On a flop with 2 low cards what are the immediate odds of making the nut low on the turn in 08 with A2xx (with xx being high cards)? what about from turn to river? should be slightly higher as turn is a high brick and we still have same number of outs.

The site o8poker.com http://www.o8poker.com/Strategy/keypercent.php shows that a low is made 59% of the time from flop to river on a flop with 2 low cards when holding 2 low cards.
should one just consider the odds from flop to turn to be ~30% (59/2) and similar odds from turn to river and look for pot odds of around 2.5 to 1 to call?

going by the following math: (16 unseen low cards) / (45 unseen cards) we get an even higher 35% odds of hitting low by turn so there must be something wrong with just going with this. Does somebody have some insight /explanations? I think its related to the fact that a lot of the outs are going to have been dealt out in the average case.

Also, seems to me that odds should be the same for BigO except when we hold several low cards besides our A2 (maybe A287x on J65). any confirmation? / comments?

Exercise:

Suppose one throws an ordinary six-sided die eight times. What is the probability that one sees a "1" at least once?

It may be tempting to say that


The correct answer

When you understand this, I suggest you try to solve your question from the beginning, not believing what some o8-site says. I guarantee you it's much more useful for you compared to someone just giving you the correct answer.

amok--- i like it

tonyK

if you hold A2KQ and with the turn card revealed the board is 85QJ,
then there are 16 cards (the 3s,4s,6s, and 7s) low completing cards, and the remaining deck contains 44 cards, so 16/44 =.3636 or 36.36% is the probability you will have the nut low on the river. in odds i guess its 4:7 for making the nut low, 7:4 against.

if you hold A2KQ and with the flop revealed the board is 85Q,
then there are 16 cards (the 3s,4s,6s, and 7s) low completing cards, and the remaining deck contains 45 cards, so 16/45 =.3555 or 35.55% is the probability you will have the nut low on the turn. in odds it is worse than its 4:7 for making the nut low.

if you hold A2KQ and with the flop revealed the board is 85Q,
--and you want to know the probability that you make a low by the river, then you must consider that there are 2 cards to come--
with a deck of 45 cards there are 990 possible 2 card combinations. c(45,2)
here is a situation where the complement is easiest, so how many of the 2 card combos are where both cards don't complete a low...if 16 do, then 45-16=29 don't.
there are 406 possible 2 card combos of 29 cards, c(29,2)
therefore, 990-406 =584 possible 2 card combos that complete the low. (some are just it fell on the turn, some are it just fell on the river and then others are where both the turn and river are low)
584/990 =.5898 or 59%

we use 44, 45 and c(45,2) because as far as we know the cards others have been dealt are unknown so we don't factor for them. ofc if an opponent turns over his cards then you account for those 'known' cards. if he turns over 3K, then one of your 16 low completing cards is know and 16 becomes 15, and the 'unknown deck' of either 45 or 44 becomes 43 or 42, and the 990 possible 2 card combo's is also obviously reduced.


with regard to Big O where you have been dealt 5cards and not 4, you should see how the equations change.
you should also be able to work out when you have an additional low in your hand.

really not a lot for discussion.

BUT.... in hands where you hold the bare A2 there are 6 cards (the remaining As and 2s) that could hit either street and defeat your nut low. It’s not a simple 14/45 and then 14/44 calculation. 59% is the figure used in a prior post I believe.

Obviously this doesn’t factor into the river (either you hit the low or not) ... but should when calculating odds after the flop. 13% of the time (6/45) the turn counterfeits the nut low draw. My match could be off.

There may be times a live A or live 2 draw are the best river low draw I suppose.


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your hand =A2KQ, the board =85QJ, if river is an A or river is a 2 you do not have a low! (you didn't have a low on the turn)

your hand =A2KQ, the board =85Q if turn is an A or turn is a 2 you do not have a low on the turn! (you didn't have a low on the flop)

your hand =A2KQ, flop =85Q, if the turn river combo is A2 or 2A or A[9-k] or [9-K]A or 2[9-k] or [9-K]2
you do not have a low. if the turn river combo is A[3,4,6,7] or [3,4,6,7]A or 2[3,4,6,7] or [3,4,6,7]2 you do have a low it is just not the nut low, which in my explanation i did not say you would have the nut low i said "that you make a low by the river" and "complete the low".
in op's post its the same "a low is made" no mention of it being the nut low.


conclusion: much of what you have posted is nonsense.

Pretty sure OP was asking specifically about the nut low...

“On a flop with 2 low cards what are the immediate odds of making the nut low on the turn in 08 with A2xx (with xx being high cards)? what about from turn to river?”

Tough to ignore the fact cards may come to block or counterfeit a nut low. Assuming a low hits on either the turn or river (or both).

I don’t think pointing this out is nonsense. Lots of bets are lost in this game with people drawing to half the pot with no backup.


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Just wanted to pop in and say this is an awesome answer.

amok, ngftw ,

thank you for the insight. I guess the 35.55% odds on the flop and 36.36% odds on the turn are more useful as they represent the equity required to draw to the nut low on each of the 2 streets in question.

given those percentages looking for 2 to 1 pot odds in half the pot on any of flop or turn to draw to nut low seems like a good strategy.

going by amoks complementary probabilities the to 59% total from flop to river can also be obtained as follows:
pr(low by river on the flop) = pr (at least one low on turn or river)
= 1- (pr (no low on turn) x pr (no low on river))
= 1 - (29/45 x 28/44) = 1 - (0.6444 x 0.636)
= 59%