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.

[MarkGritter]

Here's some calculations I did in an earlier thread about drawing one to 876 or better. (One draw only.)

There are 560 distinct ways to make a badugi. (56 starting hands, 10 outs for each.) The median of the resulting badugis is 932A.

The median jack-or-better badugi under these conditions is somewhere in the 87's. (The median 9 or better is somewhere in the 85's, not shown below.)

I think this really illustrates the power of drawing smoothly (and I try to draw much smoother than 876 in the half-pot game.) Anybody drawing to a T is worse than more than half of the badugis made by a player drawing to an 8.

Spreadsheet explanation:

Left hand column lists all possible drawing hands. Each finishing hand (top two cards only) are shown along the top. The intersecting cell contains the number of outs for the drawing hand, assuming he isn't breaking a badugi.

At the bottom we total the number of ways to make each finishing hand, and keep a cumulative total so that we can eyeball where the median is.

[MarkGritter]

I did some math about standing pat on the last draw here:

http://forumserver.twoplustwo.com/sh...Number=3918135

If your opponent all have a 32A and are drawing to the same suit (the worst case for you):

Any badugi is a 35:9 (80%) or better favorite vs. a single opponent.

The worst badugi is still a 60% favorite vs. two opponents.

The worst J-high badugi is only a slight dog (49%) vs. three opponents.

[RoundTower]

I wrote a program that manipulates badugi hands. It's not very advanced. What would you guys like to see it do?

Not promising anything but I will listen to all suggestions.