456 vs A27

Discuss

No math to back it up, but 456 for me.

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Am playing A2xx every time and for redraw potential.

Since most players play 2 card starters under 4 and good 3 starters, you are more live imo with A27x also.

I'd prefer 456 to A28 though.

If positional players play to kxxx doesnt really matter which.

My experience is limited so I will follow this thread.

I know in 2-7 234 is slightly preferable over 267. By that token, which is favored here? Someone could please plug in the hands and run the math.

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A27.
You can improve to nut 3 cards more easily.
Still would also go with A37 > 456. Then around like A47 it gets close.

If I have a three card seven, I'm not breaking it to draw two cards. Instead, I'm drawing one card. The odds of making a one-card draw are better than the odds of making a two-card draw.

48 unkown cards.
probability of catching one of three in a three card draw is
P=1-C(45,3)/C(48,3)=1-14190/17296=0.1796
Roughly one time in six you'll improve to a six badugi and roughly one time in three you'll improve to a four-card 8, 9, T, J, Q, or K badugi . Drawing one card to A,2,7, the other half of the time (roughly) you'll miss and end up with a three-card seven.

Drawing to catch two cards in badugi is a bit like making back-door draws in Omaha or Omaha-8. They're simply low percentage plays.

Keeping the A2 and trying to make a six or better four-card badugi, there are 8 favorable cards and 12 possible combos:
3, 4
3, 5
3, 6
4, 3
4, 5
4, 6
5, 3
5, 4
5, 6
6, 3
6, 4
6, 5
Drawing for two cards from 48 unknown cards, there are 48*47/2=1128 ways to make a two-card combination. Of these, 12 (the twelve shown above), make a four card six or better badugi for Hero.
Thus the probability of catching both cards you need on the first draw is 12/1128=0.01064.
On the first two-card draw, there are 8*40=320 combos that have only one card Hero needs. P=320/1128=0.28369
(And then there will be 46 unknown cards and assuming you draw one card on each of the remaining two draws, hoping to catch either one of two cards you still need... 46*45/2=1035 ways to draw 2 more cards.
1+3*43=130 ways to catch one of the three cards you need (out of 1035 possibilities).
Thus 0.28369*130/1035=0.03563 is the probability of catching one of the eight cards you need on the first draw and then one of the three cards you still need on the second or third draw.

On the first two-card draw, there are 780/1128 ways to catch none of the eight cards you want. The probability of that is 0.64149.

Does that check thus far?
28+320+780=1128... OK.

On the second draw there are 46*45/2= 1035 possible two-card combos. If we completely missed on the first draw, there are still the same 12 favorable combos. 12/1035=0.01159.
On the second draw, there are 8*38=304 combos that include exactly one of the eight favorable cards.
Probability = 304/1035=0.29372
Then going on to the third draw and drawing one, there are still 44 unseen cards. And there are three favorable cards. 3/44.
Probability = 304/1035*3/44=0.02003

On the third draw, with 44 unseen cards, there are 44*43/2= 946 possible two card combinations. Assuming we have not gotten any of the eight cards we needed on the previous two draws, there are still 12 favorable combinations for making a six or better four-card-badugi.

The probability of catching both cards you need is 12/946=0.01268.

Collecting:
0.01064+0.03563+0.01159+0.02003+0.01268=0.090507

So if I did my math correctly (never a guarantee of that, although I do try to get it right), drawing two cards to an ace/deuce, you'll make a four-card six badugi about one time in eleven. (The other ten times in eleven you'll miss).

With 456 you need
A, 2, or 3 to improve to a six badugi, or 7 to improve to a seven badugi.
With A27 you need
3, 4, 5 or 6 to improve to a seven badugi. (You can't make a six badugi).

So it's the same for making a seven... that is you need one of four cards either way. But with 456, you can make a six badugi.

Therefore I'd rather draw one card to 456 than A27.
(I don't like drawing two cards).

Buzz

a27 you can squeeze any 2 sider and know you make it.
456 you can squeeze and no sider and make it, so it's a more fun sweat....

4-5-6 also equity favorite heads up vs A27.....


Buzz Al your math Ignores making a better 3 card

True and a very good point. I don't think 654 is a very good three-card badugi. And three-card badugis do win their share (That's from my very limited experience playing in loose, mostly five, six, or seven handed badugi games). I have only played badugi as a fixed-limit game... pot-limit or no-limit, I don't have a clue.

Also if Hero makes a seven four-card badugi, 7654 is the worst of the sevens. (But having a seven and getting beaten by a better seven seems relatively rare).

I have an aversion to two card draws when needing both cards. They're simply low percentage plays for full table play.

However, heads-up I'd probably draw for the best three-card badugi. That means I'd probably toss two cards from an A27X and draw two to the A2 on the first draw.

With four or more opponents drawing cards, I don't like drawing to make the best three-card badugi (with only a one in eleven chance to make a decent four carder). I don't know where my cut-off would be (between one and four opponents). It might depend on the particular opponents involved.

Buzz

A27

OK. I'm convinced.

It probably doesn't matter much if you make a seven badugi or a six badugi. (Either one probably wins). In my limited experience, a seven rarely loses to a six.

Keeping A27, you need
3, 4, 5, or 6, or any non-pairing heart to improve.
4+10=14 outs to improve.

The 3, while not making a four-card badugi, does make the best three-card badugi.

Keeping 654, there's no way to make the best three-card badugi.

