ceV vs $eV

Just gonna take a shot at answer a question posted in the comments.

The question was:
"i also read or hear a lot about people laying down hands because stack sizes don't make it worth it, what is meant by that?"

I think this question is refering to laying down a hand that is likely ahead because of the stack sizes. There are situations in poker where it is indeed profitable to do this. They do occur more in SnGs, but can also happen in MTTs.

Firstly to answer this question you must understand the difference between ceV and $eV. ceV refers to your chip equity (expected return) whereas $eV refers to your expected return in dollars. In tournaments everyone knows (or should know) that chips do not convert linearly into dollars. Ie: just because you doubled up in chips it does not mean that you have doubled your expected profit from the tournament. In fact sometimes even if you are expected to make chips by making a move it may still be the wrong move to make. To illustrate this i'll set up an extreme example.

Blinds: 5/10
Payout structure:
1st: 50$
2nd: 30$
3rd: 20$
4th: 0$

Stacks:
player A: 1 chip
player B: 4800 chips
player C: 4800 chips
you: 400 chips

you are dealt AcAs in the BB, player A folds, players B moves all in and player C folds, what do you do???

Fold of course!

Now although this is a completely exaggerated unrealistic example you should be able to see that you have +ceV (I mean you do have the best hand in poker) but calling this would be severely -$eV due to the payout structure and current chip stacks.

Reason: You're almost guarenteed to cash here if you fold because player A only has 1 chip left. Although you're obviously a massive favorite with AA here, you gotta fold because you simply cannot risk your tournament life here with any holding. Finishing out of the money here would be a complete catastrophe. I'd also like to mention that doubling up barely increases your $equity because you're still a massive short stack compared to 1st and 2nd.

Again this is an extremely exaggerated example and you will rarely, if ever, find a place where folding AA is the correct move. It is just something to keep in your mind that +ceV does not always = +money. Also these situations are more prevalent in sit n' gos than multi-table tourneys just because of the payout structure. I'm no pro at these sorts of things by any means (blue's probably the one to ask about sngs) but recognizing these sorts of situations are extremely important for anyone looking to become a high-stakes SnG player in particular. I recommend searching 'ICM poker' or 'Independent chip model' on google if anyone really wants to learn more about this sort of thing, as I am sure there has been a lot of discussion posted on this topic.

I hope thats what you were asking about and that it at least gave some insight about what people are talking about when they talk about folding because of stack sizes.