What's Luck Got To Do With It?

            Recently, a friend of mine posted on Facebook the definition of a "mondegreen."  Apparently this is one of those situations where you hear a friend belting out the wrong words to a song because they sound a lot like the ones that were actually sung.  We've all done it at one time or another.  Today is my turn.  Who remembers Tina Turner's classic song What's Luck Got To Do with It.  Okay, I know the word was "Love" and not "Luck".  But there isn't much room for love in a casino.  Some of you may be surprised to hear me admit that there might be some room for luck in one.


            Well, in the short run, there is.  There is none in the long run.  Over the long run, your payback WILL approach the theoretical payback of the game.  Will it be the the maximum payback of the game?  No.  This will depend on the strategy you use.  I can't promise you 99.6% on a full pay jacks or better machine if you throw Low Pairs to go for 4-Card Straights.  But, over the long run you WILL get the payback that goes with the strategy you use.  How long is the long run?  The depends on the game.  For video poker with so much payback in the Royal Flush, it will take a while.  It also depends on how often you play.  I can't tell you it will take two years if you play a few hours a month.  For a game like blackjack, it might take only 20 or 30 hours of play and you'll find yourself very close to the theoretical payback.


            The short run, however is a very different thing.  The short run is very much impacted by luck.  Of course, some people just call it 'hot streaks' or 'cold streaks'.  I experienced this very much just last night.  I sat down to play a single play Double Double video poker.  In the span of about 30 or 40 minutes I was dealt three of a kind a total of 12 times.  I didn't hit a single four of a kind.  What is the probability of this?  How bad was my luck?  Well, for a simple calculation, I could say that there are 47 possible cards and I get to draw 2 of them.  So, I should hit it about 1 in every 23.5 times.  So, missing 12 in a row doesn't seem all that odd. 


            As it turns out, this is the exact probability (4.26% or 1 in 23.5).  Going through some slight more complex computations, we find that the probability of going 0 for 12 is 61.98%.  It is clearly the most probable outcome.  But that leaves over 38% chance of hitting at least 1.  To be more precise, a 30.32% chance of 1, a 6.73% of 2 and about a 1% chance of 3 or more.  But, I hit ZERO.  Needless to say, it was not a profitable 40 minutes!


            I then moved to a multi-play multi-strike game.  This is not a game for the faint of heart.  The next 30-60 minutes were very good.  I didn't have to keep track of how many three of a kinds I had without hitting Quads because I hit Quads from every angle.  I hit them from Trips.  I hit them from Pairs.  I hit them on the 2nd and 3rd levels of multi-strike (which multiplies the payouts by 2x and 4x, respectively).   If anything wasn't going my way it was that none of these Quads were Aces or 2's - 4's with a kicker.  So, they paid, but they weren't quite jackpot level.


            Then my machine went stone cold.  Over the next hour or so, I barely hit a four of a kind at all.  I didn't even get many three of a kinds giving me a good chance to hit one.   I did eke out a couple of Quads, but always on the bottom level.  Before I knew it, my winnings were gone and I was digging deeper into my bankroll.  Over this period of time, I had a few shots at some big hands.  A few three of a kinds on the top level (8x payout), but with only 1 or maybe 2 of the 5 possible hands.  No 'luck'.  Missed all of them.


            As my bankroll dwindled the maximum I was willing to go on a single night, I was dealt three 2's on the top line with 1 hand.  Not only did I hit the Quads, but it hit with the kicker.  The machine had been cold in every imaginable way for an hour and in the blink of an eye, I had all my money back and then some.  The whole night pretty much hinged on ONE hand.  Not only did I get my 4.26% chance of getting the Quads, I got the roughly 1% chance of hitting it with a kicker!


            If I played on a regular basis, I would get my fair share of Quads - bonus ones, with kickers, Aces, etc...  Admittedly, I can't even fathom how long the long run is for a Multi-Play Multi-Strike game where getting Quads is important but even more important is getting them on the top 2 levels.  But, it really doesn't matter which game you are playing.  In a 3-4 hour session, how you do will be defined by the hot streaks or the cold streaks, which many call luck.  In the long run, the hot and the cold will even out to the mathematical probabilities and how you do will depend on the strategy you play and the game which you choose to play.