## How can I become guaranteed to move first in an encounter?

3.5e is a very exploitable game and I am vaguely aware of a number of ways to make it highly probable that my character will be the first to move in any given combat encounter. To name just a few examples: Pun-Pun has an arbitrarily high bonus to initiative, Supreme Initiative appears to do what it says on the tin, and Celerity seems to stack in interesting ways. However, given that multiple tricks for moving first exist, it is clear that not every trick for moving first can guarantee that you always move first.

In the interest of greater cheese, I want to know if there is any way to guarantee moving first. I do not require the user to always have this guarantee. For example, I am happy if it’s only a once per day trick. However, when whatever cheese is used in order to get this guarantee, I want it to work regardless of both the opponent and the level of cheese used by said opponent. If the opponent can use some sort of Contingent Celerity abuse to move before I can, then my trick isn’t good enough.

Does any such trick for guaranteed first moves exist?

Note: Given that I’ve already referenced Pun-Pun and Salient Divine Abilities, you may safely assume that any level of cheese is on the table. Furthermore, please do not forget that there exists methods to be immune to surprise rounds. For example, the Divine Oracle has the extraordinary ability Immune to Surprise.

## What is an $O(n \log(n))$ binary sorting algorithm with a guaranteed low scaling constant on the run-time?

Let $$O_c(f(n))$$ denote that $$c$$ is the scaling constant for the run-time (e.g. $$\text{run time} \leq c\cdot f(n) + B$$ if $$n$$ is large enough)

The absolute lower limit on the run-time for a binary sorting algorithm is $$\log_2(n!) \in O_{1}(n \log_2(n))$$.

My question is, is there an actual sorting algorithm guaranteed to achieve that optimal scaling of $$c=1$$ on average? Or what’s the lowest possible scaling constant? And what sorting algorithm achieves the lowest (or a very low) scaling constant?

As a baseline, Quicksort achieves a scaling constant of $$c = 2 \ln(2) \approx 1.39$$, as explained on Wikipedia (see recurrences subsection).

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