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  #1  
Old 09-05-2002, 10:26 PM
C Dubya C Dubya is offline
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Default Drawing for low

Online 2-4
Ac2cTsQh in the big blind.

2 callers to MP, who raises. The raise most likely means A2 but I've seen this player raise with good high hands and good 2 way hands. 6 of us play for 2 bets each.

Flop 7s6s6h
No high for me. I'm playing for 1/2 or 1/4 of the pot. EP bets, same MP raises. 4 call, including me. 10 big bets. Should I have considered letting this hand go?

Turn Jc[7s6s6h]
Checked to MP,who bets. CO raises. All call. Is my call correct? If I've calculated correctly, pot odds are 2.75:1 and I'm drawing at 1.75:1. BUT there is the possibility (probability) that I'm drawing to be quartered.

River: Js[Jc7s6s6h]. MP wins with spade flush after river checked around. He did have A2 of course.
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  #2  
Old 09-07-2002, 08:36 AM
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Default Re: Drawing for low

Repeat after me:

"Scoop focus, scoop focus, scoop focus."

The flop didn't hit you hard or even semi-hard. You have no counterfeit protection, no high. I wasn't entirely sure...were you were last to act on the flop? If so then maybe, just maybe, you could take one more off. Anything else, it's a no-brainer ditch. Others wiser than me will tell you why it's a no-brainer even if you WERE last to act.

Hand-reading skills are necessary, but not sufficient. The courage to act on those skills is also crucial.

Sorry to come at you like a ton of bricks. I think we've played together and I *know* you've done much better than this.

All the best,

Gorilla
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  #3  
Old 09-07-2002, 09:17 AM
Buzz Buzz is offline
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Default Re: Drawing for low

"Online 2-4
Ac2cTsQh in the big blind.

2 callers to MP, who raises. The raise most likely means A2 but I've seen this player raise with good high hands and good 2 way hands. 6 of us play for 2 bets each."

Calling seems right to me. Besides the A2 combo you also have the nut club draw
and some nice high card combos (AQ, AT, QT).

"Flop 7s6s6h
No high for me. I'm playing for 1/2 or 1/4 of the pot. EP bets, same MP raises. 4 call, including me. 10 big bets. Should I have considered letting this hand go?"

Yes.
You need any 8, 5, 4, or 3 without an ace or deuce on either the turn or the river.
4* 4*3/2 + 16*12/2 + 16*25 = 520. (never a guarantee my math is correct)
520/990 = 0.525 is the probability you'll make the nut low.
Odds are thus about 11 to 10 you'll make the nut low, close to even.
But because of the strong possibility of getting quartered you should fold here.
However continuing is only a small mistake, IMHO.

"Turn Jc[7s6s6h]
Checked to MP,who bets. CO raises. All call. Is my call correct? If I've calculated correctly, pot odds are 2.75:1 and I'm drawing at 1.75:1. BUT there is the possibility (probability) that I'm drawing to be quartered."

28 cards on the river are bad for you. 16 cards are good for you.
Therefore, as you have stated, your hand odds are 1.75 to 1.
16/44 = 0.364, the probability of making the nut low, may be more useful (see below).

It's not clear to me exactly how much is already in the pot.
I think you meant there were 10 *small* bets (not big bets) in the pot before the flop.
(10 small bets = 5 big bets)
If so, and if you have four opponents, they are putting in a total of 8 more big bets
on the third betting round, making a total of 13 big bets.
You'll put in 2 big bets on the third betting round to call.
Let's tentatively assume that there will be there will be one bet on the river
and that two of your your opponents will call.
Let's estimate you'll get quartered for low about half the time.
When you make the nut low and win half the pot, you'll win 6 big bets.
When you make the nut low and win a quarter of the pot, you'll win 1.5 big bets.
When you miss on the river you'll fold and will lose 2 big bets.
Assuming you'll get quartered half the time,
0.364*(.5)*6 + 0.364*(.5)*1.5 - 0.636*2 = +0.09

Since the number is positive (though barely so) calling is reasonable, IMHO.
It's close. If we had estimated your chance of getting quartered at more than half,
then the total would have been negative and folding would be in order. As I already
wrote, it's close.

Here's the calculation if you estimate you'll be quartered 60% of the time:
0.364*(.4)*6 + 0.364*(.6)*1.5 - 0.636*2 = -0.07

"River: Js[Jc7s6s6h]. MP wins with spade flush after river checked around. He did have A2 of course."

If you had known for certain MP had A2, then you should have folded after the flop.
However, you weren't certain. I guess the lesson for you is to somehow get to the point
where you are more certain about the cards your opponents hold.

Just my opinion.

Buzz
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  #4  
Old 09-19-2002, 03:20 AM
rr2000 rr2000 is offline
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Default Re: Drawing for low

Generalizing this, Suppose I have a A2xx (xx = high cards) hand and the flop has a nut draw (2 lows not containing A or 2) but offers no hope for high. When should I fold/play? Assume that there was a bet from a MP player preflop and there are 5 players on flop.
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  #5  
Old 09-19-2002, 02:18 PM
chaos chaos is offline
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Default Re: Drawing for low

I would definitely call preflop. Any A2 suited is a good hand plus you have the high card combinations.

