Video Poker Video poker question about odds

I just got back from Las Vegas and had a great time. I was at South Point Casino and got super lucky with a royal flush. I was playing JoB 9/6 and was playing quarters. I was dealt a 10 and King of diamonds and just as I was hitting the draw button I noticed I had another high card. According to my little cheat sheet, I was supposed to hold the 2 high cards. I guess muscle memory took over and I hit the draw button and up came the Jack ,Queen and Ace of diamonds. I was stunned and didn't realize right away what I had. Anyone know how to calculate the odds of drawing 3 cards to get a Royal Flush. Oh, I love Las Vegas.

 

Paging Dr. Tringlomane

 

Holding 2 to a royal will result in a royal 1 out of every 16,215 attempts.

 

Thank you very much.

 

:evillaugh

Yep. Still haven't hit that for a royal in the casino. Not so patiently waiting. :evillaugh

Chances of making of completing a royal by number of royal cards held.

Hold 4: 1 in 47
Hold 3: 1 in 47*46/2 = 1 in 1081
Hold 2: 1 in 47*46*45/(3*2) = 1 in 16,215
Hold 1: 1 in 47*46*45*44/(4*3*2) = 1 in 178,365
Hold nothing: 1 in 4 x 47*46*45*44*43/(5*4*3*2) = 1 in 383,484.75

Nice hit Mark!

 

That is correct ... needing 3 specific cards on the re-draw, out of the remaining 47 would yield the following :

3/47 x 2/46 x 1/45 = 1 out of 16, 215

 

This is exactly what I did at Main Street Station on Sept. 11. It's in my trip report.

 

I think that in the "hold nothing" scenario, you need to divide by 4, since it can be any one of four suits. Or just divide by (20*4*3*2) instead of (5*4*3*2)

 

I hit one on a re-draw once holding nothing. I knew it was a long shot but I didn't know it was over a million! $2000 Winner!!!! BIng Bing Bing!!!

 

Whoops you're right! By the time I got to holding no cards I was into copying the pattern too much. Thanks!

I made it seem four times less likely because I screwed the math up. Doh. But throwing away all the cards isn't super common either, so throw both factors together, and one can expect a "throwaway" royal to show up roughly once every 14 million hands played or so.

 

Several years ago in the lobby area of the old Fitzgerald's, playing a nickel Multi-Strike - threw away all five cards of the top 8X hand and was dealt a ROYAL = $1600.00

 

Adjusted for my recent foray into Video Poker in Las Vegas.

 

For anybody who cares to know what the numbers in the above formula are:
To complete a royal flush the chances are 1 in [x! / (y! * z! * w)] where
x is the number of cards left in the deck
y is the number of cards you don't want
z is the number of cards you want
w is the number of different suits available for the royal flush; the previous posts assume that out of all five cards being discarded, none of them are a ten-value card)
! Is factorial where x! = x * (x - 1) * (x - 2) * . . . 4 * 3* 2

 

If a ten is discarded, then divide by three. I assume no one will discard a pair or more of tens nor any card higher than a ten in their discard of five cards.

 

Never hit a Royal on the draw or redraw. However, I have hit a Royal twice holding the lonely Ace. Once at Silverton and once at Rio. Guess I'm ahead of the curve on that one.

 

Right...I didn't want to make things messier than I already had...

 

Same odds (1 in 383,484.75) for getting a dealt Royal on the first five cards?

I believe that;s the only Royal I've ever gotten on a VP machine (with the exception of an occasional Royal on one hand of a 100-play VP machine), even when holding 4 to the Royal on a 100-play machine. Unfortunately, the dealt Royal was on a penny 100-play machine where I was playing 1 cent per hand. It was probably DDB I was playing and the 100 Royals paid something like $125 total ($1.25 per hand)..

 

No a dealt royal is harder than trying to draw one after you had garbage. With the deal you have 52 cards available to you, with the redraw you only have 47 left.

So the odds of a dealt royal is: 1 in 4 x 52*51*50*49*48 / (5*4*3*2*1) = 1 in 649,740

And royals are worth $2.50 each with one penny bet. Ironically my only royal in Vegas (2 others in other cities) was also on a 100-play game at Flamingo. Good news is I was playing max credits per line, making each Royal worth $40, but the bad news...playing only 6 lines because Vegas had kicked my ass that trip up to that point. So I got paid roughly what you did.