Amulet of regeneration
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An amulet of regeneration increases its wearer's regeneration rate by 40, greatly hastening the HP recovery rate of your character. This benefit becomes less pronounced as your max HP rises, but its effect is always substantial. When natural healing is unavailable, the amulet's effects are less impressive; deep dwarves and bloodless vampires gain no HP regeneration whatsoever from wearing it, but it does help you recover from sickness significantly faster.
However, this healing comes at a cost. Every turn that the amulet provides any HP- or sickness-recovery effect, your metabolism is increased by 3 (twice that of the average character). This metabolism increase does not apply when you are at full health and not sick, so there's no need to fear it starving you when you don't even need healing. Also, characters that have no hunger clock to speak of (mummies and lichform) can wear them without fear, enjoying the benefits at no cost.
Desirability
Sources of regeneration are generally very welcome. Reducing the time spent recovering between battles makes it less likely for new enemies to spawn on your current floor or find you while wandering, and is very welcome for players looking to maximize their score. Don't be afraid to swap it out for a needed resistance, however, if you suddenly find yourself facing down a source of mutation or paralysis.
History
The amulet of regeneration will be added in 0.16, replacing the ring of regenration.