to have a backdoor low draw, BDLD, requires that your hand consists of atleast 2 low ranks and that the board contains exactly 1 low rank.
a deck consists of 8 low ranks.
with exactly 2 low ranks in your hand and 1 on the flop, the turn-river runouts that complete a low are the combinations of 5 non-pairing low ranks and the subsequent 4 non-pairing low ranks.
10 combinations of 16 each =160 combinations of the total 990 possible board runouts (where order doesn't matter) (and opponent's range is not taken into account). 16.12%
with exactly 3 low ranks in your hand and 1 on the flop, the turn-river runouts that complete a low are the combinations of the 4 non-pairing low ranks and the subsequent 3 non-pairing low ranks plus the combinations of the 4 non-pairing and pairing one of the 3 low ranks in your hand.
6 combinations of 16 each + 12 combinations of 12 each =240 of 990 board runouts. 24.24%
with exactly 4 low ranks in your hand and 1 on the flop, the turn-river runouts that complete a low are the combinations of the 3 non-pairing low ranks and the subsequent 2 non-pairing low ranks plus the combinations of the 3 non-pairing low ranks and pairing one of the 4 low ranks in your hand plus the combinations of pairing 2 of the low ranks in your hand.
3 combinations of 16 each + 12 combinations of 12 each +6 combinations of 9 each =246 of 990. 24.84%
when you hold A2J9 and you have a BDNLD and your opponent can have any hand, you have a ~16.2% probability of making a low at showdown. consequently, 8.1% is the upper bound of your avg. pot equity from low. if pot odds are such that you need 26% equity to make a plus EV call, you need atleast 16% equity from high.
Quote:
Originally Posted by AKQJ10
I must admit, I still don't understand what I'm missing. I hope someone will take a shot at providing a real explanation so I can learn from the holes in my own thinking.
i would think if you've glanced at what i posted above you will have recognized your error, but as it seems you think i should be very explicit in my posts,
Quote:
Originally Posted by AKQJ10
six nonpairing low ranks remain before the turn
24 cards remain of those low ranks
is wrong. its 5. 8-2-1 =5
5 nonpairing low ranks
20 cards remain of those low ranks
Quote:
Originally Posted by AKQJ10
If that should happen:
five nonpairing low ranks will remain before the river
20 cards remain of those low ranks
is wrong. its 4. 8-2-1-1 =4
4 nonpairing low ranks
16 cards remain of those low ranks