No blue axolotls spawn

*Update*

This analysis turned out to have an error that makes part of it wrong, plus developer kingbdogz tweeted that blue axolotls can only be gotten by breeding, so this comment and my following one should be disregarded. See my later comment for accurate information.

After studying the 1.17.0 Vanilla Behavior Pack and experimenting, I have come to the following conclusions:

1. Blue axolotls do not spawn in a world spontaneously (i.e. during the regular mob spawn cycle).

2. They also do not spawn from a spawn egg.

3. If cheats are enabled, you can spawn one using the command /summon axolotl ~~~ minecraft:entity_born. This always and only spawns a blue baby axolotl.

4. If cheats aren't enabled, you can spawn one by breeding two axolotls, but they must be of different colors, When you breed axolotls of the same color, the baby always inherits their color. When you breed axolotls of different colors, the baby has a 1199/1200 chance of inheriting its color from one of its parents (chosen at random) and a 1/1200 chance of mutating. Unfortunately, the behavior pack doesn't tell us how the mutation color is chosen. It might always be blue, or it might be one of 3 colors (random, excluding parent colors), or it might be one of 5 colors (random, including parent colors).

This gives us the following probabilities for spawning blue axolotls:

For the last condition, the probabilities depend on how the mutation color is chosen:

To summarize, the chance of ever seeing a blue axolotl in a survival world with cheats disabled is incredibly small, but possibly as high as 1/1200 per spawn attempt under the most favorable conditions. This could be improved with cheats enabled, but only by a player who knows the tricks (special command parameter or breeding blue parents together).

On the other hand, Mojang's official sources, as well as developers' unofficial or semi-official videos (see slicedlime), have anecdotally described the probability as "very small", which is consistent with the test results. But this doesn't seem like a natural choice of words to describe the situation if there were actually no possibility unless the player deliberately tries to breed one, and in the latter case the probably depends on how hard the player tries. It seems likely therefore that either my interpretation and analysis is wrong, or that Bedrock does not behave as it was intended to. It may also behave differently from Java edition, but I don't have a way to evaluate that.

As background, my conclusions 1–3 above are based on the fact that the axolotl.json entity description in the behavior pack only defines two spawn events for creating the entity. The first one, named minecraft:entity_spawned, creates an adult axolotl with an equal chance (25% each) of being pink, cyan, gold, or brown, but never blue. The second one is named minecraft:entity_born and it's specified to be called after successful breeding. It makes the spawned axolotl a baby and tests whether its color has already been set, setting it to blue if it hasn't.

Although it's conceivable that some external entity or logic might be able to modify the component of an axolotl entity that defines its color (which is named minecraft:variant by the way), I think it's unlikely that the code designers would allow this because such a practice is incompatible with the philosophy supporting the add-on interface and would make add-on development chaotic and arcane. However, if it's done anyway, it would invalidate my entire argument.

Blue axolotls are only spawned through breeding, and it's incredibly rare.

Mojang has confirmed (thanks, Cojo!) that blue axolotls are intended to spawn only through breeding, as a mutation with a 1/1200 probability. A bug in Java 1.17 currently allows them to spawn naturally on that platform; it will be fixed in the next release.

Summary of probabilities for spawning a blue axolotl:

• Blue axolotls do not spawn naturally, and a spawn egg will not spawn one.

• If cheats are enabled, you can spawn a baby blue axolotl using the command /summon axolotl ~~~ minecraft:entity_born.

• If cheats aren't enabled, breeding has a chance of spawning one. The probabilities depend on the colors of the parents:
  |Parents' colors|Probability of baby blue axolotl|
  |Neither one blue|1/1200 (~0.038%)|
  |One blue, one not blue|1201/2400 (~50.038%)|
  |Both blue|certainty (100%)|