I have often wondered how important getting 4 to a royal was to the
overall number of royals for a given game.I was somewhat surprised at
the results, since I expected 4 to a royal to account for more than
half of the royals.
I calculated that for 9/6 JOB 6.26% come from dealt royals and 30.95%
come from 4 cards to a royal ( remember you keep the 9 to K str flush).
This of course is for perfect strategy play and full pay game.
For 10/7 DB ( full pay) and perfect strategy 7.40% from dealt royals
and 36.82% from 4 cards to a royal ( you also keep the STr Flush here).
The difference is that (using Win Poker Statistics) you get a royal
every 40391 deals for JOB and 48048 deals for DB. ( the main cause for
the difference is holding 3 cards to a flush with 2 HC in DB)
However both of these only account for 37 to 44% of the royals. I
wonder if anyone has calculated the % of royals that come from holding
3 ,2 , or 1 HC(ss) to a royal?
I think that full pay deuces and NSU deuces would be more difficult to
calculate the royals for holding 4 cards to a royal since you keep Wild
Royals with 4 HC to a royal, but do not keep the natural str flush with
4 HC to the royal.
If anyone would like more details of my calculations email me at
bobbj@aol.com
Bob from PA