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Consider a piece that moves as a Man, but that is not removed from the game
when captured; instead, the Immortal is placed in the owner's hand, and
can be dropped on any empty square in his first or second rank on any
future turn (instead of making a regular move).  What is the value of such
a piece?

For purposes of exchanges, one could argue the material value is zero;
meaning that compensation required for the owner to be willing to exchange
it is equal only to its positional value.  But the more interesting
question is, how much material would you be willing to sacrifice from your
starting array in order to start with an Immortal?

Obviously, this value must be at least as much as a Man, and is probably
very much greater.  Any ideas on how to estimate it, other than brute force
playtesting?

Some factors to consider:

- While it is easy to imagine an Immortal gobbling up entire armies one by
one, one should keep in mind that it is slow, and realistically probably
cannot force an exchange against most enemy pieces unless it has support.

- However, a piece is never 'defended' against an Immortal's attack, no
matter how many pieces stand ready to recapture.

- Unless I'm mistaken, a King + Immortal (or even King + Man) can force
mate against a lone King.

- The minimum material required to force an endgame mate against a player
who controls an Immortal is significantly increased.