Thursday, April 18, 2013

Customer Power

            There were two different articles that appeared today that on the surface appeared only marginally related.  Yet, to someone like me, I found that they were far more important to one another than meets the eye.  The first article discussed the upcoming building boom here in Las Vegas.  Several major casino building projects are in the planning stages and Las Vegas may, in a few years, welcome its first major new casinos in several years.  One of the sub-plots of this article was some local columnists discussing what they felt was needed to build a perfect casino.

            In reading these suggestions, I can't say that I have a lot of hope that many (any?) of them would be implemented.  One of the suggestions dealt with the idea of putting the attractions near the front of the casino and the casino way in the back.  Another dealt with moving the restaurants closer to the self-parking garages.  Yet another suggested that casinos go smoke-free (I'm all for this one!).  The one that got my attention was the one that requested that casinos do away with blackjack that pays only 6 to 5 (instead of the traditional 3 to 2).  This one also mentioned better paying slots, but the focus was on blackjack.

            For those who have read my column over the years, you know I'm all for 3 to 2 blackjack and do my best to warn people about playing 6 to 5.  Roughly, 1 in 21 hands will be a blackajck.  That's about 2 hands per hour.  If you're a $5 player, this will cost you about $3/hour.  This may not seem like a lot, but it will increase your loss rate by about 300%!  A 99.5% game quickly becomes a 98% game and now you're playing a game that requires a great deal of strategy with a payback that is in the same range as many of the table games with little strategy.

            That brings me to the 2nd article I read today.  It talked about how gaming revenue in Las Vegas was WAY UP compared to last year, for the month of February.  A significant portion of this was due to the Chinese New Year occurring in February of this year vs. January of last year.  But, even when this is accounted for, revenue was still up.  Revenue on the strip was up even more than the rest of the city.  It is on the strip that we find virtually all of the 6 to 5 blackjack tables.

            6 to 5 blackjack was created because over time blackjack Players were getting better and better and the hold at blackjack tables was dropping.  Casinos have a lot of overhead to cover - from Dealer salaries to the massive electricity bills.  While every business should run efficiently, this is not exactly the case of they should keep the customer happy at all costs even if it means eking out a small profit.  Casinos are expected to make huge profits at the tables and slots to help offset many of the things they provide at low cost or free.  I have no idea what the cost is to present the pirate ship battle at the Treasure Island, but they've been doing for about 20 years for free every night.  The money to do these performances comes from the gambling side of things.

            So, the casino decided to come up with a way to greatly increase the house edge on blackjack.  They could have tweaked the rules a bit - use larger shoes, limit when the Player can double, etc..  But, these have limited practical impact to the house edge.  One of the most common Player errors is not doubling on soft hands when they should.  So, eliminating this as an option doesn't really help the casino at all.  So, they chose to pay blackjack at 6 to 5 and take a bit out of the bankroll of the good and bad player alike.

            Now, if you've been going to a buffet on the strip that give you free drinks included with the price of the buffet and all of a sudden they tell you that they're going to start charging you for your sodas, you might think twice about where to eat.  Yet, for some reason, paying 6 to 5 didn't have much of an impact to the amount of money people wagered on blackjack. 

            However, if we look at the report about Las Vegas gaming revenue for February, we find that the biggest spike occurred on the Strip.  If you head out to the casinos in the 'suburbs' where you find more local Players, you'll find almost NO 6 to 5 blackjack.  Local players tend to be better players (or they don't stay local very long) and the better player knows that playing 6 to 5 blackjack is very hard on your wallet.   You need to learn a complex strategy just to be able to earn a 98% payback?  A Player can sit and play a relatively simple game like Three Card Poker and earn the same payback and have a chance for a larger single payoff (with Trips of a 3-Card Straight Flush).  And, if you're not an accomplished blackjack Player, your real payback could easily drop to 95-96% which leaves a Player with very little chance of having a winning session.

            But, if nobody complains about having to pay for the soda, AND they have the same number of customers this month as they did last month (or more!), then there is little reason for the casino to go back and give out free drinks at the buffet.  This is even more true at the tables.  If a Player is just going to sit and take his 6 to 5 payout with little regard to the impact to his wallet, who can blame the casinos for making this their basic offering.

Thursday, April 11, 2013

The Definition of Payback

            I never get through a holiday without a serious discussion of what I do for a living with someone I've never met before.  Family (and friend) functions tend to bring together people for a large meal leaving them with loads of time to discuss all sorts of things.  As I have one of the more unique jobs around, my vocation tends to take up a larger than proportionate amount of the time we spend together.  This past holiday season was no different.

            First I listened to one person tell me how he has a system for roulette.  Admittedly, he didn't get a chance to explain it to me in much details when I had to tell him that it doesn't work.  No system does.  He told me how each time he came to Vegas, he would use this system and invariably walk away with a few hundred dollars.  Of course, his sample size was about 6-12 sessions, which isn't exactly statistically significant.  Based on what he told me, I commend my new found friend for his discipline which can be an important part of any successful gambling story.  Know when to get out when you are ahead.  But, that said, if you really have a system that nets you $400 in an hour or two, it is forever repeatable, which means you do it every night and then you send out a team of people to repeat your system.  No 'real' system could work only if you use it once every few weeks.

            Next up in the discussion came my favorite topic (ha!) - slot machines.  The system here was to attempt to outguess when the machine was going to pay off by altering the amount wagered for each 'pull'.  It was hard to keep a straight face when we got to this point.  I've heard of people varying their bet when playing blackjack in an attempt to guess the next cards.  If you do this well, it is card counting.  If you simply try to outsmart the shoe, you're just guessing.  If you try it with a slot machine, you are definitely guessing. 

            We've all seen the disclaimer that says 'past performance is not an indication of future returns'.  Nothing could be more true with slot machines.  What happened in the last spin has absolutely no bearing on what happens in the next one.  A slot machine is programmed to have a winning spin some percent of the time.  Every time you spin the wheels, the chance of winning is this exact percent.  With some combinatorial math we can also say that the probability of having X winning hands in Y spins will be some percent (assuming we know the probability of winning in any given spin).  But that is only true for the next Y spins.  We absolutely, positively CANNOT use any of the past spins in our calculation.  If the past 100 spins were losers, the probability of winning on the next spin is still whatever it is.  If the past 100 spins were winners, the probability of winning on the next spin is the same percent. 

            When I suggested to my new friend that he might want to avoid slot machines due to their 92+% payback, which makes them some of the worst payers in the casino.  Of course, when you look at the machine you have no way of knowing if it is programmed at 98% of 85%, which is as much as part of the problem as the average of 92+%.  My friend wanted to know how this payback was calculated especially when taking into account the way he plays - altering his wager from spin to spin.

            I explained that the payback used for any game is the highest payback that can be obtained by a Player assuming he plays using the best possible strategy he can.  For a game like video poker this means he uses perfect strategy to play each hand and that he plays max-coin in order to get the benefit of the 800 for 1 payout for Royal Flushes.  For slot machines, there is no strategy, so that does not impact the payback.  With slots, the impact of max-coin can frequently be even greater than with video poker.  Not only do you buy additional lines with additional wagers, you sometimes also buy additional combinations of winning hands.   As a result, playing less than max-coin can be even more punishing to your bankroll.  The payback of a slot machine thus assumes a max-coin play on each spin.

            Payback (for any game) is the amount that a Player can expect to have returned out of the TOTAL amount wagered.    The amount you buy-in for is completely irrelevant to this definition.  If you sit down at a blackjack table for $20 and play 100 hands of a $5 table, you'll wind up wagering about $565 (when you account for splits and double downs).  With a 99.5% payback, you can expect to lose about $2.80.  This works out to be 14% of your buy-in, but if you had bought in for $100 it would've been 2.8%.  Just further proof that the buy-in is not relevant to the payback discussion. 

            If you play 1000 hands of video poker (quarter machine, max-coin), you'll wager $1250.  If you're playing full pay jacks or better with a 99.5% payback, you can expect to get back $1243.75.  No matter how much you put into the machine, you should expect to have lost $6.25.  If you play less than max-coin, your expected loss will be higher.

