Some way to close off the double-slow-digestion loophole by which you can survive indefinitely without food, by abusing the fact that ring hunger is counted on certain different turns for the left and right hand. Suggestions include:

• Ring (and amulet) hunger is always counted on every 20th turn. This prevents the slow digestion trick, but makes it somewhat easier to avoid ring hunger from most other rings (though not significantly harder).
• As above, but the hunger is offset by some random phase, determined by a hidden value that is constant in your game, such as ubirthday.
• As above, but the random phase is different every 20 turns (e.g. by deterministic hashing of turns/20). Effectively, one turn in every 20-turn chunk will cause ring hunger, but it’s not possible to figure out which.
• Have a random 1/20 chance of each ring causing hunger on every turn.