Re: [DL] 5 Deck of Cards - PS This will be long folks...

["Jeff Tolle" <jwtolle@hotmail.com>]

Doh.  Once again I went off on a long diatribe that was correct, but totally 
off topic!

OK - Now I'd like to remidy the situation.  (Arrgh - run away!  I can hear 
the cries now.)

I can't run the numbers right now, but I think you may be wrong here.  Let 
me try inductive reasoning to tell you why I think the numbers will change.

Lets assume, as you say, the increase in cards to pull (from 52 to 65) 
offsets the increase in pairs to get (or three of a kind, etc).

Lets assume we are trying for four of a kind.  Remember we are going on the 
premise that adding a suit does not affect the odds of a "non suit related 
hands" (ie it doesn't affect flushes.)

Well by that logic, there should be no change in the odds if there were say 
8 suits - like if you had two decks.  This does not sit right with me at 
all.  It seems to be much more likely to draw a pair from two decks of cards 
(given a pull of 5 cards - bad roll Mr huxter) than from two decks.

Still don't buy it.  Lets be a little more rigerous shall we.  In a regular 
deck of cards you have but one chance of getting 4 of a kind.  In a deck 
with 5 suits you have 5 ways of making 4 of a kind.  To offset this increase 
in odds, you would need 5 times as amny combinations of draws from a 65 card 
deck than a 52 card deck.

The actual increase (assuming a draw of 5 cards - again, bad roll for the 
huxter - why did I put that d4 sin Smarts?) is somewhere from 2.9 millin 
combos to 8.3 million.  Not enough to offset the increase in the number of 
possible ways to draw 4 of a kind.

My gut feeling tells me that this logic will play out for all "like card" 
combos.

It will take some time to figure out the numbers, but I think (hope) they 
will bear out this hypothesis.

By the way - this one's a doozie of a problem.  Just ask any probability 
expert.  They HATE poker problems.  Most of them I know give up and run a 
program to test all possible combos.

A'int probability fun?

Jeff "My family crest reads: 'But I digress'" Tolle
-------------------------------------

>From: "Leybourne, Brian" <Brian.Leybourne@airnz.co.nz>
>
>
> > IANANDIPHOTV, but here is my statisitcal reasoning.  BTW, not
> > only am I not Alan, I am not a statistician.  You are correct
> > that adding a card changes the chances of > drawing any one
> > card.  The formula to calculate the probability of drawing AT
> > LEAST ONE Joker is thus:
>
>
>But Jokers aside (I was really talking about the 5th suit, not the
>wildcards, they were an afterthought) the odds shouldn't change right?
>(Except for flushes?)
>
>Brian "??" Leybourne.
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