I'v been finding this happening more often then I'd like and its turining alot of potential winning sessions (playing 10NL) of half a buy in or more into an even day or +- 0.20$. Here is one that happenend yesterday. The session was going well untill near the end when i have A9 in the BB. A few people call 2 in mp 1 in lp and the button.

Flop Comes back AxA rainbow. After the flop only me and the button are left after some action and I know he is on an ace. In this position should I just check/fold in fear of a better kicker or play to get value out of A rag suited. The guy ended up with AJ and happily ate the sessions proffit.

Any advice for this kind of thing, thanks.