I'd like to know when you're dealt a badugi in Badugi, where does that hand stand in relation to another random badugi hand? i.e. both hands have four different suits and ranks.

• Example 1: I'm dealt a J-high badugi (Jh 8s 7d 3c). Roughly speaking, what are the odds that I'm ahead of another random badugi?

Implicitly, assume you stand pat on all three rounds.

• what are you looking for? a number? or how to play such a hand? Feb 15, 2012 at 15:05
• Are you also assuming your opponents stand pat? If not, what are they drawing to? Feb 15, 2012 at 17:58
• Yeah, it's as though you're all-in in round 1, and everyone stands pat each round
– CjS
Feb 15, 2012 at 18:51
• Really didn't understand whats this question contribute. All you want is how many hands you can beat? Feb 15, 2012 at 20:20

I was thinking about how to explain my question a bit more and then realised I could work out the answer.

I wrote a small python script to count all the badugis one can be dealt.

``````715 badugis in total
4 high:    1,  0.1% of tot. Cum   1,  0.1% of total
5 high:    4,  0.6% of tot. Cum   5,  0.7% of total
6 high:   10,  1.4% of tot. Cum  15,  2.1% of total
7 high:   20,  2.8% of tot. Cum  35,  4.9% of total
8 high:   35,  4.9% of tot. Cum  70,  9.8% of total
9 high:   56,  7.8% of tot. Cum 126, 17.6% of total
10 high:   84, 11.7% of tot. Cum 210, 29.4% of total
J high:  120, 16.8% of tot. Cum 330, 46.2% of total
Q high:  165, 23.1% of tot. Cum 495, 69.2% of total
K high:  220, 30.8% of tot. Cum 715, 100.0% of total
``````

To answer my example, a J-hi badugi is a favorite (53.8%) over any random badugi. Nearly 31% of all dealt badugis are K-high etc.

• I purposefully ignored suits because it doesn't change the answer. Surely there are 4!=24 combinations of suits for each badugi, regardless of level. So the 24 is a constant factor and doesn't affect the result.
– CjS
Feb 16, 2012 at 7:04
• nice work man;-) Feb 19, 2012 at 11:39