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.