Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 2nd, 2019 at 9:39:14 PM permalink
What are the odds of being dealt 4 to a royal flush, example akq10 of clubs and then drawing 96 hands with zero royal flush???? Or is this rigged?
AxelWolf
Joined: Oct 10, 2012
• Posts: 18652
April 3rd, 2019 at 12:13:21 AM permalink
Quote: Joelesely

What are the odds of being dealt 4 to a royal flush, example akq10 of clubs and then drawing 96 hands with zero royal flush???? Or is this rigged?

Not hard at all. You should have had a little over 2.

Is this single line VP? If so, did you hit any royals on other draws? if not that would be over 6 cycles(depending how you play) still possible.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
ChesterDog
Joined: Jul 26, 2010
• Posts: 924
Thanks for this post from:
April 3rd, 2019 at 4:25:47 AM permalink
Quote: Joelesely

What are the odds of being dealt 4 to a royal flush, example akq10 of clubs and then drawing 96 hands with zero royal flush???? Or is this rigged?

The probability of not getting a royal flush within the first 96 draws to 4 to a royal is 13%.

A very good approximate formula for the probability of not getting a royal in a particular number of cycles, N, is: P = e-N

96 is 2.04 cycles. (2.04=96/47) So, the probability is: e-2.04=0.13

The bad news is that you still have a 13% chance of not getting a royal in the next 96.
7craps
Joined: Jan 23, 2010
• Posts: 1977
Thanks for this post from:
April 3rd, 2019 at 7:14:42 AM permalink
Quote: Joelesely

What are the odds of being dealt 4 to a royal flush, example akq10 of clubs

should be easy to calculate the PROBABILITY using a calculator.
(someone else can explain 'odds' that are related to probability but is not the same as)
`gp > (binomial(4,1)*binomial(5,4)*binomial(47,1))/binomial(52,5)%1 = 47/129948gp > 1.*%1%2 = 0.00036168313479237848985748145412010958229gp > 1/%2%3 = 2764.8510638297872340425531914893617021`

(binomial(4,1)*binomial(5,4)*binomial(47,1))/binomial(52,5)
in words
4 suits that can be the Royal (4choose1)
5 ways to choose the 4 ranks of the Royal (5choose4)
that leaves 48 cards for the last on the deal, but 1 of them is the 5th card to complete the Royal.
47 cards remain choose 1 = 47
47*5*4/combin(52,5)= 940/2598960=47/129948=the probability
Quote: Joelesely

and then drawing 96 hands with zero royal flush????

1 chance in 47 of getting that 5th Royal complete card (I am well over 100 times without any Royal in that situation)
that means 46/47 is the chance(probability) of NOT getting the 5th card to hit the Royal.
(46/47)^96=0.1268695734152(rounded)
about 1 in 7.8821 (10 in 79 or even 100 in 788)
Quote: Joelesely

Or is this rigged?

no, just my opinion
winsome johnny (not Win some johnny)
Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 3rd, 2019 at 8:25:59 AM permalink
What's the max draws on 4 royal to complete royal guaranteed? 1/1000?
Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 3rd, 2019 at 4:47:36 PM permalink
According to your math a little over 1000 draws would be 0.00%?
Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 3rd, 2019 at 4:48:46 PM permalink
According to your math a little over 1000 draws would be 0.00% of not getting the royal?
Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 3rd, 2019 at 4:56:07 PM permalink
Not single line. I played 96 times. I got 4 to a royal dealt and discarded the 5th and it dealt 96 times the 5th card.
7craps
Joined: Jan 23, 2010
• Posts: 1977
April 3rd, 2019 at 5:25:26 PM permalink
Quote: Joelesely

What's the max draws on 4 royal to complete royal guaranteed? 1/1000?

there really is no guarantee. It happens when it happens
because the event is an independent event
(unless the code in the machine is rigged like it was done in Vegas back in the late 1980s.
The American Coin Caper. Book: Licence to Steal. Can be found in Google books.)

(46/47)^1000= 4.5706055837236273344319610670313054778 E-10

I went almost 20 years before I got that 5th card for the Royal. (Age 21 to age 40)
Forget now how many rounds that was but it was a lot.

My best effort was when I lived in Reno and got 3 Royals in the same afternoon at 3 different casinos.
could not have been more 1,000 rounds played. And they were all on Deuces Wild. just 2 of them needed that 5th card to complete.
One Royal, after they paid me the progressive, the very next hand was dealt 3 Deuces, and yep, the 4th fell! My wife screamed at me because I was winning so much and she could only muster a few 4oaks!

one almost never knows when that Royal will hit.

My last 16 Royals, 15 have been when I needed 2 cards to complete
and 1 was just a few weeks ago when I needed 3 to complete. (In Hearts)

hope this helps
winsome johnny (not Win some johnny)
Joelesely
Joined: Mar 20, 2019
• Posts: 17
April 3rd, 2019 at 5:32:48 PM permalink
Thanks for the reply I'm not sure if you understood but I've played vp that runs each hand 96times and even royal won't pay 800x bet it gets divided by 96 hand vs bet. So royalhitting on 1 of the 96wins doesn't put me that much ahead. In fact in one casino online I played each hand 500 times and 1royal hitting in 500 plays less then 2x my bet lol. So not hitting royalwhen drawing each hand 500x times is terrible cause it hardly pays. The only time i would get 800x is if i got a dealt royal or if all 500 hit royal lol . But anyway i didnt hit 3 royals in over 3 cycles then 3royals hit in a 53 draw 4 to royal. Also had 3 to a royal hit 2x royal on 53 hands/draws lol.