Being alert, though not necessarily, usually indicates, perhaps subconsciously taken as, alertness to present. Say I am playing a game and being alert to what might go wrong in the coming moves. Is there a word specifically stressing such state of mind?
I don't think words like clairvoyant or prescient quite do it - they imply more certainty in my mind. Foresightful might capture the sense better though.
It sounds like anticipate
: to think of (something that will or might happen in the future)
The adjectival form is anticipatory
Premonition or Precognition would fit.
Premonition is a feeling of anticipation of or anxiety over a future event; presentiment - Example : He had a vague premonition of danger.
Precognition is the knowledge of a future event or situation, especially when this comes from a direct message to the mind, such as in a dream or by extrasensory means, rather than by reason
Also Foreknowledge (awareness of something before it happens or exists).
Say I am playing a game and being alert to what might go wrong in the coming moves.
You are on the ball.
Alert and efficient or effective: If you don't get on the ball, you'll be fired.
Indicating intelligence or ability: The tests show your students don't have much on the ball. The new manager has a lot on the ball.