How can perpetual check draw?

Perpetual check used to be listed as one cause for draw - but dropped, sometime on 1960s.

On grounds that perpetual check would eventually cause draw under some different rule - either threefold repetition or no progress in 50 moves.

How?

Threefold repetition, sure.

But 50 moves?

Since only 2 repetitions can appear (3rd of any position would draw under that rule), there must be at least 25 distinct positions for perpetual check, in order to draw under 50 move rule without threefold repetition.

Is there any known perpetual check which did chase through 25 different positions without giving a chance to escape check?

Sometimes it's possible. I don't have a game in mind, but this a common enough pattern, the king can't come up the board.

In a real game the other pieces are stuck behind pawns and such. Either giving mate if they have a free move, or white is up a lot of material so the queen keeps checking.

1 . . . Qb3 and the game is over from there. The queen stays a knight's move away from the white king--never giving check--and the king moves up the board. Why on earth would the queen keep checking?

It's the geometric pattern I'm showing, not the position itself. Read the two sentences below the diagram.

Not all perpetual checks happen on the same few squares, sometimes the king is confined to an area. Sometimes the area can be large.

Here's something similar to a casual game I had. If black a bit cheeky (or by accident), he can let the white king can visit most of the board, but it will never escape the checks if black plays well.

The reason for removing "Perpetual Check" from the list of draws is because Perpetual Check is merely a subset of repetition.  Three-Fold Repetition may take more than 5 moves to execute.  Three-Fold Repetition could also occur via a series of "non-checks", and so Three-Fold Repetition covers more than Perpetual Check, but all Perpetual Checks will eventually reach 3-fold repetition if all other items, like 50 moves, were removed.  There is only a finite number of positions in chess.

Here's an example of a position where White can force perpetual check, but it could take more than the 5 moves used in the "back and forth" scenario.  In the diagram below, it could take as long as 10 moves to get 3-fold repetition (1.Ra6+ and White continutes to check the Black King as the Black King goes Ka8-b8-c8-d8-e8-d8-c8-b8-a8-b8 - the Third case of Rb6+ by White is 3-fold repetition as all 3 cases involve the same position with the same player to move (Black) with Black having the same legal options.

Remember too that 3-fold repetition is not an automatic draw, it must be claimed. So in the unlikely event that the game proceeds with a series of "back and forth" moves but neither player claims the draw due to 3-fold rep, it is perfectly possible that the game will produce 50 moves without capture or pawn move.

The two dumb players are then faced with the option of being able to claim a draw by either rule.

Or, in a FIDE event, they can continue another 25 moves and have the Arbiter intervene.

That rule and the 5 move repetition have been adopted by the USCF.

I didn't know that, thank you. Also interesting to note that the 5-fold rep rule needs the position to show 5 consecutive times.