Helly guys,
I todays online games I see more and more REGs min raising the button. I am currently opening 2,5x and would like to know what are the benfits of the min-raise strategy from the theoritical point of view and should we adjust depending who is sitting in the blinds (fish/REG) ?

Thanks.

at a beginner level it'll make next to no difference

Thanks for your great explanation...

2.5 times is a min raise if you think about it.

i would tailor my raises to the two players left to act.

The reason behind minraising is you are investing the less to win more. Look at this example, tournament FR 50 100 10ante, you min raise you will need it work 45.4% of the time to break even, if you go 2.5 you will need to work 51% of the time. Yeah you definetely adjust depending who is in the blinds.

* It's a cheaper attempt to steal, which means you can play a wider range than a nit that opens for 3x or 4x. (This is simply due to the risk:reward ratio. You can't keep putting in 3bb or 4bb with 86s or J8o if you hardly ever win. It's better to steal for 2bb if you open a wide range, so you minimise your losses when you get 3-bet).
* It maintains more stack depth so that you can continue more often against a 3-bet. Position is more powerful when stacks are deep, partly because of implied odds. e.g. If you open pocket fives for 3bb otb, then a pot-sized 3-bet by the BB will be to 9.5bb and you'd have to call 6.5bb to see a flop, with 90.5bb behind, so you have implied odds of less than 14:1. Set-mining a small pair will be profitable, but barely. If you minraise and BB makes a pot-raise to 6.5bb, you call 4.5bb with 93.5bb behind, for implied odds of almost 21:1. Set-mining is clearly profitable with these odds.

FWIW, in the future, those regs that have learned to minraise the button will learn they should also be minraising UTG. In a game with blinds, the aim - to borrow Will Kassouf's line - is kind of to get in for the min, to win the max.

I'm seeing -and doing this- more and more in the games I play (small stakes tourneys). Especially as the blinds and antes are gone up at the later stages.

However, I'm not sure how often and against what type of players (HUD statswise) we should do this?

for me anyway i love it when i only get min raised for 2x. then i get 3.5 to 1 on a call and see who can overcome that and still win.

Smaller opens work best against good/tight players, because they will usually either fold or 3-bet, and not do much calling, except in the BB. Bigger opens work better against weak players that call too wide pre, but fold a lot post (they play 'fit or fold', because they whiff so often), or that will be calling stations with bad hands post-flop.
It's not a disaster to minraise when you're likely to get flatted a lot by fish, however. When you're going to be OOP, keeping the pot small (thus minimising your losses) will tend to work better than bloating a pot you're less likely to win.
e.g. If you open AJo in EP and get two callers who have position on you, then when the board comes Q76tt and you have no equity, it's better to check-fold and lose 2bb total, than lose 3bb... or compound your mistake by c-betting into the abyss with no fold equity. (If you open for 3bb, then your c-bet will also be larger).
If you happen to flop very well against a fish, you can easily build the pot even if it started off small, because you're playing no limit holdem. What you lack in pre-flop fold equity, you make up with post-flop value-betting.

The trend in both tournaments and cashgames (and especially online, as opposed to live) is to play much smaller pots than were common 5 years ago. Small pots begin with minraises. If poker is still being played in 2020, I honestly think people will look back and laugh, saying things like "Remember when people used to open for 3x UTG. LOL!"