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Alakazam uses Future sight (Turn 1)
Alakazam uses Calm Mind (Turn 2)

Will the future sight be boosted

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Not sure what you mean but if;

You mean what happens to Future Sight, if the Pokemon that used it boosted using Calm Mind the turn after using Future Sight.

>The damage is based on the Special Attack and Special Defense at the time of striking, not at the time it was used on the original target.

So the boost of Calm Mind would be factored into the damage taken by the opponent

You mean what happens if Future Sight hits after the target uses Calm Mind

>The damage dealt is calculated based on the Special Defense of the hit Pokemon and no longer from the one that was originally targeted. The damage is based on the Special Attack and Special Defense at the time of striking, not at the time it was used on the original target. This means that if you use Future Sight on a Pokemon with 100 Special Defense, and then your opponent switches to a Pokemon with 300 Special Defense, the damage calculations will be done as though the target has 300 Special Defense.

Smogon - So basically, the modified Special Defense stat will be used in the calculation, rather than the original one.

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