Flow state between boredom and frustration
Mihaly Csikszentmihalyi's flow theory states that engagement peaks when challenge is slightly above current skill. Below the flow channel, the player is bored. Above it, frustrated. A well-designed difficulty curve threads this needle, gradually raising challenge as the player's skill increases. Dark Souls does this: early enemies teach you spacing and timing, then mid-game bosses demand precision and pattern recognition, then endgame challenges require both. If the curve is too flat (easy from start to finish), players check out at hour five. If it spikes too hard (tutorial is trivial, then boss two-shots you), frustration kills engagement.
Adaptive difficulty and rubber-band scaling
Some games dynamically scale difficulty based on player performance. If you are stomping every encounter, the game spawns tougher enemies or multiplies damage. If you are dying repeatedly, it reduces pressure. The upside is that every player gets their own flow channel. The downside is that players may never feel truly dominant (the game denies epic moments), or conversely, never feel truly weak (the game hides the consequence of failure). The strongest difficulty curves are hand-tuned static progressions, not adaptive systems.