Badugi now on Doyles Room!

[Tom Bayes]

Hey, I have a +8BB/hour winrate at Badugi! OK, I made $0.80 in about an hour at the 5c/10c table.

Here's what I saw:
1. loose-passive as hell (I limped too much)
2. lots of people drawing 2 and 3; I'm pretty sure drawing 3 is always a mistake and drawing 2 is usually a mistake
3. lots of people chase all the way
4. lots of people will rap pat with any badugi for all 3 draws; I don't have a good feel yet for what you want to break
5. lots of people don't understand the importance of having a badugi hand with 4 different suits, but are just trying to make a 4-card lowball hand
6. We need Gritter to churn out some combinatorics for us! I'm too lazy to do it myself.
7. Didn't try the 1/2 Pot Limit (aka big-bet with training wheels), I only played limit. Full Pot Limit Badugi at reasonably high stakes is gonna be a game for people with 2 brass ones, I think.

[timprov]

[ QUOTE ]
Strategery?

[/ QUOTE ]

In a loose game, you should be safe playing 3-card sevens or better, and two cards to a five if you can get in cheap on the button or in the blinds. Post, avoid paying to draw two. Anything worse than a smooth eight probably isn't worth paying a bet to show down against a player who knows the rules. That should be a winning basic strategy.

In a tighter game rough three-card hands and badugis go way up in value, and you're going to want to knock people out at pretty much every opportunity.

[Notorious G.O.B.]

Found an article, although it appears to refer to the "only complete badugi's count as badugi's" variation:
Bagugi Strategy

[ QUOTE ]

I wonder if it's only Doyle's Room, or if other Tribeca skins will pick this up. I checked GP and they don't have Badugi showing.

[/ QUOTE ]

VC at least have it at the moment, exact same tables as mentioned.

[MarkGritter]

[ QUOTE ]

6. We need Gritter to churn out some combinatorics for us! I'm too lazy to do it myself.

[/ QUOTE ]

OK, what the heck, I'm feeling bored at work. Random math geekage:

There are 52C4 = 270725 hands in this game. How many are Badugis (4-card hands)? A badugi has one card from each suit and no pairs. So it should be 13*12*11*10 = 17160. (We can reach any possible rainbow hand despite having a fixed suit ordering, so no fancy counting or inclusion-exclusion seems necessary.) Thus badugis form the top 6.3% of hand ranking (from #1 to #715 if I got the math right.)

What hand do you need to be a favorite to win vs any possible one or two draws? (Note that if have a badugi, you are by definition holding one of your opponents' outs.)

Ignoring discards for now, there are going to be 44 unknown cards HU. Say your opponent with A23x and you hold any badugi. Then he has 13 flush cards to hit, but 1 of them is in your hand, and the A,2,and 3 don't give him a badugi either. You are a 35:9 favorite vs. a single draw. If you opponent has already dumped 3 bad cards, you are a 32:9 favorite instead.

What if you have two opponents? Again ignore earlier discards. If they are both drawing for the same suit, then there are again 9 good cards, and 31 bad cards for them. The chance that both will miss is (31/40)*(30/39) = 60%. So it seems likely your badugi holds up vs. any two players drawing one. (Maybe a little more care is needed here because the same pair card may not be bad for both players, so one player could miss and still kill the second one's out. But let's just give them both a23x for now.)

With three opponents old #715 (KQJT) doesn't look so good. 16 known cards, 36 remaining. Again your opponents are better off if they are all drawing for the same suit. Compare schd schh schh schh -- about 9 diamond outs for everybody --- with schd ssch scch schh --- only 6 outs in each suit. Then the probability that your hand is good is only (27/36)*(26/35)*(25/34) = 41%. So you have an edge, but are no longer a favorite.

If we give Hero a rough Q-high badugi instead, that reduces the number of outs by one, and a J by two.

worst Q badugi wins = 28/36*27/35*25/34 = 44%
worst J badugi wins = 29/36*28/35*26/34 = 49%

So, a smooth J-high badugi should usually be the favorite vs. 3 players. (Against the A23x/A23x/A23x example only A23J would be a favorite, but most hands are rougher than that.)

But, your opponents are unlikely to be drawing to the best case, so a Q is probably a favorite in many real-life situations too.

[Luv2DriveTT]

I think I have been discarding my J high Badugi's too quickly [img]/images/graemlins/frown.gif[/img] Thanks Mark.

TT [img]/images/graemlins/club.gif[/img]

[MarkGritter]

The math here has a small double-counting error. The card you hold of the suit your opponent needs might not actually be one of his outs, because it might pair him. (How come I think of these things _after_ I have a beer with dinner instead of before?) So in the best case some of your opponents may have another out. In the silly a23x vs. ultra-rough badugis situation this is not a problem.

[CurryLover]

[ QUOTE ]
(Note that if have a badugi, you are by definition holding one of your opponents' outs.)

[/ QUOTE ]

Oops. Not quite true. Your opponent could be drawing for a diamond. You might have the 3 of diamonds in your hand, and he doesn't need it because he has the 3 of spades in his hand.

[MarkGritter]

[ QUOTE ]
[ QUOTE ]
(Note that if have a badugi, you are by definition holding one of your opponents' outs.)

[/ QUOTE ]

Oops. Not quite true. Your opponent could be drawing for a diamond. You might have the 3 of diamonds in your hand, and he doesn't need it because he has the 3 of spades in his hand.

[/ QUOTE ]

Yup, you're right. I noted that (in a response) after I'd gotten some beer into my system to clarify thought.

Badugi should provide some interesting analysis challenges, I'm interested to hear what insights you have.

[CurryLover]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
(Note that if have a badugi, you are by definition holding one of your opponents' outs.)

[/ QUOTE ]

Oops. Not quite true. Your opponent could be drawing for a diamond. You might have the 3 of diamonds in your hand, and he doesn't need it because he has the 3 of spades in his hand.

[/ QUOTE ]

Yup, you're right. I noted that (in a response) after I'd gotten some beer into my system to clarify thought.

Badugi should provide some interesting analysis challenges, I'm interested to hear what insights you have.

[/ QUOTE ]

I've been doing a lot of work recently at home on padooki, and I play a huge amount of it. I'm going to be posting some of my random ideas on the game next week. I'm not as strong at maths as you seem to be, though.