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royal flush droughts and statistics

No royal in 155,000 hands is certainly below average but not uncommon.

We can report the results of an event in a number of ways with very different conclusions. Let's say I play 80,002 hands of video poker. On my first hand, I hit a royal. On hand 40,000 I hit a royal and on hand 80,002 I hit a royal. Now, I can say I hit 2 royals in 80,002 hands ( about average). I can say that I have hit 2 royals in my last 40,003 hands ( above average). I can also say that I went 80,000 hands ( hand 2 to hand 80,001) with only one royal ( below average).

To get a better perspective for the 155,000 hands ( or whatever it was) without a royal, you need to define the experiment and then repeat it a number of times. If it is a 'feature' of the machine, it should be repeatable. If the machine is fair, the above streak will only happen a couple of times per hundred cases. A hundred cases is 15.5 million hands.

Excellent summary of a complicated event John. Dick M.

"John.G.Zaroff" wrote:

No royal in 155,000 hands is certainly below average but not
uncommon.

We can report the results of an event in a number of ways with very
different conclusions. Let's say I play 80,002 hands of video poker.
On my first hand, I hit a royal. On hand 40,000 I hit a royal and on
hand 80,002 I hit a royal. Now, I can say I hit 2 royals in 80,002
hands ( about average). I can say that I have hit 2 royals in my last
40,003 hands ( above average). I can also say that I went 80,000
hands ( hand 2 to hand 80,001) with only one royal ( below average).

To get a better perspective for the 155,000 hands ( or whatever it
was) without a royal, you need to define the experiment and then
repeat it a number of times. If it is a 'feature' of the machine, it
should be repeatable. If the machine is fair, the above streak will
only happen a couple of times per hundred cases. A hundred cases is
15.5 million hands.

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