Initiative vs Material

1. When your pieces are far more active. If sacrificing a pawn gives all your pieces attacking scope while the opponent's pieces are passive, the initiative is worth more.
2. When the opponent's king is exposed. A pawn sacrifice that opens lines toward the king is almost always worth it.
3. When time is critical. In sharp positions, a tempo is worth more than a pawn, don't waste time capturing if it costs your attack.

1. When the position is closed or stable. Initiative matters less when there are no open lines.
2. When you can consolidate. If you can accept material and defend for a few moves to neutralise the threats, do it.
3. When the endgame is near. Initiative fades in endgames; material advantage grows.
4. When the opponent's "initiative" has no concrete threats. General activity without specific threats is not true initiative.

Before accepting or sacrificing material, ask:

1. How many tempi will this cost/gain?
2. What specific threats does the initiative create?
3. Can the defender consolidate in 3-5 moves?
4. What does the endgame look like? If the initiative creates concrete, ongoing threats that the defender cannot easily neutralise, it's worth the material. If the threats are vague or the defender can consolidate, take the material.

Kasparov and Tal were masters of sacrificing material for initiative. Karpov and Petrosian were masters of accepting material and defending. Study both styles in the legends archive. AlphaZero's games brilliantly illustrate how modern engines value initiative over material.