We should have 1:2 value bluff ratio on the flop, 1:1 on the turn and 2:1 on the river.

If we check the flop and turn, we still have to have 2:1 value bluff ratio on the river?

If we have 1:2 value bluff ratio on the flop, 1:1 on the turn. If we have 60 combos of bluff on the flop, we have to check fold 30 combos of bluff on the turn?

^Do we need a check call range on turn? to balance check fold range?

The above value bluff ratio is assume you pot size bet all street?

How's the value bluff ratio change if we bet half pot on all street?

I'm not even going to stab at this one. Those ratios seems way too high but I will be reading some of the items that came up on Google when I searched the basic topic.

One thing I will mention, which online may not even be a consideration, is that you really need to consider your opponent and these ratios will need to be adjusted based on your read of their style and range. Don't light chips on fire when your opponent doesn't even 'see' what you want them to see ... or is a calling station or P.O.W. GL

I don’t like any system that doesn’t take the board textures into account.

^ This ^.

Janda's first book had some interesting theories about value:bluff ratios, but real poker doesn't work like a toy game. You don't always have a perfectly polarized range and villain doesn't have pure bluffcatchers. Every street changes the strength of ranges, so sometimes you should be value-heavy and sometimes you should be more bluffy.
You can recognise that you can bet with more unmade hands on the flop than on the river, but there's no magic ratio.

Thanks for all the reply! Not get the answer I want tho.

The "GTO" value bluff ratio, 1 to 2 value bluff ratio on flop, 1 to 1 on turn and 2 to 1 on river.

If we check the flop and the turn, do the 2 to 1 value bluff ratio on river still apply?

Or the 2 to 1 value bluff ratio on river only apply if we already bet the flop and bet the turn?

It's a mathematical concept that doesn't care about ranges or previous streets.

The odds for the other player are always 2:1 if we bet pot (and he has at least pot behind) no matter if we potted or checked the previous street.

IMO Bluffs are more about telling believable stories than anything else.

This is true vs almost all player types, with the exception of (clueless players) and (crushers) imo.

I think you can get away with unbelievable stories vs clueless players.

I think you need value hands in all lines vs crushers, thus you can also have bluffs in all lines vs crushers.

You're coming at it from the wrong angle. Modern indifference theory doesn't use traditional (value:bluff) ratios anymore, except on the river.

So you want to get to the river with a good mix of hands in all realistic action sequences with a range that can earn part of the pot in many ways. You want to have monsters that can win huge pots, strong hands that can win big pots, draws that can hit river cards(hint: sometimes this is as weak as a 6* out pair draw in a checked down pot.)

* this number must be discounted, but free draws in checked down pots are quite profitable nevertheless.

But it's not "GTO", except in artificial/toy games where one player has a polarized range (value and bluffs) and the other solely has mid-strength bluffcatchers. Real poker is not like that. On most boards, both players have a mixture of nuts, mid-strength, draws, and air.

That said, if you get to the river and want to bet POT, then I think the range you bet with should have about 67% equity against a calling range (i.e. it's roughly 2:1 in favour of value). Some hands will win much more often (the nuts), some will win slightly more than half the time (thin value), and some will almost never win when called (bluffs).
On the earlier streets you'll bet with more unpaired hands, but they should often have a chance ("outs") to turn into value hand later on.

P.S. To answer one of the other questions in your initial post, if you choose to bet small, your betting range should contain fewer bluffs, because you're more likely to get called when you bet small. e.g. If you bet half pot on the river, 75% of your range should be beating the calling range, and you can only "get away with" bluffing a quarter of the time against an optimal opponent.