Pennies from Heaven

When we got there, we were pleasantly surprised. While they certainly didn't appear to have any positive games, they were at least playing some respectable games. They also had my wife's favorite, 100 Play Video Poker. That was enough to convince her, so we played for a little while. My wife played Double Double Bonus, paying 8/5 which means the payback was about 96.7%. This isn't a great payback, but when you play Penny Video Poker, you have to expect to not see Full Pay machines.

So, how can I both advocate 'Expert Play' and still not give my wife grief for sitting at a 96+% game? Well, if we were going to sit down and play this game night after night for a week, or on some sort of regular basis, I'd have to expect to get clobbered. If, however, we're going to sit down for an hour or so, we have to realize that anything can happen. Playing a lower paying machine just means it has to 'happen' sooner instead of later.

Like the expression commonly used for the NFL, in any given 2-3 hour session, almost any machine can be a winner. Hit a Royal on almost any machine, and you can be pretty sure your session was a big winner. Tell me that Jacks or Better machine paying 6/5 is absolutely going to hit a Royal in the next 500 hands and I'll take it over that completely random 9/6 Jacks or Better. The key to Expert Play is the 'long run'. In the long run, you will do better playing the 99.6% machine over the 95.5% machine.

In a short session, you can always get lucky and hit that big hand. Maybe it's a Royal or maybe it's a big Double Bonus Quads. Hit just one of these and you can be fooled into believing that it doesn't matter what paytable you're playing. Don't fall into this trap.

So, how did my wife do? Well, she got lucky…BIG TIME. She had been playing for about an hour, and we were starting to think about leaving. She was playing 1 coin on each of a hundred hands. She had started with 2000 coins and was down to about 700 coins, having played about 230 hands (I knew this from her cashback card). So, she played about 23,000 coins at 96.7%, which means to this point her machine was a bit on the 'cold' side as she was down 1300 coins instead of 750. Basically, the machine was playing pretty much as one would expect.

Then came 'the Hand'. I'd like to say she was dealt Four Aces or a Royal, but it wasn't THAT good. She was dealt THREE Aces and 2 cards that were not the needed 2,3 or 4 kicker for the big Bonus Quads. Before she hit the 'Draw' button, I did some quick math and figured that if the hand played out 'on average', we'd be about even and could go get some dinner.

She hit the Draw button and the cards started to deal out. When the draw was done, we were pleasantly surprised to find that we hit 7 Four of a Kinds, a nice bit above average. Better yet, SIX of these, were with a 2, 3, or 4 Kicker! Nice extra bonus having each bump to 400 coins instead of 160! The hand in the end was worth more than 3000 coins!

As we collected our money, my mind went to work on just how 'lucky' we were. When I got back to the hotel room, I ran a quick program that simulates 100,000 hands of 100 play poker, starting with Three Aces, and counting up the number of Total Quads and the number of Total bonus Quads that come up. The results of this simulation are in the table below:

From this table, we can see that starting with Three of a Kind, we can expect on average to get right about 4 Four of a Kinds. To get 7 as we did, will occur about 7% of the time. Not exactly a massive longshot, but clearly a favorable outcome. As for the Bonus Quads, we hit a HUGE longshot. Hitting 6 of them will occur .046% of the time or about once in 21,700 tries.

There are two very different things that could be learned from our session. Some will use this luck to convince themselves that it doesn't matter what machine you play. Others, such as ourselves, know that it simply takes this type of luck to make yourself a winner when playing on a low payback machine.