A big re-raise largely has to be viewed as a sign that you're holding a monster and it gets enormous respect in most circumstances. Generally you want to assign a frequency to your four-bet bluffs and this will very much vary depending on your table make-up. Against a relatively good TAG player you want to be four-bet bluffing him at least once for every three four-bets you're making for value. Having a balanced four-betting range will make your overall win-rate go through the roof and make you far tougher to combat, and in order to achieve this you need to bluff occasionally.
Let's say you open from middle position with 5-6 suited, the TAG on the button three-bets and the decision is back to you. This is a spot where you should definitely four-bet bluff on occasion.
Hand ranges for four-betting are very much player-dependent. Generally you want some sort of value to your hand so that you have some chance of winning the pots in which you are called. You might elect to four-bet with A-5 suited because you have an Ace, reducing the chances that your opponent is holding a hand like A-Q or A-K that he can five-bet all-in with, as well as the fact that the hand that can flop big.
Heads-up, A-5 suited fares pretty poorly in three-bet pots, so calling is not an option. Four-betting allows you to win preflop a good chunk of the time, or flop a decent draw and make some moves with equity post-flop.
Supposing the villain calls and the flop comes 3-4-8 rainbow (with one of your suit), giving you a backdoor flush draw, a gutshot and an overcard. You can definitely check-raise all-in here in a four-bet pot.
Cold four-bets
Cold four-betting is a really neat way of increasing your win-rate, but should be used relatively sparingly. The idea is that aggressive opponents who are trying to steal the blinds get into a three-bet dynamic, then a player with no investment in the pot elects to four-bet as his first action. This play looks incredibly strong and has a pretty decent success rate when your image is clean. The opponents you can use this on are fairly specific. Generally you want a loose-aggressive opener and a tight-aggressive three-bettor and you want to be four-betting from one of the blinds. You should definitely not be doing this against a monkey who will not notice the fact that a conventionally super-narrow/strong range has just entered the pot. To an aggressive fish A-Q looks like Aces and you'll get yourself into trouble.
So who should you target? Four-betting players that can think will have much better results than weak-tight robots and fish. With weak-tight players and rocks in general, their three-betting range is narrow already so four-bet bluffing them should be very low on your list of options. Instead you should be looking to play a wealth of small pots and steal their blinds at a prodigious rate. Fish, on the other hand, like to see flops, and once the pot gets big (as it will in four-bet pots) they will have issues folding. There are far easier ways to exploit these guys than four-bet bluffing.
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