This depends on the spell, but most spells will make a single critical strike roll per cast, but will check critical strike chance separately against each target.
The way chances work is you have a percentage chance to do something, which is a number from 0 to 100. The game rolls a random number from 0 to 99, and if the chance value is higher than (not equal to) that random roll, you do the thing. It’s pretty easy to see that this gives correct behaviour; the random roll can only go as high as 99, so a chance value of 100 will always happen (for performance reasons, the roll is often skipped for this case), and a chance roll of 0 is never higher than the random roll, so a chance of zero never happens. But a less obvious consequence of this, and one which critical strikes in PoE take advantage of, is that the random roll and the chance are fundamentally two separate values – and you need both to evaluate whether a crit happens.
For critical strike chance, specifically, most skills make the random roll when the skill is used, and stores the value of the roll. Every time the skill calculates a hit against an enemy, it uses that stored roll, and compares it to the critical strike chance of that hit. So if all the hits have the same critical strike chance, then the result will always be the same, because both the roll and the chance have the same values each time – the chance will either always be higher or always be lower or equal. But in some cases, some hits will have different critical strike chance to others – some of the enemies could be affected by Brittle or Assassin’s Mark, or might happen later after some critical strike chance buff has been applied, etc. The skill still only made one critical strike roll, but if some hits have a different critical strike chance, then it’s possible for some hits to be critical and others not.
For example, a single cast of Ice Nova with Spell Echo will make a single critical strike roll – let’s say it rolls 14. There are a bunch of enemies in range, and initially the skill’s chance to critically strike each of those enemies is 12% – Ice Nova’s base of 6% with 100% increased critical strike chance. The first nova hits each enemy, and each time it compares the chance of 12 to a roll of 14, and thus none of these hits are critical strikes. But the user has some chance to inflict Brittle, and some of these hits inflict Brittle on the hit enemies, applying some value of +X% to critical chance for future hits against that enemy. Now when the spell repeats, the critical strike roll is still 14, but some of the hits from the repeat still have 12% critical strike chance and again fail to crit, while others have higher critical strike chance because of Brittle – and for any of them where the effect of that enemy’s Brittle is higher than +2% to critical strike chance, the crit chance for that hit will be higher than the roll of 14 and thus those hits will be critical strikes.
Some skills are exceptions to the above, and instead use a different critical strike roll for each hit, or periodically re-roll the chance for a “set” of hits. This is generally for cases where the number of times the skill tries to hit things when the skill is used once is arbitrary – usually because it’s related to something outside the skill itself, such as Tempest Shield, which hits things each time you block, or Orb of Storms, which hits things when you use other lightning skills. Channelling skills that hit while being channelled also fall into this, because a single use of a channelling skill lasts for as long as you hold the button, rather than taking the cast time like regular skills.
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