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The rule for the English variant says "Each mobile piece must move once before it can move twice", but it should say "Each mobile piece must move once before any piece can move twice". (Then the same change should be made for twice before thrice, of course.) Also, it would be clearer if the rules common to all three variants were listed first, and then the differences listed separately (perhaps summarized in a table, even). In particular, all three have the rule that you must escape check on the first move of a series, or else you're checkmated; and that the number of moves you get on your turn is equal to the turn number.
Indeed in progressive chess the repetition rule regards the position of the pieces at the end of a turn, not at the end of a move.
The rules for English Progressive Chess (ENPR) are not correctly reflected here. Part 2 states, 'When a player gives check, he forfeits any remaining moves in that sequence. His opponent will then add one more move to this truncated count.' The first sentence is right, but the second sentence is wrong; therefore, the third sentence is irrelevant. The turn number dictates the possible number of moves. For example, if White, on the 9th turn, checks on the 6th move, it is then Black's turn with ten moves allowable. The truncation of White's 9th turn is just that, and nothing more. Also, the language in Part 3 is misleading. The opening sentence is a good rough guide, but doesn't withstand literal scrutiny. More precisely it should begin with 'In each turn' rather than 'In each sequence'. In ENPR jargon, a sequence is a series of movements with a turn whereby all mobile units have moved, making it possible for another sequence to commence in that same turn. So, in a single turn, some units may move twice while others move only once or are unmoved (immobilized). It should further be noted that a player may move to block friendly units in order to achieve second sequence moves for prominent pieces. However, third sequences and beyond are very rare.
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I've seen on an internet chess chat site a Canadian Candidate Master claim that (in at least one of the three main variants of Progressive Chess, if not all), Black has a slight advantage, if playing 1...d6 + 2...Nf6 against most White first moves,
In trying to tentatively estimate the value of the pieces in Progressive Chess (in its main variants), I'd guess that the long range pieces may be generally worth, say, one and a half times what I give them as in standard chess. Thus: P=1; N=3.49; B=5.25; R=8.25; Q=15 and the fighting value of K=4 (though naturally it cannot be traded).