We want at least a 50% chance hand is best preflop. Otherwise you are speculating on flaws that may or may not exist in your opponent's game.
First, you should be able to predict how frequently the initial raiser raises.
Secondly, you assume that the calling opponent has a hand range in that opponent's upper half range.
Thirdly, you only raise with a hand that has a 50% chance of being best.
Forth, you determine chances your hand is best based upon the assumption that the top 10% of all hands would represent the top 10/40=25% of an opponent's range if he initially raises with 40% of hands in this situation.
While you could raise more than this if opponents fold to a squeeze play, the squeeze play risks a lot and the opponents can resqueeze and cause you to lose a lot of chips if you have to fold. Because there are twice as many opponents as in a 3bet, you have to be a little bit more concerned. Additionally, if the second caller does so with a tighter range of hands, you are more likely to run into a call.
So here is the squeeze % to give every hand at least a 50% of being in the top range.
Squeeze chart:
| raiser % of hands | you squeeze this % |
| 100% | 19.10% |
| 50% | 9.55% |
| 40% | 7.60% |
| 30% | 5.72% |
| 25% | 4.77% |
| 20% | 3.82% |
| 10% | 1.91% |
This assumes opponent who calls or raises does so with half the range of hand opponent raises. You should squeeze X% of the time assuming "infinitely deep chipstacks". In other words, what is the widest hand range that still has a 50% chance of being best against opponent's range.
If your resqueeze is for say a 4x pot all in, you could raise with a larger range since opponents can only call or fold based upon the flop. This prevents them from being able to speculate drawing hands. If you are pot committed all in with your 3x or 4x bet to a small raise, or at the point your all in would be 8x or 9x or 10x or up to say 15x, (your raise could be pushed for 5x all in), then you need to raise probably slightly less often since opponent can push you all in and you have to fold or take what equity you can.
The calculation is done by finding the chances opponent would have to fold if he could only play your hand range. So if a player raised 40% of his range and the caller called with 20%, you'd have to play with different ranges. So start with 10%. What is the odds a 10% hand is best? 10% is 25% of opponent's A range which means there is a 75% chance he has a worse hand. But there is a 50% chance opponent B has a worse hand. The odds of BOTH having a worse hand is .75*.50=.375 or 37.5%. That means there is a 62.5% chance they have a better hand. That's too high. You want them to only have a 50% chance of a better hand.
So if you set an excel spreadsheet up right you only have to change the 10% number until you reach around 50%. That number is about 7.6%. Then you can tweak the starting raisers range and solve for the next range. If opponents are really wild and aggressive and likely to reraise you and you'd prefer a less marginal edge because you have a looser image and/or don't have a lot of confidence that flat caller doesn't have a better hand, you can solve for having a 60% chance hand is best in that spot since you are putting a lot of chips in.
If you have a really tight image your odds of getting away with it are higher and if you think opponents will fold too often you are okay being more speculative about opponent folding to the reraise too often and playing a bit looser with hope opponent doesn't play perfectly against the squeeze, you can only look for a 40% chance hand is best so if you are wrong you still have decent hand that doesn't lose too much from behind and still should have some pretty good equity if you get called.
In a perfect poker world you could always raise with any two and opponent would always fold too much and never adapt to you. But that is not reality. So by being somewhat selective you give yourself some "outs" so to speak if you are wrong. By forcing yourself to at least wait for a 40% chance your hand is best you aren't just throwing your money away by wildly gambling and betting too heavily on an unknown without a sure edge. Instead you expect to show just a mild loss if you are wrong and opponent either is close to perfect or adapts quickly, but if you are right you still have plenty of opportunity to exploit for greater gains.
By forcing yourself to at least play when you have a 60% chance or less and at least 40% or more, you aren't playing emotionally, and prone to error out of fear and greed. Instead you are playing at least somewhat strategically. If you had to choose either one, playing too tight is far better because you extract a certain edge less often. You only limit your potential which is far better than playing a style that will just over time lose more and more money vs good competition. There may be moments of a tournament where playing more reckless is better than too tight, but that is the exception, not the rule.
At this point I think it's safe to ignore remaining players. However, you should typically assume opponents who raise 40% on average raise from MORE often in late position, the same in middle and middle late, less in middle early and even less from early position.
Let's convert this to a specific set of hands.
When initial raiser raises X% with 1 caller, you push with the following hands
100%:22+,A9+,KJ+,A3s+,K9s+,Q9s+,J9s+,T8s+,98s,
50%: 66+,AJ,A9s+,KTs+,QTs+,JTs,
40%: 88+, AQ+, ATs, KTs+, QJs+, JTs
30%: 99+,AQ+,AJs+,KQs
25%: 99+,AQ+ (sometimes fold AQ)
20%: 99+,AK
10%: JJ+
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