Is The Arena's Greatest's effect a triggered ability, and what happens if a player misses the trigger?

Ruling: Yes, The Arena's Greatest's effect is a triggered ability. If you miss the trigger (by not demonstrating awareness before it would affect the game visibly), the next opponent in turn order decides whether to resolve the trigger immediately or miss it altogether.

Sequence:

• When the battlefield flips, demonstrate awareness of the trigger (e.g., say "point for me" and tick up the score)
• If you miss the trigger in the same turn cycle, your opponent chooses whether you get the point or not
• If the trigger was missed in a previous turn, continue playing without resolving it

Nuances:

• The rule about forgetting to score points only applies to holding and conquering, not card-triggered abilities like The Arena's Greatest
• Best practice is to increment both players' scores immediately when the battlefield flips to avoid disputes
• Demonstrating awareness verbally ("point for me") before taking other actions is sufficient to avoid missing the trigger