Restrictions on Being Captured

How much is a piece worth that can't be captured?

Of course, if the piece can capture and has reasonable powers of mobility and capture, it's worth your whole army, and more, right?

Imagine a game where White has only the King and an uncapturable Knight on g1. It's pretty obvious that Black can win. Gradually give White more material, and you discover that it's probably impossible to get an even game because either White wins by material advantage if he can defend his King long enough, or Black wins quickly by checkmate. See Alice's Army.

Or consider a piece called the Nemesis; it moves like a King, but only towards the enemy King, it may not be captured, but it may not capture anything except the enemy King; a highly interesting and romantic piece. (I got this piece from H.J.R. Murray's history, but I may remember some specific rules incorrectly.) This uncapturable piece may not be valuable in a conventional sense, but its importance in a game far outweighs its value.

Or consider the Bishop in FIDE chess. The Bishop at f1 can never be captured by the enemy Bishop at f8. Does this have any effect on its value?

Finally, what about an uncapturable piece that cannot capture? Its value would be only to get in the enemy's way and block his pieces. With enough mobility, would this piece be worth a Knight?

For a capturable piece that cannot capture, see The Black Ghost.

What about an uncapturable Ghost? Is it worth a Knight because it blocks the enemy pieces so well? Is there a limit to how much blocking you can use, so that one iron ghost is worth a Knight, but seven iron ghosts are worth less than seven Knights (or their equivalent, for example two Knights, two Bishops, and two Rooks)? (Actually, if you have 6 or more Iron Ghosts, you can easily draw against the FIDE-chess army.).

I think that an Iron Ghost is worth five or ten times as much as a capturable Ghost. This is just a chessmaster's feel for the value after a small amount of experimentation: Ghost equals half a Pawn, Iron Ghost equals a Knight or Rook, either estimate could be very wrong.

If we consider a piece that can teleport anywhere and capture anywhere, well of course it's checkmate. But the theoretical mobility is 63.0, as opposed to the Knight's 5.25; making it worth twelve Knights, plus a bonus for the forking power of moving in so many different directions, plus a bonus for having long-distance moves, and so on.

The Ghost, on the other hand, has a mobility of only 44 or so (because it can't capture, it can't move to any occupied squares). This is still as much as 8.4 Knights. Its actual value is only 0.02 of its mobility; the value of an Iron Ghost is 0.12 of its mobility.

If we consider a piece that can teleport anywhere and capture anywhere, but isn't allowed to capture the enemy King (and therefore cannot ever give check or mate), its mobility is 63.0, and of course it's worth more than a Queen. Let's call it a Ravager, since it's easier to discuss it if it has a name.

Against the FIDE-chess army, the Ravager can capture two Rooks at the start of the game, but then all the enemy pieces will be defended, and unless the Ravager has some other pieces on its side to help it, it is an easy win for the FIDE army.

Against the Remarkable Rookies, the Ravager is really pitiful. Everything except the c-Pawn is defended at the start of the game, and the Ravager needs lots of help.

The Ravager has as much mobility as twelve Knights, and twelve Knights (reminds me of Shakespeare) are equal in value to a Queen, two Rooks, two Knights, two Bishops, and five Pawns; pretty much the whole army! However, its capturing power is lessened by its inability to attack the King, and its value is greatly lessended by the levelling effect (it can't afford to capture a defended piece).

In order to win, the Ravager needs enough of an army helping it so that, first of all many enemy pieces can be traded off, and after that, it will be hard for the opposition to keep everything defended. If we subtract the size of that army from the size of a normal army, we have the Ravager's practical value.

It would take a lot of games to get the right answer, but I suspect that the Ravager's practical value is not much more than a Queen and a Rook, plus whatever undefended stuff it can capture in the opening position.

Remember, its inability to check means that it fares poorly in the simple Pawnless endgames; the Pawnless endgame of King plus Ravager versus King plus two Rooks is an easy win for the Rooks, and even a pair of R4 or a pair of WD might beat the lonesome Ravager.

This subject is really unfinished, but I have to drop it in order to get on to the next section.

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