In Shaw's Arms and the Man, why does Bluntschli say that the bet would rob Major Petkoff?

Bluntschli says that the bet would rob Major Petkoff because Catherine is sure to be right about the whereabouts of the major's favorite coat. So, if Major Petkoff bets against both Catherine and Bluntschli, he will be sure to lose a tidy sum of money.
In Act III, everyone is relaxing after lunch, when Major Petkoff exclaims that he would be more comfortable in his old coat. His wife, Catherine, tells him that his coat is probably hanging in the blue closet, but Major Petkoff disagrees with her. He accuses his wife of being obstinate and insists that the only items in the blue closet are two of Raina's old dressing gowns, Catherine's waterproof coat, and his own mackintosh.
Unmoved by her husband's argument, Catherine calls upon their servant girl, Nicola, to fetch the major's coat from the blue closet. In the meantime, Major Petkoff proclaims that he will bet any piece of jewelry Catherine can order at the jeweler's against a week's housekeeping money that the coat isn't in the blue closet. He also calls on Bluntschli to take up the bet, but the latter refuses. Bluntschli replies that Catherine is sure to be right about the coat and he would essentially win the bet, thus "robbing" Major Petkoff of his money. In the end, of course, it is proved that Catherine is right, and Nicola is able to retrieve the major's coat from the blue closet.