Specific hand would help, it's prob player dependant & stack sizes would help. If we assume its equal stacks, then once he pots the flop you really need to know what his tendencies are as to whether you would peel one, if he is going to shut down once the Ace or flush card hits then I'd prob fold to his bet. If you are likely to get paid off I might peel one off.By the time you get shoved on you have to look at pot size, you have to put in 1080 (assuming 1500 stacks to start the hand) to win 3000, so you need 36% equity to break-even, so by calling with 35% it makes it a losing play but not by that much

You're only 48% to win assuming he only has one pair(flush + 3 aces).  If he has two pair or a set you're 36% or so.  I wouldn't be calling this so deep.  It's only going to create higher variance making plays like that =) 

I look at it this way.  The amount of money you put into the pot already is not important.  The money you put into the pot is no longer yours.  It belongs to the pot.  The only money you have is what is left in your stack.If this is the start of the game the stacks are 1500, and blinds are 10 and 20.  Villian raises to 60, you call.  Pot is 120.  Villian Cbets 75, you repop to 225, villian shoves.  I would assume about 30% equity here.  Your stack is 1215 and the pot is 1785.  I would fold. On the other hand, with 2 overs and the flush draw, you could assume your equity is closer to 45-55%.  In this case, I would check raise my grandmother all-in.The math is the same as effective stacks get smaller.  But as soon as the smallest stack is less than 30% of the pot your As4s example becomes a snap call.  I could be wrong, but that's how I would play it.

You don't really need tons of fold equity since you already beat most non pairs with your ace high, and you can get further value from this opponent.Now, against an unknown opponent you won't be able to narrow their hand range down to a degree where you're clearly happy in all spots with your decision, but that doesn't mean you can't make the right decision nor a better play than check raising.I like the comments above mine, check raising here seems to be a little too loose and there really is no reason not to check call, you have a strong nut draw and you beat almost every pair.  Further, you just end up in a lot of situations where you don't lose your stack when you don't make your flush or top pair, and can still win a very large pot, sometimes even the entire stack, when you make your hand.With some postflop reads calling becomes very clearly the best play in most situations, but even without reads I believe a call is best, it just means our adjustments from a default type line of check/call on the flop are not as drastic, since we're not able to narrow his ranges down into various sub categories (for example, bluffs pure air on the turn, also bets top pair or better, but bets smaller with 2nd pair, checks weaker pairs and draws back as well as showdown value...  with those types of reads and characteristics we can be confident in some different adjustments and lines).

If you think about check-raising, it's very important to know his cbetting tendencies.If your opponent is opening wide and c-betting close to 100%, then it can be very profitable to check-raise him with a good draw - simply because he can't continue very often.  However, if he checks back a decent amount or varies his c-betting size, then you're often setting yourself up to get it in as a slight dog.I just took about 8 buy-ins off a guy who always played his draws fast and who wasn't paying attention to my play - I hit him so hard by c-betting full pot with hands that I wanted to get it in with, checking back most of my air and c-betting smaller with weaker hands.  That guy also made very large check-raises with his draws - and whenever I shoved over that, I had him crushed.When I have a nut-flush-draw, I like to check-raise it most when I'm playing against some bad multi-tabling regular and we're deep enough, so I won't commit myself with the check-raise.  These guys often play cbet-and-done if they don't connect with the board, but fire multiple barrels if I just check/call on a drawy board, so I have some decent fold equity plus odds to improve if they just flat ... and if they shove, I can safely assume I'm beat and fold.  And if they do flat your check-raise, then often check back on the turn for pot control, so I see two cards, so the price is about the same as check/calling two streets.This might be different on higher limits, but works fine on the $50's for me.Against an unknown or a fish, I prefer to just check-call and reevaluate turn.  IMO there's just no point of check-raising if you're not sure whether you have any fold-equity and which hands they shove over the top.  Building a huge pot oop and not knowing what to do when faced with a shove is just terrible.