Clash lab
Exact clash odds and damage between one of your skills and an enemy skill. Every coin outcome is counted, not sampled: heads chance from Sanity, the front coin breaking on each lost exchange, the level bonus of +1 clash power per 3 offense levels, and the damage sum of resistances, level gap, crits and clash count.
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How the numbers are worked out
Each coin lands heads with chance 0.05 + (Sanity + 45) / 100, between 5% and 95%, so 0 Sanity is 50% and 45 Sanity is 95%. Units without Sanity, which is most Abnormalities, flip at 50%.
In a clash both sides roll all their remaining coins. If one side's offense level is at least 3 higher, it adds 1 clash power for every full 3 levels. The higher total wins the exchange and the loser's front coin breaks; a tie breaks nothing. This repeats until one side has no coins.
Each hit deals power times a multiplier. The multiplier starts at 1 and adds the attack-type resist term, the sin resist term, the level term (offense minus defense, divided by that gap plus 25), 3% per clash exchange and 20% on a crit. Resist values above 1 count in full (Fatal 2.0 is +100%), values under 1 count half (Ineff. 0.5 is -25%). The result is rounded to the nearest whole number with halves going to the even number, and never drops below 1.
Passives, statuses and conditional skill text aren't applied for you. If you know one is active, add it with the modifiers: clash power, coin power, damage up or crit chance.