I believe the table on page 220 is in error. It is based on the Hero's
perceived range of 88+, AJo+, ATs+, KTs+, QTs+ after the flop.
The flop is Qc,5d,4s so Villain knows that Hero does not have Qc in his hand, and probabilities must be calculated based on Qc being removed from Hero's possible hands.
Below are the ranges with the number of possibilities given twice, first without card removal and then with card removal.
HTML Code:
88+ AJo+ ATs+ KTs+ QTs+
==== ==== ==== ==== ====
AA-6-6 AKo-12-12 AKs-4-4 KQs-4-3 QJs-4-3
KK-6-6 AQo-12-9 AQs-4-3 KJs-4-4 QTs-4-3
QQ-6-3 AJo-12-12 AJs-4-4 KTs-4-4
JJ-6-6 ATs-4-4
TT-6-6
99-6-6
88-6-6
==== ==== ==== ==== ====
42-39 36-33 16-15 12-11 8-6
total hands with no removal: 42+36+16+12+8=114
total hands with card removal: 39+33+15+11+6
Let's calculate the probabilities of various types of hands as per page 220, using the "card removal" numbers.
SET:
QQ
3
3/104=0.0288
(agrees with the book's 3%)
PAIR OF QUEENS:
AQo,AQs,KQs,QJs,QTs
9+3+3+3+3 = 21
21/104 = 0.202
(does not agree with the book's 27%)
ANY PAIR:
88+,pair of queens
39+21 = 60
60/104 = 0.5769
(agrees with the book's 58%)
OVERCARDS:
AKo,AKs
12+4 = 16
16/104 = 0.154
(does not agree with the book's 14.0%)
NO PAIR, NO DRAW (presumably includes overcards):
AKo,AJo,AKs,AJs,ATs,KJs,KTs
12+12+4+4+4+4+4 = 44
44/104 = 0.423
(does not agree with book's 39%)
Of the five numbers in the table, I can reproduce two of them. Can anyone confirm/deny the other three? Maybe I made a mistake, but I can't figure out what it is.