The first game I played, which had bullet-time, was Max Payne. Was there any game before that to have a similar feature?
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Max Payne was released in 2001, but in 1997 MDK was the first game to incorporate bullet time as a game mechanic.
Unlike in Max Payne, where bullet time was your ability to slow time temporarily and play with in it, MDK only used bullet time as a mechanism to follow sniper shots. While this too would be repeated in other games (including Max Payne) it first appeared in Shiny's classic MDK.
In 1999 Unreal tournament introduced "bubbles" which would slow time causing the bullet time effect (in the same manner as Max Payne but not at the user's direct control).
Later that year Requiem: Avenging Angel would provide for a more direct control over slowing down time.
No matter how you slice it, Max Payne was not the first game to have bullet time.
To continue the history lesson: