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Deals damage at the end of the second turn after it is used (if we say the move is used on the first turn, then the attack hits on the third turn). Since it hits at the end of the turn, it is not blocked by Protect or Detect. It does not bypass Focus Sash or Sturdy. Contrary to previous generations, it no longer deals typeless damage, so it is affected by STAB but also by weakness and resistance of the Pokemon it hits. Its power can be boosted by Gems, which activate the turn Future Sight does damage. Life Orb now boosts Future Sight's damage, and the user will suffer recoil damage. Since it's a Psychic-type move, it no longer hits through Wonder Guard.
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. Fails if this move or Doom Desire is already in effect for the target's position, and multiple Future Sights cannot be stacked.
Future Sight should not be used competitively. It is too unwieldy to use as a main STAB, and most Pokemon will struggle to find a free moveslot for it.
Psychic is a more reliable alternative with 90 Base Power and no charge period.
Psyshock is an alternative with 80 Base Power that deals physical damage and has no charge period.
Doom Desire is a more powerful Steel-type equivalent.