[Aces McGee]

gg,

Let's assume for the sake of discussion that [ QUOTE ]
this villain had a set of 9's or a set of 8's

[/ QUOTE ] is true.

In such a case, [ QUOTE ]
therefore it was 50/50 his quads came in

[/ QUOTE ] is not true.

If we put him on a set of 9s or a set of 8s on the flop, we are essentially putting him on six hands, not two:

9 [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/heart.gif[/img]
9 [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img]
9 [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img]
8 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/heart.gif[/img]
8 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]
8 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]

When the 9 [img]/images/graemlins/club.gif[/img] shows up on the river, suddenly one-third of this range is no longer possible. If we stick to the hand range you assigned him on the flop, he can now only have:

9 [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img]
8 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/heart.gif[/img]
8 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]
8 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]

Thus, by the river, it is three times as likely that he has eights full than quad nines.

There are other considerations, of course. He could have a bigger range on the flop. Or he could be so passive that he would put you on KK when you went to five-bet the flop and only raise the river here with quads. But your contention that he is equally likely to have 99 or 88 independent of his action on the river is incorrect.

-McGee