[Buzz]

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So what is the conclusion then

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Hi Greg - I think whether or not you can show a profit with this hand after this flop and early betting depends on how many of your opponents chase and whether there are raises on the 2nd and 3rd betting rounds.

If they all chase to the river and there’s no more raising, then I think you average a profit by continuing after the flop. However, if they make it expensive for you to chase, and if one or more of them drops out, then you’d do better to fold.

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how much of a mistake is chasing here....?

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I would classify taking one off here as a small mistake.

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what odds does Hero need to make chasing correct?

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Very difficult to estimate because we don’t know how Hero’s opponents are going to play on subsequent betting rounds.

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Nitpick – win half 13%, win a quarter 9% -- that seems awfully high, I’d think you get quartered less than that.

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Very reasonable. Not a nit-pick at all. Thanks for the calling attention to the matter. After giving it more consideration, I think <font color="red">win half 15%, win a quarter 7%</font> is better here. I'll try to explain.

I think getting quartered or sixthed for low depends somewhat on what the nut low is, and it also depends on how many opponents were originally dealt cards (and to a lesser extent on how many opponents actually saw the flop). I think typical opponents will see the flop when dealt A2XY, A3XY, or 23XY.

Then, when the nut low ends up being ace-deuce, ace-trey, or deuce-trey, in a typical nine player low limit game, I think:
• 61.07%, you have sole possession of low,
• 34.68, you get quartered for low,
• 4.17%, you get sixthed for low, and
• 0.08%, you get eighthed for low.

I don’t try to remember those numbers. And anyhow they’re a bit different for more or less than nine opponents being dealt cards, and they also depend on the propensity of your opponents to play starting hands with A2XY, A3XY, or 23XY. Rather than remember those exact numbers, I remember that you tend to not split the low about 3/5 and you tend to get quartered (or sixthed) the other 2/5 with any of these three hands.

There are varous factors operating here, some in opposition to others. At any rate, I can easily remember 3/5 and 2/5 - and that’s at least in the ball-park, which is good enough for me under game conditions.

In my experience, players typically “take one off” when they have a nut-low back-door draw.

But you’re right. I estimated the magnitude of getting quartered on the basis of the 23XY being the nut-low on the river (as it actually was in this case). If 24XY or 34XY ends up as the nut low on the river, then I think at least some players will have folded a hand that would have quartered Hero. After a flop of ATT, when Hero does back-door the nut-low with 2346, the deuce-trey combination is actually only used about 59% of the time, with the deuce-four or trey-four combination being used the other 41% of the time. (You can never make the nut low using a card other than a wheel card from your hand - so that any combination involving the six from 2346 is not the nuts for low).

Obviously how often you get quartered or sixthed depends on how pre-flop tight your opponents are, but I think almost all of my opponents, rightly or wrongly, are going to tend to see the flop with A2XY, A3XY, or 23XY. (X and Y, rightly or wrongly, can typically be almost anything).
When it comes to A4XY, a few will tend to fold.
When it comes to 24XY, or 34XY, a few more will tend to fold.

At any rate, since some of your opponents will tend to pre-flop fold 24XY or 34XY, I agree "win half 13%, win a quarter 9%" is a bit high. I think win half 15%, win a quarter 7% is probably better for 2346 after a flop of ATT. (Win half 16%, win a quarter 6% seems too low for getting quartered or sixthed). Keep in mind that to keep it simple, I’m giving Hero the same credit in chips won for getting sixthed as getting quartered. Although the chance of getting sixthed is not great enough to cause much concern, it’s not minuscule either. The ratio of getting quartered for low to getting sixthed for low with A2XY, A3XY, or 23XY in a typical nine handed game is roughly eight to one. (However, the probability of getting eighthed is miniscule and not much different from getting sixthed anyhow).

Does that extra little bit (win half 15%, win a quarter 7% instead of win half 13%, win a quarter 9%) make it over the hump so that playing a nut back-door low draw with back-up becomes +ev? Gee, I don’t know. I don’t think so, but it’s really hard to know with much certainty how a group of unknown opponents are going to play after an ATT flop.

I have played in a private games where Hero should probably “take one off” here. I hate to admit that because I think it’s generally bad advice to suggest or imply drawing exclusively for back-door lows is worth while. That’s just my opinion.

Although it seems only a small mistake to take one off here, you can dribble away a lot of chips making small mistakes against decent opponents. In addition, when you chase on the second betting round, you tend to get stuck for additional bets on later betting rounds because of the size of the pot.

That's just my opinion.

Buzz