Consider highly unbalanced variants of chess in which one player's (the player with the weaker set of pieces, the defender) goal is simply to survive as long as possible. For example, full set of pieces on the attacker's side versus lone king, or lone king and a piece or two.
Might want variants in which pawns do not promote, because once the attacker has several queens, mating quickly becomes trivial. What happens to pawns on the eighth rank? Staying a useless pawn is probably the most critical, getting in the way of the attacker's other pieces. Other possibilities: disappears immediately, or the defender can spend a move causing a pawn to disappear, or pawns not permitted to advance beyond (say) 4th rank.
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