Checkless chess or prohibition chess is a chess variant where giving check is forbidden unless it is checkmate. All other rules are as in regular chess.
This is stalemate if White is to move in this variant. 1.b5+ puts the black king in check but does not deliver checkmate, so it is illegal.
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In variants where a check is considered checkmate if the only responses are cross-checks, then White checkmates with 1.Re2 or 1.Rd5, as all king moves would result in discovered check from the black bishop.
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Some variations in the rules of checkless chess exist:
The rule change of checkless chess has a profound impact on the way the game is played. In checkless chess, the king is immune to most attacks as long as it avoids being checkmated. Checks cannot be used to gain time or chase the king to an unsafe position. In addition, mating patterns are generally significantly more difficult to execute.
Another effect of this rule is that the king, immune from attack, is now itself a powerful force. The king can defend pieces by placing itself so that capturing the piece would place the king in check. The king can advance into the enemy position, creating havoc in the enemy camp as enemy pieces need to avoid moving to squares where they would put the king under check. However, such a plan may be risky since getting the king trapped in the enemy camp may subject it to an untimely checkmate.