            Slot machines are no different.  If you spin the wheels 1000 times on a nickel machine with 27 lines, you'll wager $1800.  You won't know the exact payback of that machine, but if we use a generous 95% payback, you can expect to get back $1710 of that $1800 wager and sustain a $90 loss.   If you choose to vary your bet from spin to spin, your payback might be even lower, raising your expected loss.

            In all these cases, the paybacks are expected 'long-term' paybacks.  Long-term can mean different things to different games.  In a 2-3 hour session of playing, your results can and will greatly vary from the examples shown here.

Thursday, April 4, 2013

When 2 is better than 3

            When my father developed the first strategies for video poker, a few surprises definitely showed up.  Playing 4-Card Flushes over Low Pairs was not such a surprise, but playing the Low Pair over 4-Card Straights was.   One of the other significant surprises was how to play the numerous hands that contain High Cards.   If you had 3 High Cards of the same suit, it wasn't much of a surprise to hold all three.  Even if one of those 'High' cards was only a 10.  A 3-Card Royal is a pretty strong hand, even if it takes a bit of a long shot to actually hit the Royal.

            Without the mathematical analysis of video poker to guide the Player, most found themselves holding on to all cards Jack or Higher.  This would probably be the right play if you were sitting at a Poker table.  When playing Poker, there is little benefit to drawing a Royal over a Straight or a Flush.  All are very likely to leave you as a winner and the amount you win will not change based on your final hand value.  In the meantime, you'll increase your chance (or will you?) of grabbing a High Pair which will may be enough to win the hand.

            But video poker is not table poker and a Royal has a good deal more value than a Straight or a Flush - 200 to 130+ times as much.  This makes taking the risk of getting the Royal far more worthwhile in video poker than table Poker.  As a result, the decision of what to do when you're dealt a J♥, Q♦, A♥ not as clear as one might think.  Let's take a look at the detailed analysis.

            If the Player holds the 3 High Cards, there are 1081 possible resulting draws.  32.2% of the time the Player will wind up with a High Pair.  If the Player holds only the 2 suited High Cards, he will wind up with a High Pair 30.3% of the time.  So, the probability is a little less, but we're not talking a huge difference.  The Player may only have 2 High Cards instead of 3, but he will draw 3 cards instead of 2 helping to even things out a bit.

            Moving on, with the 3 High Cards, the Player will draw a Two Pair about 2.5% of the time.  With the 2 High Cards he will pull a Two Pair about 4.4% of the time.  The score has been quickly settled with the High Pair frequencies.  For as often as the Player will wind up with fewer Pairs he will wind up with more Two Pairs.  Given Two Pairs pay twice as much, this puts the 2 suited High Cards in the lead.            The pattern continues with Trips, with the Player drawing about twice as many by holding onto only the 2 suited High Cards.  

            Things turn around when we look at Straights.  It should be no surprise that the probability of drawing a Straight goes way up when you hold 3 High Cards as compared to 2 High Cards.   The exact probabilities will be impacted by the specific cards, but in this particular case the probability with 3 High Cards is about 1.5% vs 0.3% for 2 High Cards. 

            For the 3 High Card hands, the hands stop there.  There is ZERO chance of drawing a Flush, Full House, Quads, a Straight Flush or the Royal.  For the 2 High Card hand, we still have a 1% chance of drawing a Flush and slim, yet possible chances to get a Full House, Quads or the elusive Royal.  In this particular case, there is no chance for a Straight Flush, but if I had chosen a suited J-K for my example, this would exist as well.

            If we were to ignore all the hands Flush and above, the two hands would have nearly identical expected values, with the 3 High Card hand slightly higher, However, there is no reason to ignore these hands.  In fact, we specifically play the 2 High Card hand for the specific reason that we have the opportunity to draw all these relatively high paying hands simply by discarding the 1 off-suit card, all while barely impacting the overall expected value of the lower hands. 

            As a result, the decision is not really a hard one to make, even if it was an originally surprising part of the strategy.  Our 2-Card Royal with an Ace has an expected value of about 0.58.  Our 3 High Card expected value is a mere 0.46%. 

            This type of hand is a fairly common one and repeatedly playing it the wrong way will take a bite out of your bankroll.  This is why the 'seat of your pants' approach or using table Poker strategy can be quite ruinous to your results.  Sometimes, 2 can be better than 3.