Padookie Math Thread

[fnord_too]

I'll start. I'm sure Mr. Gritter peobably has solved the game in one of the existing threads, but I figured I would start one to dump the work we are doing. (I guess this means I need to get a Doyels Room account to actually play the game.)

Counting: For any distinct Padooki, there are 24 possible combinations.
4's - 24
5'2 - 96 (we have to have a 5, and there are 4 ways to pick 3 ranks from the set (A,2,3,4) )
6's - 240
7's - 480
8's - 840
9's - 1344
T's - 2016
J's - 2880
Q's - 3960
K's - 5280
Total: 17,160

To check this, there are 13*12*11*10 = 17,160 possible Padookis (Paddokies?) so we are good so far.

Total possible 4 card hand = 270,725, so there is about a 6.3% chance (~1 in 16) of being dealt a Padooki. It looks like a J is about the median pat Padooki one will be dealt given they are dealt a pat Padooki.

I will come back and do some more math later, but by all means dump your calculations here.