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Monday, May 23, 2005

Badugi Hand Rankings
We have been playing Badugi a wee bit wrong. For those who think the game is stupid, please skip this post because I am about to get into some Badugi minutia.

I had previously described the game here, based on info I gathered on 2+2. But revisiting the 2+2 forums I found this post by Greg Raymer describing the game. Here's the part that surprised me:
If nobody has a 4 card hand, then the lowest 3 card hand wins. For example, Ah2d3s4s beats Ac2c3d4h, as the former is a 3 card hand of A23, and the latter a 3 card hand of A34.
I would have thought the two hands would split the pot. I guess I was wrong (I'm inclined to believe the WSOP champ on this one).

Now, I really do not think this situation -- two non-rainbow hands of the exact same ranks -- has come up in our home games, although I could be wrong. But it certainly might have affected the way people have been playing their hands. If you're drawing 1 card, and you've got Ac2d3h and then you get the king of hearts, that's not nearly as bad as we thought. We had been playing that you'd have a "king-high double," and would lose to any lower double, but according to Raymer's explanation you've actually got the best 3-card hand there is, and will therefore beat any non-Badugi hand. That's a pretty big difference.

But wait, there's more.

We were mostly right that paired cards are bad, but they're not as bad as we thought. Raymer writes that "If you hold Ah2d3s4s, you cannot play the 4s, as it is the same suit as your 3s. Similarly, Ah2d3s3c, you must not count one of your 3s, as they are paired." We had been playing that pair absolutely kills your hand, as it would in standard lowball. That is, we'd been playing that any non-paired hand, even if it had two or even three of the same suit, would be better than a pair. I guess we were wrong on this count, too, and I'm certain that that situation has come up in our home games.

This "can't use cards of the same suit or rank" rule is confirmed in this RGP thread. Toward the end of it, Steve Badger explains that AKJT, all hearts, would beat quad queens, not because unpaired cards are better than quads (as in standard lowball), but because the first player has a better one-card hand (ace vs. queen).

So if you've got Ac2d3h and draw for one card, then any club; any diamond; any heart; any ace; any deuce; and any three all have exactly the same effect on your hand -- they don't improve it, but they don't make it worse. Cards that you "can't use" don't matter in ranking the hands. Wacky. Strategy-wise, I think this gives players even less reason to fold at the river, and makes it even more of a gambling game :-)

So to be clear, here are several examples of (really bad) Badugi hands and how they would rank, from best to worst::

KcQdJhTs (4-card hand, aka a Badugi)
KcQcJhTd (3-card hand)
KcQhJdJs (3-card hand)
KcQcJdTd (2-card hand)
KcKdJcJd (2-card hand)
KcQdQhQs (2-card hand)
KcQcJcTc (1-card hand)
KcKdKhKs (1-card hand, the absolute worst there is)

If you overthink all this, it can make your head hurt. But really it's not that bad. You just can't use cards of the same rank or the same suit, and 4-card hands are better than 3-card hands.

That is funny that you thought pairs were wworse than being suited, because I thought that suited was worse than pairs. So would would have thought that Ac3d5h5s would beat As2h3c4c.
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