I think calling 2 bets on the flop is marginal. You only stand to make a small amount of money if you don't get quartered. I think the percentage of time you do get quartered would have to be fairly small for your hand to be profitable. I would fold and wait for a more profitable situation. Playing these marginal situations may add a little to your profit (when you don't get quartered) but add a lot to your swings. You beat this game by scooping pots not getting value in marginal situations.

I would fold on the turn. Besides what Buzz has pointed out, you also run the risk of it costing you more than two bets as it is a real possibility that the MP, who rasied on the flop and bet out on the turn, might reraise here.
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  #6  
Old 09-22-2002, 07:18 PM
Buzz Buzz is offline
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Default Re: Drawing for low

rr2000 - Good question. Let’s look at each betting round.

1st betting round. I think you generally should play A2HH (bare ace deuce with two high cards). At this point you’re not playing for half the pot. You’re hoping for a scooper. When you hold A2HH, the flop you really want to see is top full house, but flops with top trips, nut straight draws, and at least two playable low cards are also playable. For example, when you hold Ac2cTsQh, the flop you really want to see is AAQ, but flops like QcJc8h, AA8, QQ8, TT8, KJ8, and 987 are also very playable. There also are some combination flops that are playable.

Although it may appear there are more high flops than low flops, it will turn out that with Ac2cTsQh, there are more flops where you will catch the nut low draw than flops where you catch a high fit. With the nut low draw, your justification for staying in the hand after the flop will seemingly be your nut low draw, but actually you should still hoping to scoop with a high only hand. (At least that’s my thinking).

2nd betting round. Flop was 7s6s6h. You wanted to see AAQ, but instead you got a flop where you caught the nut low draw. That’s the norm for playing Ac2cTsQh. If the flop had been 9c7s6h you would have at least had a chance for a back-door draw to a flush for a possible scooper, but the way it is you have no realistic chance for high. If you continue playing, you are only playing for the low half the pot.

When someone bets or raises after a flop of 7s6s6h you can’t tell if one of your opponents has a two-way hand with a six plus ace-deuce or not. Perhaps the person who has raised has a hand like Ah4h6cKc., or perhaps Ah2h6cKc - or perhaps something else. There are lots of reasonable possibilities and many of them include A2XX. Thus you very well may be quartered or sixthed here, even when you do make the nut low. In addition, an ace or a deuce on the turn or river will kill your hand.

Putting it all together, I think you fold Ac2cTsQh to a double bet on the second betting round. From the big blind, I think you check and call a single bet if it looks like there will be no raise after you have called.

3rd betting round. Turn was Jc, making the board 7s6s6hJc. If you played correctly on the 2nd betting round, you are not still in the hand if there was a raise on the 2nd betting round.

As an aside, note the importance of being in either early or late position here to stay out of trouble. If you had been in mid position, if someone in front of you bet, if you called from mid position, then if someone in late position raised, and if the person who originally bet only called, you would be almost forced to call the raise. In this case you would still be in the hand after a raise on the 2nd betting round.

Assuming you played correctly on the second betting round, the reasoning on the third betting round is similar to the reasoning on the second betting round. I think you fold Ac2cTsQh to a double bet on the third betting round.

Generalizing, I think you are getting favorable odds to limp to a single bet but not a double bet on either the second or third betting round. If you’re going to play Ac2cTsQh from the big blind after a flop of 7s6s6h and a turn of Jc, then I think you check and call a single bet but check and fold to a double bet on either the second or third betting round.

You also would not be wrong if you folded Ac2cTsQh to a single bet after a flop of 7s6s6h. It’s a marginal (break-even) situation. The reason for continuing in marginal situations is to enhance your table image. You expect to break even on marginal flop fits over the course of a year, but by playing these marginal flop fits you tend to increase your profit when you have a nice fit with the flop. If you play too tight you may not get much action when you really want it.

Just my opinion.

Buzz
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  #7  
Old 09-22-2002, 11:05 PM
Buzz Buzz is offline
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Default Re: Drawing for low

Chris - Don’t know as it matters very much, but I mis-read your post when I originally wrote “It's not clear to me exactly how much is already in the pot.” Nor do I know how I came to mis-read your very clearly written post. My apologies.

There were 6 large bets in the pot after the first betting round, then 10 large bets in the pot after the 2nd betting round with three opponents.

"Flop 7s6s6h
No high for me. I'm playing for 1/2 or 1/4 of the pot. EP bets, same MP raises. 4 call, including me. 10 big bets. Should I have considered letting this hand go?"

I earlier wrote, “Odds are thus about 11 to 10 you'll make the nut low, close to even. But because of the strong possibility of getting quartered you should fold here. However continuing is only a small mistake, IMHO.

That still seems correct to me, except that a small mistake on an early betting round tends to be compounded on later betting rounds. If you make a small mistake by calling on the river, that’s the end of your small mistake. However, if you make a small mistake on an early betting round, you may be compounding your error even when (because of the size of the pot) you correctly call on subsequent betting rounds.

Since I had originally mis-read your post, my numbers and consequently my thinking has also changed a bit regarding the third betting round.

