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You may have noticed that the game seems to have two similar effects: invisibility and "designate as non-target". I have done some testing (and watched some videos) and figured out how the effects differ.

Invisibility: Guaranteed to work when cast. Enemies will not do anything unless hit with a physical attack. A successful physical attack will not break invisibility, but it will allow the enemy to attack you briefly. Enemies will not react if hit with spells (so invisibility + attack spells lets you kill enemies without them getting a chance to retaliate). Some enemies ignore invisibility.

Non-target: Has a percentage chance of success, checked when you first cast the spell. Enemies will not move or physically attack you, but can still use spells against you (and will use spells in melee range, which they don't normally). If the option "can cast offensive spells" is "N", then damaging an enemy (whether physically or with magic) will break the effect. Casting an offensive spell that does not hit an enemy will not. (Do reflected spells cast by enemies break the effect? Does poison/continuous damage cast beforehand?) If "can cast offensive spells" is "Y", then the effect will not be broken by attacks or spells; combine this with spell resistance/reflection and you are basically invincible.

Two notes about the costs of the spells:
1. If you are a Nightblade, both spells cost only half in the spellmaker. (This also happens with Open.)
2. Non-target's cost can get very high, as the success rate and duration are multiplied, and enabling "can cast offensive spells" increases the cost by a factor of 4 (with good reason, it's a very powerful effect). It is possible for the cost to overflow and become small; even double overflow is possible with this effect, which will (for some reason) crash the game. (You will get the DOS prompt, but it won't respond to keyboard input, forcing you to close DOSBox (or reboot if playing on bare metal).)