How many “compressible” strings are there?

Let’s say that a string of length $ N$ is “compressible” iff its Kolmogorov complexity is less than $ N$ . To keep it simple, we can assume binary strings for this.

It is easy to see that almost all binary strings of length $ N$ are incompressible by using the pigeonhole principle.

So my question is, how many strings of length $ N$ are compressible?

In particular, let’s assume that $ K(S)$ is the Kolmogorov complexity of binary string $ S$ , which is of length $ N$ . Then I have the following three questions:

  1. Of the $ 2^N$ binary strings $ S$ of length $ N$ , how many have $ K(S) < N$ ?
  2. Of the $ 2^N$ binary strings $ S$ of length $ N$ , how many have $ K(S) \leq N/2$ ?
  3. Of the $ 2^N$ binary strings $ S$ of length $ N$ , how many have $ K(S) \leq \log N$ ?

All of the above are for sufficiently large $ N$ .

Warlock multiclass Sorcerer….How many level of sorcerer [on hold]

I want to multiclass my yuan-ti warlock great-old-one with a sorcerer sea origins. Im thinking of 5 lvl warlock and maybe the rest in sorcerer. We have a group of 4, including me. We have a half-orc blood-hunter profane soul great-old-one / minotaur cleric of the forge / forest gnome druid. Im more utility in my style. My invocations are = mask of many face/improved book. I want to take repelling blast for my next invocations. Im a warlock lvl 4 but i will take my lvl 5 in warlock to get repelling blast. My lvl 6 will be in sorcerer sea origins for background reason. In fact, my 6 first lvl are already decide BUT after that….My level 7… sorcerer or warlock…..Help me decide please….

How many times does a Mature Animal Companion attack per encounter without orders?

The Mature Animal Companion feat for Rangers (CRB p173) is really ambigious:

If you have the Hunt Prey action, your animal companion assaults the prey even without your orders. During an encounter, even if you don’t use the Command an Animal action, your animal companion can still use 1 action that round on your turn to Stride toward or Strike your prey.
(emphasis mine)

It makes a lot more sense with use instead of have, otherwise I might not even have a Prey for it to Strike.
But in that case, next round, when the Prey is still alive, will my Animal Companion just stand around?

Can you target specific spells with Greater Dispel Magic? How many?

Greater Dispel Magic works as Dispel Magic for the Targeted Dispel option.

This functions as a targeted dispel magic, but it can dispel one spell for every four caster levels you possess, starting with the highest level spells and proceeding to lower level spells.

Additionally, greater dispel magic has a chance to dispel any effect that remove curse can remove, even if dispel magic can’t dispel that effect. The DC of this check is equal to the curse’s DC.

Nestled in the Dispel Magic Targeted Dispel option is the ability to choose which spell you dispel

You can also use a targeted dispel to specifically end one spell affecting the target or one spell affecting an area (such as a wall of fire). You must name the specific spell effect to be targeted in this way. If your caster level check is equal to or higher than the DC of that spell, it ends. No other spells or effects on the target are dispelled if your check is not high enough to end the targeted effect.

Does Greater Dispel Magic inherit this clause? If so, do you have to select one spell to roll multiple checks against or do you select one spell per check?

Why does price change in second page in many apps

In food delivery apps and cab aggregator apps there is price difference in India.

In food apps – I add the items from restaurant menu. it shows total of 240 rs. I navigate to place order page. All the additional charges and taxes are shown now.

In cab aggregator apps they show a price in first page and when you chose a particular category or variant and proceed to the second page all the taxes and deposits and other fares get added and price gets inflated.

Isn’t this a dark pattern? As a user I often feel misled and confused with this kind of pricing tactics. Is it just me or anyone else feels the same? So the question is why does the industry practice this? I have some theories, but I am interested in knowing what others think.

How many spells can a triton cast per long rest using its Control Air and Water trait?

The triton’s Control Air and Water feature says that:

Once you cast a spell with this trait, you can’t do so again until you finish a long rest.

Does that mean a triton can only cast one spell using this trait per long rest, or can they cast each of their spells once per long rest?