vpfw rng

[New2vp]

Using 9/6 Jacks or Better as an example on single line with perfect play, the royal flushes come in these varieties:
 
Dealt 5       6%
Dealt 4     31%
Dealt 3     40%
Dealt 2     20%
Dealt 1       3%
Dealt 0     0.3%
 
And you see one royal out of every 40,391 hands on average.
 
It is tempting then to think that on 100-play you will see one every 404 hands on average, but you will only see them about once every 546 hands, about 26% less than expected unless you don't factor in what follows.
 
15% of the hands that contain royals contain more than one, sometimes many more.  To some it may be surprising that 37% of the royals in 100-play are from hands that contain multiple royals.  For that reason, you have to be a bit more patient than looking for them every 404 hands.
 
The breakdown for 100-play is:
 
63% of royals are from hands with exactly 1 royal
11% of royals are from hands with 2 royals
  9% of royals are from hands with 3 royals
  6% of royals are from hands with 4 royals
  3% of royals are from hands with 5 royals
  1% of royals are from hands with 6 royals
  1% of royals are from hands with from 7-99 royals
  6% from hands with 100 royals
 
Note that this does not indicate that hands with one royal occur only 10 times as often as the dealt royal hand that ends in 100 royals (63/6).  Hands with one royal occur more than 1000 times as often.  But the 100-royal hands add 100 times more royals to the population than the hands with 1 royal, so they end up being 6% of the total. 

[scorpio2]

i see,so it would maybe be easier to play progressives to get to the rf quicker,if it hits your machine,or you could play the many hands alone,as dancer does,forcing it to hit?

[Eduardo]

Playing a progressive would only make it hit sooner if you changed your strategy, right?

[shadowman]

That's right, Eduardo. The odds of hitting RFs are not changed simply because it's a progressive. You will get more RFs by changing the cards you hold.
 
For example, take K(QT)64 where the QT is suited ... most of the time in bonus games the proper hold is the unsuited KQ, however, once a progressive increases to a particular point (game dependent) it becomes a better stragegy choice to go with QT. This also applies to 3RF over a high pairs, etc. By making these kind of strategy changes one's chances for the RF go up. 

[scorpio2]

I THINK I GET IT,SO on a 100 play machine,you would have to play individual lines 43,000 times on each line,not just 430 times for all lines,to get the average rf to hit?

[shadowman]

Both are equivalent. You should average out to one RF for every 43K hands no matter what line they are on. Over time, assuming you play millions of 100 play hands it should eventually average out to 43K hands on each line.

[bigsteve5273@yahoo.c]

I learn something every day on this site.  40% of RF's are achieved by being dealt 3 cards of the five over 4cards dealt which gives us only 30% of the RF's received.  If I had thought about this carefully I may have seen it.  One interesting thing is that when playing 100 play, we are actually playing only one hand once the cards are dealt but we are playing 100 chances on that hand unless you dump all 5 cards in which case we are playing 100 different hands again.  I've often thought why not have a 43,000 play machine for those of us who suffer from supposably infrequent RF's.  Finally, I play to win using computer generated strategies. That is entirely different than playing only for the most royals.

[New2vp]

Steve, you'd need a lot of royals to play even 5 minutes with that 43,000-play machine unless your first couple hits were lucky.  You would still go through some droughts.  For any sequence of 18 hands, you would have a 10% chance of seeing NO royals at all.  On average, you would see one or more royals only every 8.4 hands.
 
73% of the time (like when you hold a pair) it would be impossible to hit any royal.  Though you would virtually always hit royals when holding 3 or 4 to the royal, 7% of the time you would strike out on all 43000 hands when holding 2 to the royal; 79% of the time when holding a single high card; and 89% or 92% of the time when drawing 5 new cards (depending on whether you discarded a ten).  All this is based on 9/6 Jacks or Better computer-perfect strategy.
 
I had some extra time to calculate this useless trivia since both of my picks (plus my chances at the office pool) were getting blown out in March Madness' Final Four Saturday evening.  With 3 to the royal, you would be in the range of 24-56 royals 99% of the time; starting with four, the interval would be 838-992 royals. 

[MikeA]

NEW2VP..How 'bout them Jayhawks!  Never thought they would get past NC. Even though the current players on the J-Hawk team never played for Roy Williams, you'll never see another "grudge match" much more intense than that one last night <LOL>  Williams left KU a few years ago to take the position at NC.  Obviously, a lot of folks in Kansas were not pleased with that decision!I may have to get me a ball-marker with the KU logo.  Okay....I'm ready for the jokes...but that is what they are called....mark your Golf Ball on the green!

[shadowman]

Not to mention the cost of the 43K lines. Even a penny machine at .05 a hand comes out to $2150 per hand.
 
Now for a few other thoughts.  
 
The royals would only be worth $40. The screen with 43K hands spread out on it would take an ENORMOUS display. I don't think my eyes could pick out much of anything. However, I assume they'd use another technique where they would just summarize the hands and you could select a set of hands to look at if you wanted to. And, of course, all those W2Gs for any dealt winners.