I am adding words in [boldface] to correct some statements made on this page:
It is not possible [in general] to achieve checkmate with king and one falcon against the enemy king. The situation is [not] akin to the inability of king to [force] mate with only two knights or only one bishop against king. However, the rook and king together of course can checkmate opponent's king. Therefore, the rook becomes generally more valuable than the falcon in the end game. It is important to approach the end game bearing in mind this relative weakness of the falcon. For example, one must have at least king, falcon, and some one other piece to have [more than] a [slim] chance for checkmate against lone king.
I am adding words in [boldface] to correct some statements made on this page:
It is not possible [in general] to achieve checkmate with king and one falcon against the enemy king. The situation is [not] akin to the inability of king to [force] mate with only two knights or only one bishop against king. However, the rook and king together of course can checkmate opponent's king. Therefore, the rook becomes generally more valuable than the falcon in the end game. It is important to approach the end game bearing in mind this relative weakness of the falcon. For example, one must have at least king, falcon, and some one other piece to have [more than] a [slim] chance for checkmate against lone king.