Eyes Wide Open

            I finally discovered something that has a lower payback than slot machines – New Jersey Turnpike tolls!  As I write this, we’re back on the East Coast for personal business.  After landing at Newark, we had to drive up to the Boston area.  I couldn’t believe the toll from Newark airport to northern end of the Turnpike.  It was $3.60 to go about 20 miles.  Throw in the $12 toll to cross the George Washington Bridge to cross into New York and I was out more than $15 after only being on the road for 25 minutes!  It takes quite a bankroll to drive on these roads, and with NO chance of winning.  We had only left NJ less than a year ago and all these tolls had gone up considerably since we left!

            On a more serious note regarding slots, I received a very good question from a reader this past week.  He acknowledged what I had written several weeks ago that the average slot machines paid only 92-93% and that video poker generally paid 97-100+%.  He asked that given that casino gambling is just a form of entertainment, what is so bad about the idea of taking $100 of your bankroll to go for a huge jackpot on a slot machine, especially given that winning a similar amount at video poker would take a long time with smaller wins along the way.  I have to admit, that it took me a little while for me to come up with a response.

            I think the best I can come up with is that if you go in with your eyes open as to what you are doing then I can’t really say there is anything wrong with it.  Gambling is entertainment and if it brings you enjoyment to take part of your bankroll and put it into a low payback slot machine with a jumbo-sized jackpot, that is your choice.  If I have any issue with the concept it is that it is very hard, if not impossible to go into this with your eyes truly open.  Yes, you can know the size of the jackpot, but you don’t know the probability of actually hitting it. 

            The other issue is that it is standard practice in casino gaming that if the game has a huge jackpot (usually Progressive) then the payback of the game tends to be even lower.  This is true for both slot machines and even table game sidebets.  Outside the casino, this is even truer for things like Lotto.  Most state lotteries have paybacks in the 50-60% range.  Players are willing to play games with very low paybacks in hope of winning that life altering prize.   Again, however, in the case of Lotto, we are able to compute the probability of winning the top prize.  This is not the case for slots.

            While the low payback of regular slots is concerning, and the presumed even lower payback of a Progressive slot is even more concerning, the biggest concern still belongs to the notion that there is no way to know anything about a slot machine.  We don’t know the probability of the jackpot spin or any other result.  We have no way of knowing the overall payback of the machine by a simple glance at the glass.  In a place like Nevada, the payback can be no less than 75% so that is about all we really know.

            So, that all said, if you feel that you want to play a game that has a life-changing jackpot with a portion of your bankroll, I can understand the desire to try your hand at a slot machine.   It is probably the only chance you have for a multi-million dollar prize.  If you are looking for a gigantic jackpot, I would personally recommend a Pai Gow Poker sidebet or the Six-Card sidebet for Three Card Poker.  The prizes will only be in the few hundred thousand to $1 million, but you’ll still be playing games with higher paybacks.

            In the end, it is your money and you have to decide how you want to spend it and what provides you the most enjoyment.  If chasing a mega jackpot on a low paying machines with a portion of your bankroll is what brings you joy, I won’t stop you.

            

Jackpot Power

            As we get deep into the political season, we're all going to be frequently reminded how it is possible to make numbers say just about anything we want them to.  Quite frankly, it is not just the arena of politics this happens in.  It can be done with all types of math - casino math, included.

            By now, many of you well know that a full-pay jacks or better machine pays about 99.5%, which is a very solid number for a casino game.  Many of you may even be aware that the Royal Flush contributes 2% of this amount.  But what does this really mean?  It means that if the machine was defective and NEVER dealt a Royal Flush, but dealt all the rest of the hands in the frequencies we would expect, the payback of the game would be closer to 97.5%.   This is about the same payback we would get from a short-pay (8/5) jacks or better machine so should we expect roughly the same experience?

            ABSOLUTELY NOT!  One of the measures I like to use is what I call a 'session simulator'.  This process simulates a session of play for a particular game.  For video poker, I use 3 hours of play at 700 hands per hour.  For this particular demonstration, I ran 1000 of these sessions under 2 conditions.  The first was a full-pay jacks or better machined that NEVER paid a Royal Flush.  To be clear, the only way this could ever really happen would be if the machine was broken or rigged.  As I don't believe the latter happens in any reputable casino, nor would a broken machine likely stay on the floor for this many hands - this is merely for illustration purposes and to prove a point.

            In this scenario, the Player still managed to walk away a winner about 28% of the sessions.  This compares to about 29% when a regular full-pay jacks or better is played.   Why is there such little impact to this?  Under normal circumstances, the Royal would hit only about every 20 cycles or so.  Some of these cycles would already be winners, so the Royal Flush doesn't change this.  It only changes the magnitude of the win.  In the cases where the session was about to be a loser, the Royal most likely flipped ONLY these into winners.  However, when we look at the long run, the overall payback of ALL the sessions put together was where we expected it to be - at about 97.5%

            When we put the 8-5 jacks or better machine (with the Royal occurring as it should), we find that the Player wins only 14% of his sessions.  His winning sessions are cut by half!  The overall payback of all the sessions is also what we would expect it to be at 97.5%.

