“Second nuts”

Absolute number of combos doesn't really matter, only relative.

If villain's range is only the one combo of nuts on the second board, you lose 100% of the time.
If villain has 120 combos total on the first board, you lose 10% of the time.

Also, not all nuts are equal.

Especially in a game like deep stack plo where you can flop the nuts and still only have like 30-35% equity vs your opponent's hand.

Because it's a meaningless waste of time.

I’m not sure how you can say absolute number of combos don’t matter. If the board runs out so there is only 1 combo of 55 that beats you or if there are 12 combos that beat you on the first board you are 12 times more likely to be losing on the first board than the second. There are 12 chances he was dealt KJ there is only 1 chance for 55.

I know not all nuts are equal, that is what I said in my initial post.

You are free to believe whatever you want. If you want to make claims like that it would be good to explain why.

Let's say you are correct. What do you gain from looking at things this way?

Yes, it's always more informative to count in terms of combos rather than hand types.

Different types of nuts / 2nd nuts (and air) also have different dynamics due to some nuts blocking 2nd nuts, some nuts having air blockers while others don't, etc.

You're correct that raw number of combos alone shouldn't determine how you should play a hand, but any equation where (for example) y represents the number of hands you're behind, y should be measured in combos rather than hand types. You should still make it the numerator above total range width, weight it by likelihood of each combo showing up on that node, equity should still be in the equation, etc; but that side of the equation is still largely increasing in proportion to how many combos there are per hand type.

Do you play AA the same on AKJTx as you do on AKKxx? If not, why not?

And just to get out ahead of this inevitable reply: You cannot simply flatten that entire part of the equation into equity. Having 51% equity against 100% of hands functions differently than having 100% equity against 51% of hands and 0% against the rest.

Of course not. Why?

Worrying about 2nd or 13th nuts - as in the OP - is not productive. What hands, and how likely are they, can beat me is a much better way to think. Of course, whatever method that works to get you to the finish line is fine. I just find what place your hand is in the gamut of "the nuts" a waste of mind-space.

I think it’s important to take into consideration how strong your “second nuts” are. You can’t just say since I have the second nuts I call.

Why do you play them differently?

You concluded--without knowing anything about the configuration, positions, node, stacks, etc--that you would play the same hole cards differently on two different boards where it's the "2nd nuts" (by traditional terminology).

I have to conclude the reason you play them differently is the vast difference in the number of combos you're behind (since all else is equal in this scenario).

Because the absolute number of combos that beat you is not relevant in any situation. The relevant factor is the fraction of your opponent’s range that beats you. You can’t just say you are 12x morel likely to be beaten on the first board. We don’t have enough information to conclude that. We need more detail on how the hand played out to make any such conclusion. Suppose on the second board, villain made a 10x overbet shove 300bb deep. What would be his range that does this? Maybe 55, AA, TT? We have AA so we can rule that out, hence he can have 1 combo of 55 or 3 of TT; we beat 75% of his range. Maybe villain has 120 combos on the first board in his range based on how we got to that point. If so, we beat 90% of his range. The fact that it’s 12 combos vs 1 combo is irrelevant in these scenarios.