In a chip EV situation how do larger/smaller stack sizes affect players ranges in different positions? and why?

Because blinds go up in tournaments, which means your stack gets "smaller" even with a constant chip level.

Very generally speaking, in tournament play the smaller your stack (in BBs) the looser and more aggressively you have to play in order to avoid getting blinded out or being forced to shove with ATC. Your strategy options become increasingly limited as your M goes down, until ultimately all-in is your only option left.

Your question doesn't usually apply to cash games. If you can't pull out more money then the stakes are too high for your roll or it's time to quit for the night.

I more meant in a cash game or in a single hand situation where future hands are not considered.

I think it does apply to cash games.

I don't understand how bankroll would have anything to do with optimal EV decisions.

Only if you self-limit your stack to play a short stack strategy. You should put enough money on the table to support your playing style, not the other way around.

This isn't really what I'm talking about. You still have to establish a strategy, and you can't always have a constant stack in a cash game because you can't take money off table.

Here are some of the factors relating to stack size in cash games in no particular importance order:

Aggression: The larger your stack, the more aggressive you can be (wider ranges, bigger bets) and get better fold equity.

Bullying: Opponents may want to avoid fighting the big stack guy making bluffing a profitable gambit. It is easier to bluff a small stack than a large one. Short stacker has no bullying power and is often pot committed and has little or no fold equity .

Bust factor – without an adequate immediately available bankroll, playing with a short stack may induce poor play (playing scared) for fear of busting and having to go home

Implied odds: The bigger the effective stack, the bigger the implied odds. You lose implied odds against short stacks so low pairs for example do not have odds to set mine short stacker(s)

Pot committed: The smaller the stack the more pot committed one is, perhaps forcing one to bet in somewhat unfavorable circumstances.

Short Stacking OTOH – short stacks can sometimes take advantage of desirable pot odds not available to larger stacks

Stack to Pot Ratio (SPR) - A whole strategic theory has been developed based on this concept- see the book Professional No-Limit Hold’em

As stacks get bigger you also have to worry about negative implied odds.
Hands like A10 and KJ should be played carefully to avoid losing a big pot when 2nd best.

Hands like low pocket pairs, or king high flush have a chance to be on the bad side of set over set or flush vs flush and should also be played carefully when you have a big stack

Big stack meaning 100bb or higher

I really think big stack in cash games is over 200+bb as most places you can buy in for 100bb

Obv stacks influence cash game.
With a short stack say 50bb eff we play most high cards that make pairs with good kicker, avoid playing speculative hands.
With 100bb play with speculative hands makes much more sense.
Deep stack 200bb+ also changes game:
-position is more important, the higher SPR the higher value of position
-pre we prefer hands able to make nuts, A2s>87s etc
-stackoff range narrower, e.g. hardly ever gii with bottom set is good

A good place to understand the importance of different stack sizes is in tournament (MTT) poker format. As you will quickly realize the stack sizes factor in as one tries to devise a GTO, Nash equilibrium type strategy. To better understand how it alters ranges play around with ICMizer or Nash push fold charts. This is why you will see on TV pros asking each other "How much did you start the hand with" r similar in both cash games and tournaments, as it allows them to tailor every street of action right from the get go.

Not really sure I agree with this at all. I agree that part of the power of a large stack is the value of leverage... ie. a bet of 50 bb's OTT with 200 bbs behind - can imply a very leveraged bet and get an inordinate amount of FE. But when a big stack takes on a short stacker - effective stacks are based in the short stack - removing all potential leverage. I'd say it is much easier for one big stack to bluff another Big Stack than to bluff a SS.

Additionally when a SS goes all in (even with marginal single pair hands) - the Big Stack has no implied odds to call any draw. Knowing this - the SS can represent the marginal made hand and bluff more effectively than the larger stack.

As stacks gets deeper, you'r allowed to use bigger sizes and balance that with the proper bluffs, so you get to play more parts of your range profitably. While in shallow stack play you generally can only use small bet sizes and balance those sizes with the proper bluffs, which allow much less bluffs than bigger sizes.

Other than that, the deeper the stack's get, the more important it is to be able to make the nuts with pf hands. Meanwhile on shallow stack play, absolut hand strengh of the pf hands are more important.