I'll start with 3 betting:
someone raises(usually 2x, 2.5x, 3x, 3.5x, 4x, or 5x) with an unknown range(no reads on this player yet). There are some questions to ask yourself as the action unfolds in front of you:
what range should he or she raise from that position for that sizing? This gives the baseline 3 betting range from which adjustments are made depending on the answers below:
how many players are left to act behind me? Fewer opponents = my hand increases in strength. More opponents = the stronger my hand needs to be to 3 bet.
are the players behind me tight or loose?
tight players let you get away with lots of 3 bets, even smaller sized 3 bets. Loose players will tend to make me want to be value heavy, for a larger size.
do they 4 bet often? If yes, tighten up, if no:
do they call often? If yes, you have options including 3 betting a larger size raise, or eliminating the weaker hands from your 3 betting range, or both.
do they fold often? If yes, loosen up with the hands that you think are near the call/3bet profit margin(hint: if calling is profitable, which it is with a certain range that is currently undefined on the lower bounds, but defined on the upper bounds by the bottom of the 3 betting range, then it would follow that 3 betting needs to be MORE profitable than calling).
Often you have a fold/call/3bet decision that features many different opponents behind you and in the blinds. This is when I stick to my default ranges and decision process preflop, as I would vs a table of unknowns(this implies that I hope, or think, but not knowingly endeavor, that my strategy performs well vs all field types, but doesn't imply that I think this strategy is actively exploitive).
After you consider all of that(you'll develop mental shortcuts by playing and analyzing which will make you better at thinking critically at game speed), you need to put the opener on a range and decide on what your ranges should look like vs that range with zero reads.
2x raises allow the widest opening range because the investment is small(think about open shoving 100 big blinds, should be ridiculously tight right? It works both ways.
2.5x raises should be slightly tighter
3x raises even tighter, this is my default.
3.5x is a pot sized raise, this is getting serious.
4x is inflating the pot to the effect of threatening a substantial chunk of the effective stacks.
5x I basically only see this in live games with rare exception, but I don't think it's a good size particularly for two reasons: the correct range for 5x will be very tight and most players don't have the ability to fold all of the hands that they should, which will result in losing lots of money when someone gets a hand behind them(marginally unprofitable hands in your preflop range are a substantial liability, particularly with lots of players behind you). The other reason is that these same players that raise 5x will usually call a normal pot sized 3bet(zero 3bet fold equity = 3 bet a value heavy range) and now they're playing a low spr super inflated pot, in which they have invested about 50% of the money(due to the 5x and pot sized 3bet) with a ****ty range that includes a bunch of hands that are already inherently unprofitable(due to the 5x raise), facing a (should be) value heavy range from a player in position(ouch) or in the blinds(could be worse, but still not an advantageous position).
Once you put them on either (a) a range that is strategically aligned with the raise size, or (b) a range that is not strategically aligned with the raise size, you should do a bunch of work with an equity calculator to determine how profitable you estimate certain hands to be in certain situations.
Ok mumbo jumbo time is over.
100bb no limit holdem:
co raises 3x, I'm on the button vs a table of unknowns:
I 3 bet this range for 10x: 99+, AJo+, A9s+, A5s-A2s, KQo, KJs+, QJs, JTs.
I call this range: 44-88, ATo, A6s-A8s, KJo, K9s, KTs, Q9s, QTs, J9s, T9s, 98s, 87s.
I fold everything else. Notice that if you put the call range into an equity calculator card matrix, the hands that closer to the top left form the profit margin shared with the bottom of the 3 betting range, which should be a value greater than zero. The hands closer to the bottom right of the card matrix will be those closest to zero ev.
Bolded to note that the hands on these margins are the most vulnerable to ev loss, and also have the most opportunity for ev gain, when faced with nonstandard situations, which is where all the above mumbo jumbo fits in.
It's on these margins that I deviate from my default strategy like this:
vs tight passive players behind me, I call more hands near the zero ev margin, and I 3 bet more often with the hands at the top of my calling range.
vs loose passive players behind me, I call more hands near the zero ev margin, and I call more hands from the bottom of my 3 betting range.
vs loose aggressive players behind me, I fold more hands near the zero ev margin, and I call more often with the bottom of my 3 betting range.
vs tags behind me, I play default ranges based on position.
