I've always shied away from multiplayer SNGs because I've never been a big studier of ICM, but I've been taking a closer look at it lately.

Something that I've noticed is that ICM makes assumptions on the chance that you win and as a result it alters your preferred strategy. However, changing your strategy will also alter your probability of winning. With that probability changing, you also change the value of your chips and your strategy should change yet again.

I've been in SNGs where I am the big stack and two short stacks are trying to not get 3rd. On some level it makes sense, but I think they often take it too far and it is very unlikely for either player to get first.

I'm thinking ICM would be more accurate if it is calculated and a strategy is formed. Then repeatedly recalculated to get closer to what is actually the best strategy.

I've seen posts like "This player should fold KK because of ICM." I mean, it could make sense, but then I also think about the chance of them ever getting 1st place when they are folding hands like this and it just isn't very high.

I think I heard something about the short stack at a final table rarely ever gets first place. I think short stacks play too nitty and large stacks play too loosely, but it is justifiable since the short stacks aren't calling off enough.

Maybe I'm out of my element on this one, but I just never really got on board the "fold for survival strategy" or "I'm a big stack so I can be a bully". Maybe this is why I don't do so well in tournaments. I do tend to bust out just before the money a lot more often than any other spot.

Are these limitations of ICM accurate, or am I making this a bigger deal than it needs to be?

This has been done for slightly simplified tournaments, but you basically need to tweak the tournament rules to limit the number of possible stack setups throughout the tournament. This can be done by making sure all stacks stay at multiples of a small blind at all times.

An alternative offered by some ICM calculators is FGS, which works for arbitrary stack setups and takes into account the strategy for the next few rounds. It's a fairly significant improvement over vanilla ICM, even if you can only simulate a few rounds of play.

If you are interested in details, I looked into this in some detail back in 2015. You can find a comparison of "full tournament" strategies to ICM/FGS below, as well as the finishing probabilities for various stack sizes under optimal play (7.3 and 7.4, starting pg 40):
https://www.holdemresources.net/misc...ity_models.pdf

(First few pages are in German, rest is in English )

Cliffs regarding winning chances: In a 50/30/20 structure with 3-5 players, large stacks win more than their chip-proportional share of the time under optimal push/fold play, medium stacks win less than their proportional share.

I would think that there has to be quite a difference between a tourney that pays 3/9 players compared with one that pays ?/4k players. The one with 4k players will have many tables going near the bubble, which dramatically increases the chances of someone running out of chips on the next hand, thus increasing icm pressure.

To further illustrate that point, think of a double or nothing game that pays exactly 1/2 the field twice the entry fee. There would be lots of icm pressure at the bubble because there's nothing extra for 1st place.

All that to say that I'm never folding KK in a standard structure sitngo with <300bb stacks.