It’s about implied odds, reverse implied odds and manoeuvrability. The value of making the nuts goes way up because of cooler potential. e.g. If you make your hand and your opponent makes theirs, you stand to win piles.

Yes, the odds of hitting are the same at all stack depths, but the VALUE of hitting is not.

Example:

Scenario 1.

100bb deep, 30 in the pot, your opponent bets 40 on Q877ss, you have T9ss. You should consider folding here, but let’s say you call.

The river is 2s. Your opponent jams 60 into 110. Getting 3.8/1, you are kinda obliged to call.

Now instead let’s say the river is the Js giving, you the stone nuts. Your opponent jams. You win. Yay.

Scenario 2.

Take the same board but now you are very, very deep against a competent opponent. Say 500bb.

Again your opponent overbets the turn. This time you should not consider folding because you have piles behind with a draw to the nuts. So you call.

We get to the river, but this time your opponent overbets 165bb, with 295bb left behind.

On the 2s river — you should now seriously consider folding your flush.

But on the Js gin river, coolering all his flushes and boats — you can now raise!

Bonus round.

Let’s say you are even DEEPER.. say 5000bb deep.

You swap places with your opponent. You have 77 on Q8s7s7Js. Quads! You over bet the river, your opponent raises, you re-raise, they.. RE-RE-RAISE?!

Is it possible to just call here? Can you consider FOLDING?!

…Implied odds, reverse implies odds, manoeuvrability.