The Volatility of 100 Play

            Recently, for my wife's birthday we went to see her favorite musical artist - Celine Dion.  We got to Caesar's a bit early and had about 30 minutes to kill.  We found a bank of 3 100-play video poker machines with 2 available and decided to play.  When you play 100-play machines, playing 1 cent per hand really means playing $1.00 per deal, which makes you almost a max-coin quarter player on a single play machine.  Unfortunately, penny machines don't tend to pay full-pay because there simply isn't enough house advantage for the casino to cover its cost on the machine.  Add to this the fact that we were playing on the strip, and I really didn't want to think how bad the payback was of the game we played.  It wasn't really about winning as much as it was about killing 30 minutes.

            Anytime I mention 100-play, an interesting question comes up.  Does a 100-play machine raise or lower the volatility of the game relative to a single play machine.  Volatility is a measure of the streakiness of the game.  I tend to liken it to a roller coaster.  Low volatility means a little kiddie rollercoaster.  High volatility are the 70 MPH ones that go upside down with your feet dangling.   In the casino, blackjack is low volatility as most hands just either lose or pay even money.  Ultimate Texas Hold'em is higher volatility as your losses can be more than your base wager and your wins can be at odds pay.

            In video poker, jacks or better is the low volatility game as more of the payback comes from the lower paying hands.  Double Double video poker is at the high end of the spectrum as more of the payback comes from the higher paying hands.  Two Pair is reduced to a push while 4 Aces with a kicker becomes essentially a jackpot hand.

            So, how does 100-play effect this?  There are two opposite forces at play with 100-play machines.  The fact that you play 100 results from your Deal at a time lowers the volatility of the game.  To understand this better, think of the case where you are dealt a Low Pair.  The expected value of a Low Pair 0.82 (jacks or better).  Ironically, when you play jacks or better, every possible outcome isn't even close to this payback.  You can either lose and have a 0.00 payback or you can minimally get a Two Pair and have a 2.00 payback.  If you get a better hand the pays go up even higher. 

            But, when you play 100-hand video poker, when you are dealt a Low Pair, you get the net result of 100 draws.  On some of these you'll hit a quad or hit a lower than anticipated number of Two Pairs and Trips.  The net result will tend to be between about a 0.40 and a 1.20 payback.  A far narrower range of results than we see with single play.  This is indicative of a game with a lower volatility than the other. 

            So, what is the opposite force.  Even if you put the game into 'turbo' mode, you're never going to play 100-play at the same speed as a single hand.  So, while the Draw portion of the game is smoothed out by playing 100 Draws at a time, you wind up more at the mercy of the Deal.  Get dealt a few Three of a Kinds and you have a great opportunity to draw a pile of Quads and have a winning session.  If, however you spend an hour getting a lot of Low Pairs and One or Two High Cards, you're going to have a painful session.  All casino games approach their theoretical paybacks as you play more hands.  In the same amount of time, you'll get in less Deals with 100-play.  This has a tendency to raise the volatility of your session

            What is the end result?  There is a mathematical formula that can be applied to a game to determine this, but in all honesty, I didn't have the time to figure out all the possible outcomes of a 100-Play game.  My gut tells me that the overall volatility doesn't change all that much within the same type of game (i.e. Bonus Poker, jacks or better, etc...)  This brings me to the last point for today, which I have brought up many times before - proper bankroll size.

            The risk of playing for only 30 minutes (and being time constrained by your very expensive concert tix) must be taken into account as much as your bankroll.  After about 25 minutes, I found myself down about $20.  My wife gave me one of 'those looks' as I reached into my wallet to grab another $20 with only 5 minutes to go.  This was just about the time, she came back from $15 down to have a winning night (she won a whopping 0.01!).  I promised to play 'fast'.  I quickly drew some nice Quads and was back down only $15, and I knew that I would stop if I went back down the first $20.  It was a good thing that I pulled out that second $20.  A few hand later I was dealt an Ace, followed by 4 Jacks.  I had never been dealt Quads on a 100-Play machine before.   A quick $50 turnaround and I left up $35.  Proper bankroll can make all the difference in the world.  A little luck never hurt too.