play has become much easier, however.   So, this second reason may have limited practical applications.  But, if you find yourself in a situation where your bankroll will support 5 nickel play, but you only have quarter machines available, you may want to consider playing a single quarter as opposed to five quarters.

            One critical point to consider.  Just because you switch a machine from quarter play to nickel play, do NOT assume that the paytable is the same even if you are switching to the same variety of video poker.  There are no requirements that state that a machine must use the same paytable when you move from one denomination to another.   In similar fashion, don't assume that a bank of similar (or identical) looking machines all have the same paytable.  Casinos frequently and presumably purposefully mix the machines up, making sure to sprinkle higher paying machines in with lower paying ones.  I dare say that you may find no rhyme or reason to the pattern of machines on the casino floor.