Quick quiz

[Isura]

Alright, I'll give my 'answers' now.

A)I should have been a bit more clear in the OP about this. But assuming that we open in OTB, and he calls in the BB.

case 1: He doesn't slowplay two pair or TT-KK on the flop
(normal play here).

So I'd put him on 77-55, A9, T9, K9s-J9s (prob folds the offsuit versions), T8s, 97s, 76s, JT, QJ, Axs (down to A7s or A2s doesn't matter much in terms of effecting equity), and the broadway club hands (KQcc etc).

Given that, using pokerstove you get

AA ~ 74% equity
A9 ~66% equity

That's actually a pretty big difference. Reasons are that AA has more equity against two pair (not that important since its hard to get two pair or better!), and more importantly AA kills 'overcard outs' against the flush or straight draw hands. .

case 2: Now assume that villain plays tricky and can c/c the stronger hands of 98/sets/TT-KK. Then we get

AA equity ~ 70%
A9 equity ~ 52%

Now a huge difference. So even though we can now sometimes be against 'strong' hands, AA is still pretty damn good. Eliminate TT-KK from villains range but keep two pair/sets, and AA goes down to 65%, which still beats 58% for A9.

I guess we can take a few things out of this thread. Even though at first glance AA looks the same as A9, it is significantly stronger. AA is less vulnerable, and hence you bet purely for value. Where as with the A9 its for value and also protection (you don't mind if a hand with decent equity folds since they will often make up some of the deficit with implied odds). Now if the question was what do if check/raised on that board, then again equity would help us to a decision. AA dominates his c/r range (if he c/r clubs and str8 draws as well as 9x from time to time), and so we love getting it all-in on the flop before either scare cards hit or they suck out. But suppose we get c/r holding A9 there. Then getting AI is still not that bad, but calling and stacking off on blank turns (any non club 8-2, and J/T probably) would be a better play to punish his draws and also get away on bad cards that are likely to help him.