Badougi: 2-card draws?

[nate1729]

Are 2-card draws ever playable in Badougi? I'm trying to grasp the game, but it's rather difficult because I have nobody to play it with and no B&M or online cardroom to play it in.

Voluntarily playing a hand you're going to be drawing half of offends my poker sensibilities, but the chances of improving to a one-card draw are very good. Certainly it seems correct to steal the blinds with good two-card draws, and I'd imagine it's correct to limp after several limpers in late position with them. I'd also guess it's correct to fold A2xx in early and middle position, and also to most raises.

Any thoughts?

--Nate

[The Armchair]

I think a great two card draw (say, A2) in position is better than a good one card draw (236) out of position. Improving to a Badougi of any caliber is rough no matter what, but going to a three card hand is not.

The advantage of position is enormous, though, because you can stand pat with a rough Badougi (K or Q high) on the third draw if your opponent takes a card, knowing full well that they are drawing to at most 9 outs.

[nate1729]

Thanks for your thoughts.

Now, say you're in late position and dealt a K32A Badougi. You're just under 50% to improve your hand if you draw to your 9 cards. I'd imagine you'd want to break your hand in multiway pots, especially raised ones, but what about heads-up or shorthanded pots? If you stand pat on every street, your opponent will almost certainly wins if he hits a Badougi; if you break, you'll win if you both miss or if you hit and he misses; if you both hit you're a slight favorite. (Of course other strategies are possible.) For simplicity say both players are about 50% to hit

Both hit: you win 55% or so of the time.
Both miss: you win almost all the time.
You hit, he misses: you win
He hits, you miss: he wins

Which all adds up to your being something like a 65% favorite; also, you have playing advantages and might get him to break a better hand, etc. This seems to suggest that you should break many Badougis even in heads-up pots.

Any thoughts on the matter?

--Nate

[nate1729]

I have a lot to learn about this game.

--Nate

[The Armchair]

[ QUOTE ]
Thanks for your thoughts.

Now, say you're in late position and dealt a K32A Badougi.

[/ QUOTE ]

What I originally typed in: I honestly don't know, but I think I'd stand pat with any Badougi if heads up and if I had position.

What I just noticed:
A23K badougi beats (a) any non-badougi and (b) any K-high badougi other than itself. A23x, where the 4th card does not play, beats any non-badougi other than itself. That means that, in standing pat, you gain very little -- you can now beat almost zero additional hands.

At least I think that's right. Assuming it is, there is almost no reason not to pitch the K.

[nate1729]

Yeah, that's what I realized, too late to edit the post.

The more interesting question is if you have something like a jack-high Badougi. Now you only have 7 outs three times, or a 39%ish chance of improvement. Now what if your opponent is drawing (simplifying to: you have 2/5 chance of hitting, your opponent has a 1/2 chance of hitting.)

30%: he hits, you don't, he wins
20%: you both hit, you're a favorite, also you have a playing advantage because you're in position. More on this later.
30%: you both miss, you win
20%: you hit, he doesn't, you win

Meanwhile, if you keep your J, you win the half of the time he misses, and when he hits, he's probably winning 7/10 of the time. So you win something like 65% of the time. Meanwhile in the first case you win with approximately the same frequency.

The question: does the playing advantage you get when you both hit outweigh any disadvantage you might have? (For example, he might take a shot at you with a bluff, or be more apt to value-bet a weak Badougi. On the other hand you can probably value-raise a lot.)

I expected this decision to come down in favor of keeping the jack, but it seems very close and in fact seems to favor breaking. Those with playing experience -- care to add input? Am I missing any obvious factors?

--Nate

[The Armchair]

[ QUOTE ]
Yeah, that's what I realized, too late to edit the post.

The more interesting question is if you have something like a jack-high Badougi. Now you only have 7 outs three times, or a 39%ish chance of improvement. Now what if your opponent is drawing (simplifying to: you have 2/5 chance of hitting, your opponent has a 1/2 chance of hitting.)

(snip)

Meanwhile, if you keep your J, you win the half of the time he misses, and when he hits, he's probably winning 7/10 of the time.

(snip)

I expected this decision to come down in favor of keeping the jack, but it seems very close and in fact seems to favor breaking.

[/ QUOTE ]

I think your math may be off a bit. If I have A23Jb (b for "Badougi), and my opponent has a made A23 with a rag, he has only 7 outs to beat me (and perhaps one out to tie); that is, his odds of beating me if I stay pat are equal to my odds of improving by drawing one. You put it at 40%, so I'll go with that.

In that case, he'll win only 40% of the time if you simply stand pat _and_ he stays for all three draws. Here's a simpler situation:

Opponent has A23x
You have Jack Badougi (A23x) and position.

Let's assume he has perfect knowledge of both your hands after the first round of betting but before the first draw.

Opponent open-raises, you 3-bet, folds around to opponent who calls. 7.5 small bets in the pot (including blinds). He draws and hits 7.5 times out of 44 attempts (half an out for the J), you stand pat.

He is almost certain to check in any situation -- if he improves, he'll check-raise; if not, he'll either check-call or check-fold. You are likely to be in either situation.

So, he is getting 8.5:1, and if he missed, he needs 7.5:43, or just better than 6:1 to call. He has that, so he calls.

Let's say he takes one again and misses again. Again, he checks to you and you bet. Now he is getting only 5.5:1 on his call, and he needs 5.6:1 to call. It is only -EV if you won't call the river bet if he hits.

I don't think you want to give him the odds to draw out on you, and you don't want to give him a free draw (so checking any street through is bad). Also, I think you have to 3-bet the flop to make this heads up. It appears that standing pat with a J is not so good.

[bobman0330]

What if we push the situation in the other direction? Should you break a hand like K632b?

[nate1729]

Thanks for the calculations you presented. I think there's some value to just looking at the situation in a betting-free context, though, if only to get a feel for the odds and what some of the right moves might be. For example, it's helpful to know that in 2-7, a jack is something of a cutoff for a hand that's a favorite over a draw with one to come (not that you never break a jack when your opponent is drawing, but you know.) I'd like to have some similar instinctive grounding. For example, I can't imagine breaking 932Ab except under very heavy pressure, but Q32Ab seems like an easy break.

Is there anything wrong with the "hot and cold" equities I presented in the breaking-a-jack case above?

--Nate

[nate1729]

Hmm. Interesting question.

A few thoughts: there might be playing advantages to standing pat with this hand on the last draw out of position. You might get your opponent to break a hand like Qxxxb or a better Kxxxb.

I think this is a pretty clear one-card draw either in or out of position if you're dealt it.

I think hands like QT64b are tougher cases; I'd be inclined to ditch them in multiway pots or else play them aggressively on the first draw in position. If your opponent draws two you can draw one; if your opponent draws one you can draw two. Out of position I think QT64b is a fold in a full game. A hand like Q654b would be a one-card draw, I think.

--Nate