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Looking at the Homunculus Servant stat block, I noticed that for CR it's just blankt. Not 0, not number, just blank. It made me wonder, would it be affected by spells like polymorph or true polymorph? Could it transform into other creatures with no CR? Or does the nature of a Homunculus Servant technically actually make it into an object, and thus if one were to use True Polymorph on it it could turn into any tiny creature of CR9 or small such as a flameskull?

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This is not clarified in the rules, so the DM must make a call.

Technically nothing is not a number and is not 0, and so is neither larger nor smaller than any given number as you cannot compare them. The true polymorph spell says:

If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating).

This means if you do not assume a missing CR to mean 0, you could not polymorph the servant. There also is the giant fly from the DMG (p. 169), that even is a beast as required by normal polymorph and likewise has no challenge rating, but that still is not a legal target, because it also has no numerical challenge rating to compare against the servants missing numerical challenge rating.

If I were the DM, I would probably treat the missing CR as 0, and be done with it, but another DM may decide otherwise.

The servant is a creature (of type construct), not an object. Having a CR or not does not make you a creature or not. Not all creatures must have all Statistics, for example there are many that lack Reactions or Skills.

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It can transform into any creature that has no challenge rating.

True polymorph says (Player’s Handbook, Ch. 11):

If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating).

This means you must find an option whose challenge rating is "equal to" the missing CR of the Homunculus, since there cannot be anything "lesser than" an undefined value.

According to Merriam-Webster, equivalence can be non-numerical because "equal" means:

like in quality, nature, or status

Two monsters that have no defined challenge rating indeed have a challenge rating that is "like in quality" -- the quality of being undefined. One example is the giant fly from the DMG (p. 169), which likewise has no challenge rating.

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  • \$\begingroup\$ Missing is equal to missing, sure, but their challenge ratings are not equal, since they don’t have challenge ratings to compare, and TP requires that we compare challenge ratings, which we can’t do because they don’t exist. \$\endgroup\$ Commented Nov 10, 2023 at 15:24
  • \$\begingroup\$ TP doesn't require that you compare challenge ratings, it only requires that the two are "equal to" or lesser than. Lesser than is a comparison, but "equal" is an English word that means, according to Merriam-Webster, "like in quality, nature, or status." Being not-included is like in quality and nature for both of their CRs. \$\endgroup\$
    – Kerrick
    Commented Nov 10, 2023 at 17:23
  • \$\begingroup\$ They do not have CRs that were not included, since that presupposes that they have CRs in the first place that were simply not included on the statblock, which is incorrect. \$\endgroup\$ Commented Nov 10, 2023 at 17:36
  • \$\begingroup\$ Correct, and the state of both not having something is "like in quality." \$\endgroup\$
    – Kerrick
    Commented Nov 10, 2023 at 17:48
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    \$\begingroup\$ You’re making a category error here. Two creatures not having a challenge rating is not the same thing as two creature having an equal challenge rating, and TP requires the latter. \$\endgroup\$ Commented Nov 10, 2023 at 17:50

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