Seeing the same flop

[BruceZ]

[ QUOTE ]
Bruce,

Thanks. I knew that was wrong. Silly, the way I wrote the program, I was actually finding n. So the answer in this case is 175. After 175 flops, there is a 50% chance that at least 2 will be identical.

gm

[/ QUOTE ]

Here's my Excel solution:

=PERMUT(22100,70)/22100^70*PERMUT(22100-70,70)/22100^70*PERMUT(22100-70-25,70)/22100^70

70 + 70 + 70 -25 = 185.

EDIT: I fixed this formula in latter post. I now get 175.000 flops for a 50% chance of duplicating.

[MickeyHoldem]

Yes 175 is very close to the answer I got... 176... I'm not sure if you have forgotten to count the initial flop that has zero chance... or that my computations are flawed by the limitations of these wonderful machines we rely so heavily on.

If you consider order to be important... you need to see 430 flops. (I think [img]/images/graemlins/grin.gif[/img])

[BruceZ]

I get 175.000 now also, now that I've fixed my Excel kludges. The first flop isn't an issue.

=PERMUT(22100,70)/22100^70*PERMUT(22100-70,70)/22100^70*PERMUT(22100-70-70,35.000)/22100^(35.000)

= .501.

70+70+35.000 = 175.000.

This is the same as PERMUT(22100,175.000)/22100^175.000 = 50.1% chance NOT duplicating. 176 gives 49.7% chance of NOT duplicating.

[BruceZ]

I've been doing a lot of edits on the fly to the conclusion in my last post. If you check it now, it should be final. 175 is a better answer than 176. 175 gives a 50.1% chance of not duplicating, and 176 gives a 49.7% chance of not duplicating.