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

[PEGGoff@aol.com]

In a message dated 1/13/00 10:25:42 PM Eastern Standard Time, 
darious@darious.com writes:

> Your first card is X.  To get a pair out of that, you have four chances to
>  match X.  On the first pull you are seeking 5 cards out of the 53
>  remaining, second pull has you looking for 5 out of 52, then 5 out of 51,
>  and 5 out of 50. 
>  (both jokers included).  Final chance at a pair (ignoring the hands that
>  achieve better results, etc.) is roughly a 38% chance.  

Actually, it's better than that.

I'm not going to hurt my brain doing the math on it right now (I already 
suffered through it once for Hucksters & Hexes--and I ain't no statistics 
major <g>), but here's the logic behind it:

We'll call the first card drawn X; on the second draw you have 5 chances out 
of 53 (counting two jokers) of drawing a second X. If you don't succeed, you 
instead draw card Y. Now, on the third draw, you have 5 chances out of 52 of 
matching X and, failing that, 5 chances out of 52 of matching Y. Failing 
either match, you draw card Z; on the fourth draw, you have 5 chances out of 
51 of matching X or Y or Z. And so on. 

Now, since each draw is exclusive (i.e., you can't get both an X and a Y 
match on a single draw), the calculations make my brain hurt. 

Also, as this method doesn't even factor in the chances of a straight, flush, 
or other combinations, it's easier to do the calcs by simply subtracting the 
number of hands that _aren't_ a pair from the total possible hands to arrive 
at the final odds (as Allan demonstrates in a later set of posts).

John Goff