Odds of big hands on the deal

[Matt_Lessinger]

Hi all,

Long time reader, first time poster.

I’m familiar with the odds of being dealt a Royal Flush are about 650,000 to 1. I’ve never been so fortunate. However I have been dealt quad deuces in a multiplay deuces wild game, and just this past week I was dealt
five-of-a-kind in a multiplay kings-or-better JW machine! I truly had to do a double take. I can’t find anywhere what the odds of being dealt five-of-a-kind are in joker poker. I just want to know exactly how lucky I got. If someone also has the
odds of being dealt four deuces in a non-joker game I’d be interested in that too as a comparison point.

Thanks in advance!

Matt

[Jeff_Cole]

Probability of being dealt deuces:
There are 48 non-deuces that can be used in a dealt deuce hand.
The sample space is 52 cards dealt 5 at a time, which is C(52, 5) = 2,598,960.
48/2,598,960 = 1/54,145…so about every 54k hands.

Probability of being dealt 5 of a kind:
Assuming there is 1 joker, the sample space is C(53, 5) = 2,869,685.
There are 13 ranks—you want all 4 of one rank plus the joker.
13/2,869,685 = 1/220,745…so about 4 times as rare as dealt deuces and about 3 times more likely than a dealt royal (1 in 649,740).

Here is 5-card’s link to VP odds:
http://www.videopokerhelp.net/odds.htm
Lots of great info there.
Jeff