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Hi Dave - I see that 9/45 =0.2000. But that's the wrong answer!

The correct probability for one draw, if you're only drawing one card one time (and if you know Villain has a KQJT badugi) is 9/44.

I thought I was being helpful when I emboldened a response (fixed your post) to reflect the correct probability for one draw. Sorry if you took it some other way.

RubbishCards wrote: Exactly.

Buzz

Since this thread is getting some hits, I thought I'd post a problem I came upon a few years back. I wrote a badugi sim that used specified drawing parameters for the different player-agents. It used (Ta Da!) LISt Processing. It would take a player's hand, rank it as pat and identify its 1-card, 2-card and 3-card draws, and then play or fold it. The draws were identified and then rated by comparing them to the lists of all possible draws, with the "best" draw being selected.

Here's an example:

A 233 would have for 2-card draws A2, A3, A3 and 23. If the player-agent's parameters allowed, the A2 would be selected as the best draw from the ranking list that went something like: A2, A3, 23, A4, 24, 34 ... QK.

But in the above example, which is the best 2-card draw? My guess is that the A3 might prove better than the A2. How do you program something like that? The only way I know would be to brute-force it -- have it run out all possible combinations and select the best one, with a reporting mechanism for anything it considered an anomaly.

Is there a case where you would have this problem where you are also not doing something you'd never actually do, i.e. breaking A23?

When the 2 and 3 are of the same suit, I am assuming there would be a break.

Why don't you just keep the 3s then? Are you allergic to spades in some way?

OK, now I get it. Let's make it A233.

I dont understand why A3 would ever be better than A2 here?! Either way there are two deuces (2s, 2d) that will help or two threes (3s, 3d) that will help our hand.

I haven't done much more work on the calculator yet, but this seems a good a place as any to post a bit of badugi trivia I just came up with:

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), 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.

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.

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...

Correct.
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.
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.
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

Yeah I'm not saying someone will always make a badugi, I'm saying that IF it is known that they do have one (i.e. they are pat, you are assuming they are not snowing, and they are standing on ANY badugi), it is possible to narrow down their range based on the amount that they drew, and therefore have an idea of what % of the time your hand is good should you improve to a badugi yourself. In fact here are some more detailed results, for the top n% badugis in increments of 10%:

top 90%, 80%, ... down to 10%
xxxx drawing 4: KJ9A, K98A, K53A, QT7A, Q752, J976, J52A, T652, 942A
Axxx drawing 3: KT7A, K73A, QT8A, Q74A, J97A, J53A, T72A, 965A, 843A
A2xx drawing 2: K72A, QJ2A, Q52A, J82A, T92A, T42A, 942A, 842A, 652A

But like with everything, it's garbage in -> garbage out. If you think they will not pat a queen badugi on the first round then of course you can't assume that should you make a J it is good >50% of the time.

I see. Good point. The flaw is not so much that opponents in my games are snowing as that they are not necessarily standing on any badugi. You'd have to know individually what opponents would stand on.

As I wrote in my last post, I got badly burned the last time I stood pat on a ten badugi. And a ten badugi is really the same if you make it on your first draw or your second (or third); it's still a ten badugi. It still loses to a nine badugi.

I think, in retrospect, not breaking a ten badugi is probably not a very good play for me in a pot-limit or no-limit game. I can't tell if someone betting has a better badugi or not. If I have taken a draw, someone could be betting a three card badugi into me. If I stand pat, any bet into me is probably a badugi, but maybe at least a seven. (Depends, of course). And what do I do with my ten badugi? Do I fold it if someone is bold enough to bet into me? (rhetorical).

The long and short of it is I don't think I want a ten badugi. I want to either get a better badugi or simply miss and have an obvious folding hand. I don't want a hand where I'll be faced with a difficult, mistake prone, decision.

What about a nine badugi? I don't know. I have to think about that some more. (I'm obviously not an expert at badugi).

And my opponents are regularly breaking badugis and drawing for better ones.
Thanks for the data.
My current thinking is it's poor play to pat a ten badugi, (and I don't know about a nine).

Buzz

pretty much spot on from my experience... mostly about a couple months of pot-limit freerolls @ oddsmaker.
nine badugis are in that gray area, like pat eights in triple draw-the smoother
the better; altho you have a 9-card range vs. a 7-card range, villain has about as many outs w/ a 1-card draw in either case.

Is pot limit actually a fairly common / normal way of playing? I'd imagine that medicore badugis have a big reverse implied odds problem in big bet games, and strong 1 and 2 card draws go up in value. I only play limit, and in the game I play regularly (micro stakes MTT with many clueless opponents), a pat ten is basically the nuts.

WHERE CAN I FIND THESE GAMES?