4 to the Royal 3 times?????

[faygo]

[QUOTE=faygo]my story;
 
 
 

At the time, Webman and Shadowman took shots at this for you; I'll try to fill in some blanks after making some assumptions.  If we choose to consider KQJT9 suited as a straight flush and not a 4-royal, we have to consider the KQJT case separate from the other 4-royals.

If we want to know the odds on the next two hands of hitting 4-royals in which the 4 cards are in the same order and are of the same rank and suit allowing the odd card to be in any position and to be different cards in the 2 hands, the calculation for the probability is:

[KQJT]  (184 / 2598960) x (46 / 2598960) x (1/24) +

[AQJT, AKJT, AKQT, AKQJ]  (4 x 188 / 2598960) x (47 / 2598960) x (1/24) = 43,808 / 162,110,233,958,400  or about 1 chance in 3.7 billion.

The first factor is based on getting any 4-royal in any order and any suit on the first hand; the second factor is the number of odd cards that are possible to be matched with the 4-royal (with KQJT, I don't allow the suited 9 to be a possibility, which is why there is one less card there); and the third factor is there because there are 24 possible orderings of the 4 cards in the royal hold.  If you also wanted the odd card to be in the same position as the first hand, you can change this last factor from 1/24 to 1/120 (or multiply the odds that I state here by 5).

As Webman pointed out at the time, the odds are quite a bit less if you simply consider the chances of the same draw on the next hand only occurring AFTER you have already been dealt one hand with a 4-royal.  But they are still mighty slim.  If the 4-royal were KQJT, the odds would be 1,355,978 to 1; otherwise, the odds would be 1,327,128 to 1.  You get this by eliminating the first factor in the previous calculation.

All in all, pretty odd, my friend--another once in a lifetime experience!

More importantly though, good luck to marie's and your Spartans.  My Buckeyes came up a bit short tonight.  Congratulations to Tennessee fans out there.
[/QUOTE]
 
Sorry about the Buckeyes (well almost) State up 4 at the half.
 
I might be in trouble as I am starting to understand this math stuff. I could never spell it out myself but seeing it in print is starting to make sense.  Thanks new2vp.

[New2vp]

Congrats Eduardo, though I'm sorry it came at the expense of the Buckeyes.I still need Duke to get to the Final Four to win a small pool; otherwise I wrap up 2nd, with 1st and 2nd paying 80% and 20%.  I had 3 entries.  One entry was eliminated last Saturday.  The 3rd entry still might come in 2nd but the chances are pretty remote, though not as unlikely as all these 4-to-the-royal probabilities (I estimated the probability at the beginning of the game to be 6.9%; for this one to get 2nd, I need (1) Duke to get to the Championship, (2) West Virginia to beat Kentucky tomorrow, and (3) the total score in the championship game to be 154 points or fewer.)The Purdue-Duke game has been pretty tight, but the Dukies just went on a little run and are up 7 points midway thru the 2nd half.

[New2vp]

 
Sorry about the Buckeyes (well almost) State up 4 at the half.
 
I might be in trouble as I am starting to understand this math stuff. I could never spell it out myself but seeing it in print is starting to make sense.  Thanks new2vp.You're more than welcome.  Since it won't mess up any of my brackets, I'm rooting for Michigan State, too, because I'm a Big 10 fan.  Sadly, I can't simultaneously root for Purdue since that will cost me.

[Tedlark]

I thought this was a non-wagering site? LOL, good luck in your pools gang.

[New2vp]

I thought this was a non-wagering site?I'll bet you're right!

[Tedlark]

Hey I thought you math guys weren't supposed to be that funny New2vp      

[GaryP]

Thank you for the info. The gentleman who sends the video poker e-mails has said he won more than 1 million dollars on video poker so I did not know if he was being upfront about four to the Royal 3 straight times. but with this info you provided I can see how it is possible.

[Eduardo]

Just as inportant as seeing how it is possible is understanding that it is possible with fair machines. People see short patterns like this and assume the machines are not random because of it. In fact, it is something that happens in random circumstances.

[GaryP]

Edwardo, that is the basis of the man's e-mail, that the machines are not random. That is why he thinks he got 4 to the Royal 3 straight times. Thank you.

[cddenver]

Just as inportant as seeing how it is possible is understanding that it is possible with fair machines. People see short patterns like this and assume the machines are not random because of it. In fact, it is something that happens in random circumstances.


 
I had an interesting "double flip" happen not once, but TWICE in a single session recently.  On two dealt 3oak's I picked up the two dropped cards on the draw, in different suits, in the same hand positions.  TWICE.  Pretty long odds against that.  But as you say, it's inevitable on machines operating randomly that you'll hear stories of plays like that.
 
Now if it happened 40% of the time that would be different.