Hmmm

Interesting one.

So what folds if you bet?:

Probably fold the straight (at least if you bet pot) and maybe low flushes although at $20 a lot of opponents will call with any flush here.

I think this is going to come down to the opponent. If he is a bettor then this might work quite well. Against me for example it might work well. I have a feeling that you need to be willing to check again on the river though before some opponents are convinced. If you check turn and river I might bet with as little as a str8 but you won't get a full pot bet out of me and I probably don't call your raise so ...

Need to take into account that you're also giving something up on the times your opponent would call with his 6 high flush regardless.

My guess is that the more likely hands for your opponent to bet on either turn or river (sort of J high flush type hands) are probably calling here most of the time in a $20 game. If betting is your opponent's weakness however then you may get value from this.

PS You might also be giving a set of 4's a free card but I'm not sure that bothers me too much although mid or bottom set probably call turn hoping to hit their boat but fold river after they miss.