Depletion hit dice

Several OSR style role playing games employ usage (or depletion) dice to track inventory items like torches and arrows.  It's not really simpler than actually tracking individual items, but it can be more fun.

How the mechanic works:  You assign a die type (d4, d6, d8, d10, d12, d20) to the supply level of the item.  After you use some in an event (like arrows in a combat encounter), you roll the die.  On a 1-2, the die size drops one level to show depletion of that resource.  When a d4 reduces, you're out of whatever it was tracking.  This could also be used for item durability.

My new take on this idea:  Use depletion dice for hit points.

A minor hit reduces on a 1, average on 1-2, major on 1-3.  

Reduction from a d4 causes unconsciousness or death.

Level        1   2    3    4    5      6      7      8      9    10

Fighter   d4  d6  d6  d8  d8  d10  d10  d12  d12  d20

Cleric     d4  d4  d6  d6  d6    d8    d8    d8  d10  d10

Thief      d4  d4  d6  d6  d6    d8    d8    d8  d10  d10

Wizard   d4  d4  d4  d6  d6    d6    d6    d8   d8     d8