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-   -   Badugi Dilemma (http://archives1.twoplustwo.com/showthread.php?t=534582)

karpov 10-30-2007 11:48 AM

Badugi Dilemma
 
Before the last draw and HU you are first to act and you have A23Q Badugi, you know villain is drawing 1 because he acted out of turn when he called your bet. What is better, stay pat leaving him with a max of 8 outs or draw one and he will have 10 outs to beat you but you also have the chance to improve to a better Badugi and bet the river. By the way a 123 value bet won't work because he has such a rough hand the will only call you or raise you with a better hand. I believe there is a lot of math involve to solve this dilemma.

*TT* 10-30-2007 02:12 PM

Re: Badugi Dilemma
 
[ QUOTE ]
I believe there is a lot of math involve to solve this dilemma.

[/ QUOTE ]

Its already been solved, your a favorite. Stay pat. Value betting however is a different discussion, from your read it sounds like he is not paying off but I still think betting is slightly the better option.

DeathDonkey 10-30-2007 07:44 PM

Re: Badugi Dilemma
 
TT you are not understanding the problem, or you think you understand it and are just wrong. You are a favorite over his draw if you stand pat, but you are also a favorite over his draw if you break. In fact, as karpov writes in the initial post, you are almost as big a favorite if you break (he picks up the K and Q outs but you now have a redraw). I would always break here but I think its a close decision, the math can't be that nasty on it.

-DeathDonkey

*TT* 10-30-2007 09:38 PM

Re: Badugi Dilemma
 
[ QUOTE ]
TT you are not understanding the problem

[/ QUOTE ]

you are right, I missed the obvious in the question. Without accounting for dead outs:

Villain has 7 outs to beat hero if hero keeps the Q, he is likely 5.9:1 against improving to a winning hand.

If hero breaks both hero and villain have equal odds to make any Badugi - 2:1 against.

When the villain catches a Badugi then the hero is naturally drawing cleaner, but at worst this usually means the hero is around a 10% equity dog (9:1 against), at best with 10 outs the hero might be a 21% dog (3.9:1 against).


So 44% of the time when the hero breaks the villain will make a Badugi and the hero won't. 83% of the time the villain will fail to make a better Badugi if the hero stands pat with his Q. Then there is the factor of how often when both hero and villain make a Badugi that the hero's Badugi will be better (thats a bit to heavy for me, I need help with that).

All in all it looks like standing pat is still the best option but I'd prefer that someone checks my math before its the definitive answer because I am rusty.

MarkGritter 10-30-2007 11:52 PM

Re: Badugi Dilemma
 
So, if you pat he has about 8 outs (maybe 7) in 44 remaining cards, which is odds 4.5 to 1. 18% of the time he makes his hand. Let's say he gets an extra bet out of you every time. (He can't do quite that well if you play the game-theoretic optimal, but he definitely has the ex-showdown advantage when you are pat and he is in position.) So you earn 0.82 * p - 0.18 bets

Let's give him some crap like 762x. Again we'll vastly simplify stuff and assume 1 additional bet goes in on all the Badugi vs. Badugi cases and 0 bets otherwise. He has 10 outs to a badugi while you only have 9. (no Q!)

There are 1892 possible cases
In 61 of them you both make a Badugi but yours is better
In 29 of them his Badugi beats yours. (Total=90, good)
In 9*(43-10)=297 you make another Badugi but he doesn't
In 10*(43-9)=340 he makes a Badugi and you do not
The remaining 1165 cases you win with the best 3-card hand. (Check: does this make sense? (44-9)*(43-10) = 1155, close enough... there are 10 cases missing somewhere.)

So, you get 1165/1892 * p + 65/1892 * ( p + 1 ) + 29/1892 * (-1) + 297/1892 * p =
0.616 p + 0.034 p + 0.034 - 0.015 + 0.157 * p =
0.807p - 0.019

Given the assumptions above:
Patting =~ 0.82 * pot size - 0.18
Drawing =~ 0.81 * pot size - 0.02

This suggests drawing is slightly better unless the pot is very large. I think the 32A draw is actually worth more on the last round of betting than the above analysis suggests (even out of position) so I drawing is actually worth a bit more. But you'd need a game-theory solver to tell you how much it is really "worth".

Phat Mack 10-31-2007 03:19 AM

Re: Badugi Dilemma
 
[ QUOTE ]
He has 10 outs to a badugi while you only have 9. (no Q!)

[/ QUOTE ]

I'm not sure how deeply we want to get into this, but the above is only true if they are drawing to the same suit; otherwise it should be 9 and 8. Correct? (Even if they draw to the same suit, the queen is gone, so it might be 9 and 9. hmmm...)

palman 10-31-2007 04:33 AM

Re: Badugi Dilemma
 
So if the math shows it's a really close call, isn't the fact that you can win many bets on the end by breaking and can't put a bet in feeling good by standing pat on the end the deciding factor leaning towards breaking?

MarkGritter 10-31-2007 11:27 AM

Re: Badugi Dilemma
 
[ QUOTE ]
[ QUOTE ]
He has 10 outs to a badugi while you only have 9. (no Q!)

[/ QUOTE ]

I'm not sure how deeply we want to get into this, but the above is only true if they are drawing to the same suit; otherwise it should be 9 and 8. Correct? (Even if they draw to the same suit, the queen is gone, so it might be 9 and 9. hmmm...)

[/ QUOTE ]

If Hero has 32A and Villain has 654, then, yes, either they are both drawing to the same suit or they each hold one of each other's outs.

If Hero has 32A and Villain has 732, though, then they can each have their full complement of outs, for example:

3c 2s Ad (drawing to hearts: 456789TJK)
7d 3h 2c (drawing to spades: A45689TJQK)

Phat Mack 10-31-2007 03:59 PM

Re: Badugi Dilemma
 
Interesting. If they have at least one common card, and the opponent's common card is of the drawn-to suit, the blocker does not exist. Baysean analysis could tell me how often this happens, but I'm not sure I'll mess with it. [img]/images/graemlins/wink.gif[/img]

*TT* 11-01-2007 02:36 AM

Re: Badugi Dilemma
 
Mark - good catch with the Q. Need to run my numbers again to see why you found dropping the Q is a favorite I cat imagine one out would change the results that much - but obviously it has.


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