HI, what is the best play with this or similar hands and why?
I have meant Ace high has showdown value but Iam starting to doubt, what do you think? thanks
Poker Stars, $0.50/$1 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $114.74 (114.7 bb)
Hero (BB): $129.63 (129.6 bb)
UTG: $40.36 (40.4 bb)
MP: $55.45 (55.5 bb)
CO: $118.45 (118.5 bb)
BTN: $175.28 (175.3 bb)

Preflop: Hero is BB with A T
3 folds, BTN raises to $2.70, SB folds, Hero calls $1.70

Flop: ($5.90) 4 5 J (2 players)
Hero checks, BTN bets $4, Hero calls $4

Turn: ($13.90) 9 (2 players)
Hero checks, BTN checks

River: ($13.90) 6 (2 players)
Hero checks, BTN checks

This is beginner's questions, why are you posting a 100NL hand?

I suppose a river bluff wouldn't be awful, we do block the nut flush so it might work. Obviously reads would help

I apologize, this is wrong river, the river should be 6 OR Q

what is better in the situation? thanks

So you're making hands up?

Why are you posting 100nl hands in Beginners Questions?

When villain has checked back twice, you should lead quite a lot of rivers that are better for your range than villain's. (You should also be leading the turn with quite a lot of hands after the flop checks thru).
I'm not sure if AT is an ideal candidate here, but if you can list out your entire range (not necessarily on the forum) you should be able to find quite a few worse hands that could be used in preference (T8, Qx/Kx kind of stuff, and A7/A8 that block the straight). Obviously you need to have some credible value hands that go for a bet, or your betting range will be too bluffy. The one-street bluff (just on the river) seldom works very well though. If you bet AT here, villain may well look you up with AQ/AK.

I don't think it's a real hand.

Anyway, in answer to the question..

You're out of position, which limits your ability to bluff as you will struggle to get a true idea of your villain's strength.

You also have to recall that your villain showed some strength pre; whilst that may have been a blind steal attempt, you flat called and so now you're left with your villain having a super wide range.

When you get to the river and you think that your villain's bet on the flop was actually a bit weaker than was being represented, you still have to act first and who knows whether he was bluffing with air or he hit something and wanted to end the hand? You could bet, but if he connected on the flop then he might reasonably call your bet with a smaller pair having slowed the hand down on the turn.

If you make a big bluff, you could of course get called if he made something like two pair or a set on the river. You also have to ask yourself what hand calls pre, calls on the flop, checks on the turn and makes a large bet on the river? What are you trying to represent?

Finally, this is a hand where you committed chips pre and on the flop, where you possibly should have shown a bit more strength pre and less on the flop. It's still a relatively small pot, though, so is it really worth bluffing for it?

You could take a stab on the river, but I'm not sure whether that would be +EV. Depends on the player I think.

I would never bluff the river here. I am likely to check raise the flop. When I play it as posed in the op, I'll call up to 2/3 pot or so on the river. Reads can sway me to a fold vs players that value bet too thin with hands like A5o on the river and or miss bluffing value.