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.

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what are you looking for? a number? or how to play such a hand? – amigal Feb 15 '12 at 15:05
Are you also assuming your opponents stand pat? If not, what are they drawing to? – Chris Marasti-Georg Feb 15 '12 at 17:58
Yeah, it's as though you're all-in in round 1, and everyone stands pat each round – CjS Feb 15 '12 at 18:51
Really didn't understand whats this question contribute. All you want is how many hands you can beat? – amigal Feb 15 '12 at 20:20

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I put 2 hearts in there and the equity actually increased from 33 % (which was before) to 37 % ... – Radu Murzea Nov 21 '12 at 19:38
@SoboLAN I have no idea what that comment means. – Mark Fraser Nov 21 '12 at 20:19
OK, so I put 2 Badugi hands there (4 different cards of 4 different ranks and 4 different suits). And made them... battle it out. So I got equity 33 % in one hand vs 66 % in the other. The first one had a heart and a club in it. So I removed the club and put another heart in there, which means it contained 2 hearts. Which means it wasn't a Badugi hand anymore. I made them "battle" it out again. So this time the equities were 37 % vs. 62 %. Shouldn't it be 0 % vs. 100 % ? (because 2 hearts means no Badugi which means no winning) – Radu Murzea Nov 21 '12 at 21:52
@SoboLan please send me that exact cards you were using for each simulation and I will take a look. Also, please confirm whether you changed the drawing strategies or just kept the defaults. – Mark Fraser Nov 22 '12 at 0:18
Since you haven't replied I can't help you further. Although reading your second comment again I can say part of the problem is you don't seem to understand that just because you don't have a badugi to start doesn't mean you won't have one at showdown. That is what the drawing rounds are for. – Mark Fraser Nov 27 '12 at 11:45

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.

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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 '12 at 7:04
nice work man;-) – Svisstack Feb 19 '12 at 11:39