Did some testing to SoSac's AI and here are the results:
I get 2 upped ghosts out. AI killed one, and didn't play SoSac.
I get 3 upped ghosts and an eternity out. AI plays SoSac.
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I get an unupped frog out and adren it. AI doesn't care.
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I play 3 unupped frogs, one with adren. I killed AI without him using SoSacs.
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Now I use 2 upped frogs. AI doesn't care.
I momentum'ed one of the frogs. AI plays SoSac.
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Now I use 2 upped frogs and a RoL. AI plays SoSac.
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I play fahren with 36
quanta. AI plays SoSac.
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I play 5 frogs. One with adren. AI has an unupped shield. AI does not use SoSac.
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Played 3 hammers (2 flying of course). AI does not use the SoSac.
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I had 1 upped arsenic out. Infected AI with a total of 9 poison. AI plays SoSac
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Now I let the AI build 6 purify counters. I bring 3 unupped abominations out. AI won't play the shard.
I use afla on one abom. After I got 8 Malignant Cells (AI still has 6 purify counters) he uses the shard.
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I play 3 unupped aboms and antimatter one. AI doesn't play the shard.
Now I play my 4th. AI played the shard.
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Note that AI had 200 hp so remaining HP clearly isn't the triggering factor.
Conclusion: AI starts playing SoSac when you have at least 11 damage on the field. Creatures, poison, weapons, and
weapon bonuses are included. Purify is counted as opposite of poison, so you can exceed 11 damage as long as the purify counters are more than the excess damage. AI does not recognize Adrenaline bonus nor Antimatter healing. DR shields are taken into account. This means that the AI WILL die without using it if you are careful about the 10 damage max. And obviously, AI will NOT commit suicide by using it with 40|32 hp remaining.