Low Draw Pot Odds

[Murakawa]

Say there are two cards on the flop, and you have the nut low draw. Assuming you will never be quartered and you will never win high, how often will your low draw come in uncouterfited on the river (and therefore what pot odds would you need)?

Remember reading somewhere it was 71% or 59% to complete your draw uncouterfited but my guy reaction tells me it's lower...

[Habib Marwan]

prob A + prob B - prob (ab)

16/43 + 16/42 - (16/43*16/42)

61.13% holla

[Murakawa]

i had a good estimate.

thanks

was the edit in that post "hollah"?

[Buzz]

[ QUOTE ]
Say there are two cards on the flop, and you have the nut low draw. Assuming you will never be quartered and you will never win high, how often will your low draw come in uncouterfited on the river.....?

[/ QUOTE ] Murakawa - You can assume you will never be quartered or will never win high if you want to, but in doing so, you are making two incorrect assumptions.

But all right, let’s make those two incorrect assumptions and give you an answer to your question.

When you can see your own four cards plus the three flop cards, there are forty five cards you cannot see, and there are 990 possible two-card combinations of these forty five cards for the turn plus the river. If you need an explanation of this, we can try to explain it to you.

If you hold A234 and the flop is 789, then any low card that doesn’t pair the flop makes low for you and you cannot get counterfeited. In other words, there are 20 favorable cards whose whereabouts are unknown to you that make low for you if they appear on the turn or river.

There are 20*19/2 = 190 ways to get two of these favorable cards on the turn and river.

There are 20*25 = 500 ways to get exactly one of these favorable cards on the turn and river.

There are 25*24/2 300 ways to not get at least one of these favorable cards on the turn and river.

Of course those all add up to 990 (as a check).

So the probability of making the nut low when you hold A234 and there are two other ranks of low cards represented on the flop is
690/990 = about 70%. That’s optimal.

Similarly, when you hold A2KK and the flop has two other ranks of low cards, there are 16 low cards that make low for you.
• 16*15/2 ways to get two of these, and
• 16*19 ways to get one of these plus a non-counterfeiting blank,
making a total of 120+304 = 424 ways to make a nut low.
424/990 = about 43%. That’s minimal.

[ QUOTE ]
Remember reading somewhere it was 71% or 59% to complete your draw uncouterfited but my guy reaction tells me it's lower...

[/ QUOTE ]Something like that. I make the range 70% to 43% for an uncounterfeited nut low and 70% to 53% for a non-nut low.

[ QUOTE ]
..... (and therefore what pot odds would you need)?

[/ QUOTE ]Depends on where you are in the range and how many opponents will be contributing to the pot. It's different for A234/789 than A2KK/789 (the extremes, with A23K falling somewhere in between). And it's different depending on how many opponents will be putting money into the pot.

(Heads-up if you split, you get your own investment back. In other words, you win nothing. With two opponents, you get your own investment back plus you win half of what one opponent puts into the pot. That's assuming no quartering.)

But you cannot realistically ignore getting quartered or sixthed.

Buzz

[Murakawa]

Thanks. Someone chased their low against me HU and made 2 high pair just now. This better come around to me in the long run with good karma.