[Buzz]

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I believe a similar situation exists with nut low (A2 for simplicity). But in this case I think it weakens our holding. Once the 5 cards on the board have no A or 2, it is MORE likely that we are facing another A2 than it was before we see those cards. What I don't know is how this impacts the probability or if that is already accounted for when people speak of the odds of having the only nut low.

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Jim - Your odds always depend on your perspective. The more information you have, the better able you are to pin point your chances. But I think you already know that and are just wondering from what perspective the odds are figured.

The answer is when you know the whereabouts of 9 cards, then the odds are figured from a 9 card perspective. When you only know the whereabouts of 4 cards, then the odds are figured from a four card perspective.

In the interest of clarity, the vantage point from which the odds are figured and how many hands are involved should always be stated.

Let’s make Hero’s hand A2KKn and the board 34589n. In that case, Hero scoops or shares 10,000/10,000 regardless of the number of players. As the number of players increases, so do the chances one of Hero’s opponents also has the nut low (obviously). In a ten player game, Hero, as simulated, scoops 5760 and wins a total of 2035 for the 4240 non-scoops.
1017.58 = Q/4 + S/6 + E/8
4240 = Q + S + E
Two equations and three unknowns, hmm...
Fiddle faddle ...
Let’s try:
3736 = Q
494 = S
10 = E
check:
934=Q/4, 82.33=S/6, 1.25 =E/8
934+82.33+1.25 = 1017.58
check:
3736+494+10 = 4240.

O.K. looks like Q = 3736, S = 494, E = 10 works. Lucky guess. (Got it on the first approximation).

A different simulation would be slightly different. This time, it looks like A2KKn, with a final board of 34589n,
• wins outright for low 5760/10000,
• gets quartered for low 3736/10000,
• gets sixthed for low 494/10000
• and gets eighthed for low 10/10000.
About 57.6% sole posession of the low, about 37.4% getting quartered, about 4.9% getting sixthed, and about 0.1% getting eighthed. Something like that.

I calculated that a few years back. I got slightly different results for a ten player game:
56.88% sole possession
37.69% getting quartered
5.31% getting sixthed
0.1% getting eighthed.
Well... I guess that’s reasonably close to tonight’s sim values.

That’s in a ten player game with the board known and with no aces or deuces on the board. With aces and deuces on the board, as you have reasoned, things would be different.

Before you know there are no aces or deuces on the board, from your perspective you’re less likely to encounter an ace or deuce in the hands of an opponent (because there’s a chance that ace or deuce could end up on the board).

But I’m with you - what does it matter if that happens, because if it does, you’re screwed (counterfeited) anyway?

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I believe a similar situation exists with nut low (A2 for simplicity). But in this case I think it weakens our holding. Once the 5 cards on the board have no A or 2, it is MORE likely that we are facing another A2 than it was before we see those cards. What I don't know is how this impacts the probability or if that is already accounted for when people speak of the odds of having the only nut low.

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Well, that’s true except I simulated (and previously calculated) how it impacts the probability with no ace or deuce on the river. Going backwards to before the flop, it would be LESS likely. I neither figured not simulated the probability of another opponent with an ace-deuce before the flop, because as you have implied, it’s kind of a moot point. But anyhow, I think it’s approximately somewhere in the neighborhood of one third.

More importantly, if you do make it to the river with a bare ace-deuce nut low, then in a ten player game you’ll have to share the low about 43% (turned out to be ~42% in the simulation I ran tonight and for which I gave the low results above).

I mostly play in nine player games, and there I figure I’ll get quartered or sixthed (or, ugh, eighthed) approximately two times out of five with the most commonly played nut lows (A2XY, A3XY, or 23XY). It’s close to that in a ten player game.

When will you get quartered or sixthed?

On the river.

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Anybody know the gory details here?

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I think that’s it.

Buzz