Practical Poker Books
Home Sports Handicapping Trade Point Technologies PokerGameBoards Books

OOPs - Some Changes/Fixes to our Calculations
On Page 175 - AA23 >>>> Nut Low
 

To flop a nut Low with this hand, the Flop must contain 2 unpaired low cards that do not match any of the hole cards, plus a third low card that may match any of the hole cards, but may not match either of the first two cards flopped.

First card must be ranked 4 -8, probability is 20/48

Second card must be ranked 4 -8 except for the rank of the first card, probability 16/47

Third card can be any of the 12 remaining low cards that don't include the ranks of the first 2 cards plus all of the cards that match the rank of the hole cards, 8, probability 20/46

The probability of this flop is represented by a combination of these three probabilities:
20/48 * 16/47 * 20/46 = 6400/103776 = .0616712 or 6.2%
The odds are  93.8 : 6.2 = 15.1 : 1
 
Page 180
AA2X >>> Nut Low Draw (assumes x is > 8)
 
First card must me 3 - 8, probability 24/48
 
Second card must be 3 - 8 minus the cards ranked the same as first card, probability 20/47
 
Third card can be any card in the deck EXCEPT an ace or a deuce, it can even counterfeit either of the first 2 cards, probability 41/46
 
The probability of this flop is represented by a combination of these three probabilities:
24/48 * 20/47 * 41/46 = 19680/103776 = .1986392 or 20%
The odds are  80 : 20 = 4 : 1
 
On page 186 the calculation is to flop the nut low A2xx in the hole:
 
To Flop a nut low with this starting hand requires a flop of 3 unpaired cards that rank 3 - 8.
 
There are 24 such cards and the probability of the first card of the flop being one of them is 24/48.
 
For the second card there are 20 cards that will fill the bill of the remaining 47, so the probability of the second card is 20/47.
 
There are 16 possible 3rd cards out of the remaining 16 so that makes the probability of this card 16/46.
 
The probability of this flop is represented by a combination of these three probabilities:
24/48 * 20/47 * 16/46 = 7680/103776 = .074055 or 7.4%
The odds are 92.6 : 7.4 =   12.5 to 1