Buzz

Having the best hand when neither player improved is worth to much. Ask yourself how often does A27 not improve, it's a significant enough number

This is pointless/redundant in this exact hypothetical scenario.
456 vs A27 is only one pip and 1 possible hand.
In order for A27 not to be good, the other player has to have exactly 456 that A27 loses to (that you would have tied with with 456). And not only does that exact occurrence have to happen (absurdly rarely already, partly because players often start with 2 card draws that wouldn't contain 2 cards of 456), but also BOTH you and the other person have to brick all 3 of your draws for a badugi and a better 3 card. The % is minuscule. And the upshot of the A27 better 3 card is much more common. It's still not close.
It would have to be like 346 where it becomes close imo.

This...I'm not sure how this is even a question

If both improve, the exact solution is very complicated, because which wins depends on how much each improves. (From the perspective of the holder of A27, there are 14 ways A27 can improve to a three-card six or better in one draw... and presumably if either A27 or 456 improves to a four-card badugi, you'd stop drawing. But if, for example,
A27 improves to A25, then you'd draw again (hoping to catch a club or the 3 or 4).

Meanwhile from the perspective of the holder of 456, there are umpteen ways 456 can improve to a three-card five or better (and, again, presumably you'd stop drawing if you made a four-card badugi), but most of those umpteen ways to improve involve catching two or three favorable cards, low percentage plays compared to likely catching one favorable card). For example, drawing to 456 on the first draw you might catch the A, and then, still having a three-card six, you might draw again and catch the 2... and then, still having three-card six, you might draw again and catch the 3.

To be exact, you'd have to compare the probability of each of the 14 ways of improving A27 to the probability of each of the umpteen ways of improving 456.

Let's approach the problem from the standpoint of not improving.
-------
With 14 outs and three draws, I believe
P of A27 not improving = C(34,3)/C(48,3)=~34.6%.

(Thus with three draws, A27 should improve to A23, A24, A25, A26, and/or a four card badugi about 65.4%).

With 13 outs and three draws, I believe
P of 456 not improving = C(35,3)/C(48,3)=~37.8%.

Thus the probability of neither hand improving is about
0.346*0.378=~13.1%.

In other words, neither A27 nor 456 will improve in three one card draws about 13.1%.
A27 will improve but 456 won't 0.654*0.378=~24.7%
456 will improve but A27 won't 0.622*0.346=~21.5%
And they'll both improve ~40.7%. Something like that.

If the above is reasonably correct, the question is when they both improve, which improves more. In order to make up the deficit, when they both improve, A27 has to improve more than about 9.9%.

• my math: 13.1+21.5-24.7=9.9

In other words, when they both improve, of the 40.7, I think A27 has to improve more than 456 by 25.3% to 15.4%.

• my math:
  40.7=X+(X+9.9)
  30.8=2X
  15.4=X

And I don't think it does.

When they both make four-card badugis, the major way they both improve, and when that's the only improvement, then whichever gets the lower fourth badugi card wins. If they both get the same rank to make a badugi, then 456 wins. For the purpose of approximating (otherwise it's a morass) I'm ignoring various multiple draws where, for example, A27 makes A25 on the first draw and then makes a badugi on the second or third draw.

Anyhow, for heads up play when A27 is up against 456, I think I have to go with the 456. But if they're both against unknown hands, then I prefer the A27.

It's a bit like AAKQ vs. T987 in Omaha-8. AAKQ is better than T987 against unknown hands, but heads up against each other (T987 vs. AAKQ), T987 is better than AAKQ

Interesting comparison... at least I thought so.

Buzz

I agree with you, for some reason I was talking about playability when Player A has A27 and player B has 456 as opposed to player A having A23 or 456 (don't know why I read it that way as it's super rare anyways).

Agree entirely w hero value but one thing I would add is you are going to play both these hands or neither always. There is no situation in which I would call with one of them but fold the other. So it's more or less irrelevant. Just like the pointless debates in 2-7 about having 234 or 247 or whatever, you are going to play them all or none.

If you run sims for be most common situations where you would be in with these hands 456 seems to fare slightly better. Example 456 has 2% equity edge over A27 when against A2 a common situation while being identical if against 3-4. Spots like 3 way hands A27 vs 456 vs 248 the 456 will also have a 2-3% equity edge .

Tired to be as neutral as pososble wkth respect to sharing dead cards but I'm sure it would be easy enough to manipulate sims to produce whatever data you want since they will run so close

But like others have said, doesn't really matter

I wanted to clarify my meaning of With respect to OP question, thus refering to A27x (A2xx - 3 card badugi starting hand, as opposed to 34 starter as lowest card..) This would be for many of the reasons stated by others. It was an inaccurate statement oc.

Agree with DD, heard it before in 2-7TD posts some years back, and probably he has posted it many times since. Though his post may not dirrectly answer the question posed by OP, it is on point about how the hands should be being discussed and thought about.

However, it is from discussion like this that challenges players to think, outlines in comments some stuffs like calculations, speculations and theory which are always good to see, consider and understand about different views.

Thus for me, I always like these topical debates.

I believe these type of question can be mental game, and even adjust the game play for indivudals. Or develop new ideas and concepts which may fundementally change the way the game is played, in rare instances.

Just to be clear the post was about hand preference it wasn't hand A vs hand B. Obviously which hand you chose is situational but I think I prefer the A27 because it can improve to A2 3,4,5,6

I don't find the discussion of what hand have a preflop advantage interesting at all, but i would take a27. Would be a more interesting discussion how different those hands would play post, when eq run so close pre. Badugi is such a niche type of game, that there will most likely never be any serious types of discussions about the game on 2+2, but could be fun to at least discuss some.

THe problem is, anyone who is playing these games and taking them seriously is usually playing in higher stakes live cash games. Which means many of us will play against each other at some point. So I think the better players have decided it's not in their best interest to directly help their competition. There's some good threads, but it's the "tip of the iceberg" as far as 2+2 knowledge of these games.