Stay informed with the
NEW Casino City Times newsletter!
Best of John Robison
Ask the Slot Expert: How are slot machines like a pie chart?6 January 2016
It's not really surprising that you rarely get more than three consecutive wins in a row.
Consider flipping a fair coin. The probability of flipping heads is 0.5. The probability of flipping two heads in a row is 0.5 times 0.5 or 0.25. Similarly, the probability of flipping three heads in a row is 0.125 or 1 out of 8 and four heads in a row is 1 out of 16. We don't see more than three heads (or tails) in a row very frequently.
Now, tossing heads has a hit frequency of 50%. If you're playing dollar machines, your hit frequency is probably somewhere in the teens, say, 12.5%, which is a hit in 1 out of 8 spins. The chances of two hits in a row are 1 out of 64, three are 1 out of 512 and four are 1 out of 4,096. No wonder long wining streaks are few and far between.
It's much easier to get a string of winning hands on most video poker pay tables, which have hit frequencies of almost 50%. And, of course, it's easier still to get a long string of hits on many penny slots, which usually have very high hit frequencies.
Your pie chart analogy is very good — so good that I'm going steal it and use it in the future. What I really like about it is that it makes it clear that the chances don't change from one spin to another.
There are two ways I can use the analogy. Let me start with the simple example.
The pie chart is divided into sections, one for each winning combination and one for all losing combinations. The size of each section indicates how likely it is to land that combination. The largest section is the one for all the losing combinations. The section for the jackpot combination may be just a tiny sliver.
Now let's take a detour to the advanced example. Each section represents a combination that could land on the pay line. The difference between this example and the simple example is that now we've specified each of the losing combinations instead of having one big losing combination section. The winning combination sections are the same as in the simple example.
The losing combination wedges are different sizes. It's probably more likely to land bar-bar-blank than jackpot-jackpot-blank, so the bar-bar-blank wedge is larger.
We're done with the detour. In both examples, when we hit the spin button a dart is thrown at the pie chart and the section in which it lands determines the result of the spin, as you said. In the simple example, the machine would have to do some sort of additional random selection if the dart landed in the loser section to determine the exact losing combination. Interestingly enough, this is close to how the old Universal machines worked in the 1980s and led to the banning of the "secondary decision."
When we hit the spin button again, the pie chart hasn't changed so our chances also haven't changed. If it's not likely to land in any winning combination section, it's less likely to land a winner twice in a row and even less likely to land a winner three, four or more times in a row.
Of course, machines don't actually work this way. The program running the machine polls the Random Number Generator to get a number for each reel in the machine. The numbers tell the program which stops on each reel should land on the payline. The program then evaluates the symbols at those stops and makes any payouts needed.
I once had similar results to your 82-spin streak. I was playing a machine that I knew to have a low hit frequency and I went through a roll of quarters without a hit (playing one quarter per spin). That's where the similarities between your story and mine end. I lost money on the machine.
Moving on to your statement about high denomination machines, we have to be very careful with terminology. What exactly does "higher chance of a win" mean?
Does it mean these machines have higher hit frequencies? I've seen par sheets for all denominations. The hit frequency for a $25 Double Diamond is usually close to, if not the same as, the hit frequency for a $1 Double Diamond. The two machines may even have the same payback program (virtual reel layout) and thus the same hit frequency and long-term payback.
Does "higher chance of a win" mean higher long-term payback? This statement is generally true. Long-term payback does tend to rise along with denomination. Each machine has to earn its place on the slot floor. The casino can take a smaller portion of the larger bet on the high denomination machine and the machine can still pay its way.
That said, casinos usually try to have high hit frequencies on the stratospherically high-denomination machines. Seeing somebody hit for thousands of dollars on a $500 machine gets everyone's jackpot-chasing juices flowing.
Seeing somebody lose $6,500 in a couple of minutes is a buzzkill.
Send your slot and video poker questions to John Robison, Slot Expert™, at firstname.lastname@example.org. Because of the volume of mail I receive, I regret that I can't reply to every question.
Best of John Robison