            So, why do two different machines paying about the same amount create such different short-term results?  This goes to a concept of volatility.  There is a mathematical formula for volatility, but I'm afraid if I start explaining it at that level, you're all going to turn the page.  That is why I like to use the session simulator as a means of explaining what volatility does and is.  When a large amount of the payback is concentrated into a very infrequently occurring hand, there is a larger degree of volatility.  In the case of the full-pay jacks or better game without the Royals, I removed a large degree of the volatility.  This is why a game with a considerably lower payback that the original version can still have a not very different short-term result.

            So, what does this all mean for you?  There are two points I'd like you take away from this week's column.  The first is to realize how important the Royal Flush is to your long-term results in video poker.  If you are on a cold streak of Royals, your short-term results may not look all that different from 'normal', but you may find that your larger bankroll is suffering.  If you play for 3 hours at a time, you may find that you're still leaving the casino a winner 3 out of 10 times, but for some reason your wallet still seems a lot lighter than it should.  The good news is that in the long run, those Royals will show up as often as they should (assuming you are playing Expert Strategy).  Ironically, when the Royals are running hot, you'll still walk away a winner about 3 out of 10 sessions.  But, a few more of those sessions will be big winners.

            The second point I want everyone to think about is if a 'mere' 800 unit payout occurring roughly every 40,000 hands can make this type of impact to a game, imagine what happens on a slot machine that can pay hundreds of thousands or millions of dollars for a 'hand' even more infrequent.  The average payback on a slot machine is ONLY 92-93%.  If we consider that many of them will have a massive top pay that might occur only every few hundred thousand hands (or million hands), what % of the overall payback does this account for? 

            With these occurrences being so infrequent (and COMPLETELY unknown as to how frequent), the payback of the machine without the jackpot could easily be 80-90%.  I'd put this through my session simulator but as it is not possible to know the frequency of all the payouts, there is no way to do it.  Just for fun, I built an 82.5% video poker paytable and put it through the process and it showed that the Player will walk away a winner only 5% of the time.  As we've already shown, it would then be possible to create an infrequent, very high paying jackpot which will push the overall payback up, while barely changing the short-term results. 

            The end result is one that we know all too well for slots.  Very few people walk away a winner even in the short run, which pays for the handful of people who win the big jackpots.  I'll take video poker any day!

How About That Strategy? It Works!

            This pretty much speaks for itself:

http://fbg.me/App/Posts/BlogPost.aspx?pstid=29444&pstaid=462

             Someone playing a $2 full-pay max-coin Double Double Bonus Poker hits an $8000 Royal Flush starting from a 2-Card Royal!  Without knowing who hit it (and I don’t), we really don’t know to what extent this Player follows Expert Strategy.  For all I know, he discarded a Pair of Jacks to go for the 2-Card Royal.  But, lacking this information, I’m going to use this picture to demonstrate some key components of Expert Strategy.

            Play the right machine – Well, Double Double Bonus isn’t exactly the ideal machine to play with its 98.8% payback.  However, it multiple jackpots (Royal and 4 Aces w/kicker) has made it immensely popular.  From the picture we can see that the Player chose to play one that is full-pay (1/1/3/4/6/9).  Before the payout on this hand, the Player had about $535 remaining in their bankroll.  If they play a short-pay machine, perhaps the bankroll is exhausted before they have the opportunity to win the $8000!

            Know the right strategy – This is really the crux of this column.  We don’t know what hand the Player was dealt, but we do know that he held the suited J-A.  2-Card Royals make up about 7-8% of our playable hands.  Misplaying them can be rather dangerous to your bankroll.  When my father, Lenny Frome, developed his first strategies for video poker, one of things that surprised him was that most 2-Card Royals outranked 3 High Cards.  Given the unlikely odds of hitting a Royal, intuitively, one might think that you’re better off having 3 High Cards increasing your chances of a Jacks or Better or a Straight.  But by holding 3 off-suited cards, you eliminate all chances of a Flush, reduce the likelihood of Trips and eliminate Quads and the Royal.

            ‘Unlikely’ is also a relative term.  The actual odds of hitting a Royal from a 2-Card Royal is ‘only’ 16,215 to 1.  In the grand scheme of the casino, this isn’t really all that rare.  If one out of 13 hands is a 2-Card Royal and 1 in 16,215 of these will result in a Royal Flush, then we’re talking about 1 in 210,000 hands will have this ‘fate’.  At 700 hands per hour, this means about 300 hours of play.  Depending on how serious of a Player you are, this might take weeks or months, but in a casino with hundreds of video poker machines being played 10-15 hours day each, it’s happening every day all over the place.  So, why not you?

            Of course, you increase your chances of it being you if you play your 2-Card Royals correctly.  This will, of course, depend on the specific game and paytable you are playing.  In the case of Double Double, here are some key pointers:

            -  A 10-A 2-Card Royal is NOT playable.  We hold only the Ace if we have no alternatives.

            -  We Play J-Q-K-A (off suit) over a 2-Card Royal

            -  Pay attention to all of your cards and don’t just focus on the 2-Card Royal.  You might be dealt 4-5-6 of one suit and a J-Q of another.  The 3-Card Straight Flush outranks the 2-Card Royal by a considerable margin.

            -   Do NOT discard any Pairs to go for a 2-Card Royal

            This list is hardly meant to be comprehensive.  If while reading it you realized that you didn’t know these things, you might want to brush up on your game before you spend real money.  As always, it is important to learn the strategy table of the game you intend to play and stick to it. 

            This way, maybe next time I post up a picture of a big jackpot, you can sit back and say “That’s MINE!”