Miscellaneous points. I don't think you can say the decision is 'not close', but I'm not hugely commited to either side of the argument.
- Ax is an unlikely holding for villain. Most people would raise with strong Aces and either raise or fold with weak Aces. A moderate/weak Axs is possible, I suppose. On occasions where villain has Ax, betting is clearly the best option as it will invariably be your cheapest route out of the hand. If villain calls or raises given that we represented an Ace preflop and on the flop, we can be done with the hand unless we hit 2 outs.
- If we bet the flop and can follow through with our bets on future streets, we will either (a) get called down by an Ace, (b) get slowplayed to death, (c) possibly force a weak Ax to fold, or (d) force any other weak holding that is calling the flop (~TT?) to fold. I think the two positive outcomes are slightly more likely than the two negative ones, treating both as separate 'groups'.
- If we bet the flop, very few hands that we are ahead of are calling, and very few, if any hands that we are behind are folding.
- If we check the flop, we may induce a bluff from villain on the turn. Against an unknown player (as I rambled on about in the AJs thread), this is potentially dangerous, however, although less so in this example as we have position and the pot is smaller.
- If we check the flop, we do not necessarily lose the initiative in the hand, as this is a flop villain would have been expecting us to c-bet, and the fact that we haven't may actually set off alarm bells. This is read-dependent though, to an extent.