Poisson Distribution - Royal Flushes

[bigboy]

I'm going to hack VPW.  I'll add a "magic button".  When I think I've gone long enough without a royal, I'll just use it.  I think it will raise my morale. 
 
?? No need to hack. Click on Analyze, than select specific cards, than play these cards.
 

[MikeA]

Yeah Bigboy, but that's like Cheating or something![QUOTE=MikeA]I'm going to hack VPW.  I'll add a "magic button".  When I think I've gone long enough without a royal, I'll just use it.  I think it will raise my morale. 
 
?? No need to hack. Click on Analyze, than select specific cards, than play these cards.
 
[/QUOTE]

[Benford's Law]

Although I wish MikeA the best of luck in getting out of his frustrating royalless streak and I'm having a lot of fun reading about the VPW hack and so forth, I am still curious about the Poisson distribution and what the odds are of going through 10-12 cycles without a royal...
~Benford's Law

[cddenver]

Although I wish MikeA the best of luck in getting out of his frustrating royalless streak and I'm having a lot of fun reading about the VPW hack and so forth, I am still curious about the Poisson distribution and what the odds are of going through 10-12 cycles without a royal...
 
I was going to post some info of my own on this, but shadowman found it. 

[shadowman]

http://faculty.vassar.edu/lowry/ch5apx.html

[Benford's Law]

Shadowman,
         Thanks for the link.  I tried inputting all the values but putting in 480,000 for N is a value way too large for the page.  A dialog box pops up and says the N value is too large and I should try "using the page that calculates the binomial z-ratio".
My proposed input values:
N = 480,000 (conservative estimate)
k = 0
p = .0000238  (approx. 42,000 hands per royal cycle)
q = .9999762
 
If you can provide any help or answers here I would appreciate it.  I truly want a numerical quantity so I can see in a very simple way exactly how much the universe has wanted to punish and ridicule me for not getting any royals (except for Sunday's) over the last two years.  The lower the output value being generated from this problem, the more I can see how much the royal flush gods have abandoned my sweet, adorable self.
 
~Benford's Law
 

[shadowman]

I'm off at a casino right now so that is why I just posted the link. I've never used it for large values. Can't you just use the formula and do it yourself? If you do let us know the result. If not, I should be able to tackle the problem next week after our move (or maybe sooner).

[New2vp]

The probability of not having a royal in 480,000 tries is a relatively simple formula.  Just multiply the probability of no royal by itself 480,000 times.  If you want to estimate that the probability of a royal was 1 in 42000, then the probability of no royal is 41999 in 42000.
 
Then you can use Excel or some other program or calculator to determine
 
(1 – 1/42000)480,000 » 0.0000108787 or about 1 chance in 91,923.

That is more than unlucky!

[Benford's Law]

@New2vp - Thank you very much for crunching the numbers for me.  You'll just have to believe me when I say it is really true that I went this long without a royal.  I played mostly 98-100% VP and any strategy errors I might have occasionally made in my play involving a possible royal (over time) would have both instances of being "too aggressive" for the royal (ie. holding AKTs over a pair of K's in DB) or "too conservative" (ie. holding a pair of Q's over TQKs) in going for it.  Just like any other VP player, I always love getting royals, but I feel like my luck has been a car wreck in recent years....(I do have a VP playing friend who plays about 5-6 times as much as I do and has had 28 royals this year alone so far! **ENVY!**)


~Benford's LawEDIT - As an aside, about two days before hitting that royal, I played a short-pay 8/5 DDB progressive 25c (all 4-kinds or higher progressive including RF and SF).  I nabbed 4 2's (without the kicker) TWICE IN A ROW on CONSECUTIVE HANDS!  About a dozen hands later I held a pair of aces and grabbed 4 aces WITH the kicker.  Five minutes after that I was dealt quad 7's before quitting the machine after losing back $25 (but leaving with a cool $700 profit in 15-20 minutes' play!).  Now, THAT was something I hadn't seen during my entire VP playing life before!  I wouldn't even complain about my lack of royals if I could run into situations like that more often....

[New2vp]

Oh, I believe you, but that luck is poor enough to make one almost think that the machines could be somewhat suspect.  But with all the 1000's of video poker players, it stands to reason that someone has had such a run of futility at some time in their playing career.  I wish you better luck in the future.  Fortunately, based on your last post, it looks like not all your luck has been bad.