On the third betting round, your three opponents were putting in a sub-total of 6 more big bets making a total of 16 large bets in the pot. Your cost (assuming no re-raises), would be 2 large bets to see the fifth common card. With no reasonable chance for high, You were getting 3.5 to 1 pot odds to call.

Let's look ahead and tentatively assume that if you make low on the river, there will be one bet on the river and that two of your opponents will call. In that case there will be 21 big bets in the pot at the showdown, of which you will have contributed 3 big bets on the last two betting rounds. In that case, (1) when you are the only winner for low, you will win 7.5 big bets, (2) when you are quartered for low you will win 2.25 big bets, (3) when you are sixthed for low you will win 0.5 big bets, and when you miss making the nut low on the river you will fold and lose 2.0 big bets.

To make the nut low on the river, you need 3, 4, 5, or 8 on the river. The probability of catching a 3, 4, 5, or 8 on the river is 16/44 = 0.364. You should expect to make the nut low 36.4% of the time and miss 63.6% of the time.

Against random opponents, your A2 should expect to be the only nut low 57%, get quartered 38%, and get sixthed 5%. The last time I did the calculation for your hand/flop, since you strongly suspected one of your opponents might have A2, I used 50% for you being the only nut low, 50% for your getting quartered and ignored the sixthing. There’s not a big difference between using 57%/38%/5% and using 50%/50%. No big deal. This time I’ll use 57%/38%/5%.

If you had nine opponents to start, you should expect to win:
7.5 big bets 57% of 36.4% of the time,
2.25 big bets 38% of 36.4% of the time and
0.5 big bets 5% of 36.4% of the time.

You should expect to lose
2 big bets 63.6% of the time.

Putting it all together, your e.v. is:

7.5*0.57*0.364 + 2.25*0.38*0.364 + 0.5*0.05*0.364 - 2*0.636 = +0.6 big bets.

As I already wrote, (odds-wise) it's close - and the revision doesn’t change much. I agree with Chaos that since there is a chance for a re-raise on the third betting round, it’s probably best to discontinue at that point.

As an aside, I do not think anyone can mentally do the above calculations at the table with a few possible exceptions. When I was growing up there was a radio program called the whiz kids. One of the regulars was a kid named Joel Kupperman, who performed amazing feats of mathematics in his head. Maybe a Joel Kupperman could do the math while seated at the table.

The rest of us can only prepare ourselves by making doing some sample math and making some generalizations ahead of time.


If we back it up to the third betting round where you were getting 3.5 to 1 pot odds to call, and recalculate as though you were only getting 2.5 to 1 pot odds to call, there will be 17 big bets in the pot at the showdown, of which you will have contributed 3 big bets on the last two betting rounds. In that case, (1) when you are the only winner for low, you will win 5.5 big bets, (2) when you are quartered for low you will win 1.25 big bets, (3) when you are sixthed for low you will break even, and (4) when you miss making the nut low on the river you will fold and lose 2.0 big bets.

Putting it all together, your e.v. on the third betting round would be:

5.5*0.57*0.364 + 1.25*0.38*0.364 + 0*0.05*0.364 - 2*0.636 = +0.0 big bets (if you were only getting 2.5 to 1 pot odds to call on the third betting round).

Thus the break even point with three opponents on the turn seems to be odds of 2.5 to 1 (against making your hand), the point where e.v. = 0. Looks like we maybe can call on the third betting round when we are getting 2.5 to 1 or better pot odds.

Facing a single bet on the third betting round, drawing for low with a bare ace deuce, and with no chance to win for high, then there have to be six big bets already in the pot for us to get 2.5 to 1 pot odds and call. Facing a double bet on the third betting round, drawing for low with a bare ace deuce, and with no chance to win for high, then there have to be a minimum of twelve big bets already in the pot for us to call.

When there is a pre-flop raise seen by at least six players, when there is a single bet on the flop seen by at least four players, and when facing a double bet on the turn (you must have at least two opponents to be facing a double bet), then the odds will be roughly break-even for calling the double bet. Anything over that amount already in the pot is gravy. However, if the pot is further raised after you call the double bet, although you will be getting favorable odds to call the additional raises, you were not getting proper odds to originally call the double bet.

This is a dreadful way to get stuck in a hand. I think we have to carefully avoid putting ourselves in harms way. This happens when you face a raise after calling a single bet either (1) without quite having proper odds, or (2) having barely favorable odds. Although you can play the hand perfectly from that point on, your error may be compounded on later betting rounds - and there is not really anything you can do about it! You’re stuck in the hand because of the size of the pot.

Thus when it looks like the betting will be jammed on the turn, even though you might be (barely) getting proper odds to call a double bet, I think you fold your bare ace-deuce nut-low draw, as Chaos has already suggested.

Without the raises on the first and second betting rounds there wouldn’t be enough in the pot to justify seriously considering calling a double bet on the third betting round.

Just my opinion upon re-thinking my earlier post.

Buzz

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  #8  
Old 09-24-2002, 12:50 AM
rr2000 rr2000 is offline
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Default Re: Drawing for low

Thanks, Buzz.
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