vpFREE2 Forums

The big one that got away

#1

I was wondering how many royal flushes get away. (You can tell how
bored I am while waiting for my next VP trip) :slight_smile:

For example in 9/6 JOB, the royal flush cycle period is 40,391 hands.
But what is the cycle period for "potential" royal flushes?

I'm not advocating playing other than optimum strategy, but how many
royal flushes are we missing? This should be the same for all standard
52 card games. Assume ten cards are dealt with the rng. The first five
are the dealt hand and the second five are in the redeal. The first
card discarded is replaced with the first card in the redeal pile. What
is the cycle period for the potential royal flush?

We can't count a potential royal flush when the gaps forbid making a
royal flush hand.

For example:

Dealt: Ac Kc xx xx Qc redeal: Jc Tc xx xx xx Would qualify for a
potential royal flush.

While

Dealt: Ac Kc xx xx Qc redeal: Jc xx Tc xx xx Would not qualify for
a royal flush.

Anyone care to do the math?

Dennis
vp-connoisseur

#2

Cielaszyk wrote:

I was wondering how many royal flushes get away. (You can tell how
bored I am while waiting for my next VP trip) :slight_smile:

For example in 9/6 JOB, the royal flush cycle period is 40,391
hands. But what is the cycle period for "potential" royal flushes?

Assume ten cards are dealt with the rng. The first five
are the dealt hand and the second five are in the redeal. The first
card discarded is replaced with the first card in the redeal pile.
What is the cycle period for the potential royal flush?

Anyone care to do the math?

Nope. But I'll let winpoker come up with an answer that's likely in
the ballpark.

If you set all payouts to 0 with the exception of the RF (which you
may set to any non-zero value), the analysis will only hold suited
10-A for any dealt hand. This will provide the RF cycle under such a
strategy.

Of course, this isn't necessarily a complete solution of the question
you pose. For example, there will be cases where a hand containing
[10d Jd Qc x x] would call for a hold of the 10d and Jd, but the draw
cards would have completed a royal if the Qc were held instead.

My take on this is that the winpoker result presents the "best case"
outcome for someone going strictly for a royal but who doesn't know
what the draw cards are. Good 'nuf for me.

We all know I could care less about the purely theoretical example of
what potentially could be achieved in an all-knowing universe :wink:

The winpoker result, btw, is a cycle of 23081 hands.

- Harry (likewise bored ... of a certain topic :wink: