Figuring Odds of Being Dealt a Quad?

[Lucky Larry]

Tried the search but couldn't find how do I determine the odds for being dealt a quad? I play lots of multi-hand VP and I trying to figure out the rough approximation for the frequency of being dealt a quad. I have been dealt two in the last six months and my wife has been dealt around nine in the past two months. Quad 8's twice in the same night twenty minutes apart on different games. So how do I figure the rough percentage?

Thanks,

LL

PS Everyone have a great Labor Day weekend! Help the economy visit a casino.

[Eduardo]

On the deal, before even drawing any cards?

[Eduardo]

If you mean on the deal, I think it's about 1 in 4,000 if I remember right.

[New2vp]

Eduardo's memory is right as usual.  Odds are 4164 to 1.Recall there are 2,598,960 possible combinations of 52 cards dealt 5 at a time.  For quads there are 13 types and every one of these quads can be matched with one of the 48 other cards of a different rank.  So, there are 13 x 48 = 624 combinations that are quads.  This leaves 2,598,336 possible deals that are NOT quads.Thus, the odds are 2,598,336 to 624 or (dividing both numbers by 624), 4164 to 1.  Another way to look at is 0.024% of deals (1 / 4165 x 100%) will be quads on average.

[cddenver]

Thus, the odds are 2,598,336 to 624 or (dividing both numbers by 624), 4164 to 1.  Another way to look at is 0.024% of deals (1 / 4165 x 100%) will be quads on average.

 
Just in case there is any doubt on your numbers () I have a simulation that determines it the old-fashioned way, by actually cranking through all card combinations and it gives the same values.

[oej719]

I come up with the same answer.

[damule]

You mean like this:
 

[oej719]

How did you do that mr. damule?
Now that is what I call a special play on a hot cycle machine.
Life is good right?
Congrats to you.

[EDC1977]

Mule, is this recent? Congratulations! Quads w/kicker always nice.

[razuberii]

What a beautiful sight~~ Congrats~!