I could use a little help from the odd guru's (ok, mathmatical
minds) out
there to settle an argument in our Tuesday night poker game.
What are the odds of getting three of a kind with the joker
counting as
aces, straights and flushes? You need at least a pair of jacks or
better
to open in this game.
as opposed to
What are the odds of getting four of a kind with dueces and the
joker
wild. This requires three of a kind to open?
My belief is that they are pretty close. Some others argue it is
much
harder to get the 4 of a kind.
If you can give this information in the form of this will happen 1
out
of every x hands, it would help us novices to be able to understand
it.
Thanks
Brad
Amarillo
Brad,
I am assuming you meant exactly 3 of a kind in the joker
game, and exactly 4 of a kind in the deuces/joker wild
game. I also assume this is a 5 card game, and the
question is the odds before a draw. Finally, I assume
you are using only 1 joker, not 2.
For 3 of a kind with the joker as the bug:
3 Aces can be done 10 x 66 x 4 x 4 = 10560 ways
3 other with 1 A/Jkr 12 x 4 x 5 x 11 x 4 = 10560 ways
3 other with 0 A/Jkr 12 x 4 x 55 x 4 x 4 = 42240 ways
Total = 63360 ways
For 4 of a kind with deuces/joker wild:
With 4/5 wilds: 0 ways
With 3 wilds: 10 x (66x16 - (12x6 + 4x46)) 8000 ways
With 2 wilds: 10 x 12 x 6 x 11 x 4 31680 ways
With 1 wild: 5 x 12 x 4 x 11 x 4 10560 ways
With 0 wild: 12 x 1 x 11 x 4 528 ways
Total = 50768
Total number of hands with joker = 2869685
Three of a kind about once in 45 hands.
Four of a kind about once in 57 hands.
Any real mathemeticians out there can feel free and
see if did any of this wrong.
--Jeff
ยทยทยท
--- In vpFREE@yahoogroups.com, Brad Riffel <wildcat@t...> wrote: