Quote:
Originally Posted by RubbishCards
Obviously when someone has a badugi, their range of possible badugis is wider/worse the more cards they drew. We know that the median dealt badugi is Q752 (357 out of 715 possible, ignoring suit combinations),
Correct.
Quote:
therefore if someone is pat on the first round and we assume they are not breaking any badugi, then 50% of the time they have a Q7 or worse.
But I don't think you can make that assumption. If I break the median badugi, say 2
,5
,7
,Q
, then I have three draws to catch an ace, three, four, six, eight, nine, ten, or jack of spades (a total of eight cards). I'm going to improve more often than two times out of five:
8/48+40/48*8/47+40/48*39/47*8/46=
0.167+0.142+0.120=0.429
And I'm going to improve to an eight or better more often than one time out of four:
5/48+43/48*5/47+43/48*42/47*5/46=0.286.
The last time I stood pat on a ten badugi (let alone a queen badugi), I got badly burned when someone caught an eight badugi on the third draw. It was a pot limit game and cost me all my chips. I don't think I want to do that again. That queen is going into the muck, badugi or not.
Quote:
If someone is drawing 1 with A23, then there are 10 badugis they can make, so the median would be between an 8 and 9, i.e. 50% of the time they have an 8 or better, 50% of the time they have a 9 or worse.
Yes, that's true if they make a four card badugi. But they're not guaranteed of making a four card badugi if they draw. The probability of making any four card badugi in three draws, if drawing one card each time, is:
10/48+38/48*10/47+38/48*37/47*10/46=0.512
Thus it looks like the median
hand they'll make if they draw is some badugi. But since the probability of missing
any badugi about 0.488, I'm guessing the median
hand they'll make if they draw is a king badugi.
Quote:
So what if they draw 3 or 2?
According to a dodgy bit of code I just wrote:
Axxx drawing 3: median is J97A (110 out of 220)
A2xx drawing 2: median is T92A (27 out of 55)
That's it...
Interesting, but they're not guaranteed of making
any four-card badugi, even if they only draw one card, and they're even less likely to make a four-card badugi if they draw more than one card.
Don't give up.
Buzz