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So I've been doing some probabilities and thought I'd share my findings.
This all applies when you're trying to conjure up Daemons with a PL 3 power and get +1 to your rolls, by the way. Sacrifice is the easy one - 8/9 chance of casting with a Spell Familiar and no risk of Perils - but the WC3 powers aren't so intuitive. (I generated these predictions with Wolfram Alpha.)
Rolling three dice, needing at least three of them to score 3+, with a re-roll
Success: 50.5%
Chance of a PotW
Daemon Prince: 7.4%
Mortal: 44.5%
Not terrible odds if you're left with three dice to burn off, but the risk-reward is poor for a mortal.
Rolling four dice, needing at least three of them to score 3+, with a re-roll
Success: 83.4%
Chance of a PotW
Daemon Prince: 13.2%
Mortal: 72.2%
This looks like the sweet spot. A level three DP can comfortably spit out a unit when the Warp ebbs low, and the reward exceeds the risk for a mortal.
Rolling five dice, needing at least three of them to score 3+, with a re-roll
Success: 95.6%
Chance of a PotW
Daemon Prince: 19.6%
Mortal: 90.7%
If you absolutely need to summon a unit, this seems optimal. You will burn out your mortals quickly doing this, though.
If your DP with one wound remaining gets PotW on the first roll and you want to re-roll to avoid the risk, you'll have an 80% chance of successfully casting and an 80.4% chance of not PotW'ing.
Rolling six dice, needing at least three of them to score 3+, with a re-roll
Success: 98.8%
Chance of a PotW
Daemon Prince: 26.3%
Mortal: 98.5%
For when siccing Flamers on a blob is a win button - or when you've got 1W left in a duel with Calgar and it's time to Hulk out.
If your DP with one wound remaining gets PotW on the first roll, you have a 90% chance of successfully casting and a 73.7% chance of not PotW'ing if you re-roll.
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