First, the little business of the War. One of Joe's "guys," Joe Bascopolous, has wound up dead, but unlucky Joe is luck for his boss, Joe—Bascopolous was 4F, and Adams bets Zepp for his draft card. Adams wins, and for the rest of the movie he'll pass himself off as Joe Bascopolous, allowing him to put his second coup in place.
To get the dice rolling on his gambling ship idea, Adams/Bascopolous approaches a local war relief organization (headed by Gladys Cooper) to set up a "charity" casino to fund a relief ship for the European theater. Adams charms the head of the group, but gets a stink-eye reception from her second, a socialite Dorothy Bryant (Laraine Day), but Adams manages to win her over, as well.
What is great about the movie is its danger. During the middle of a war, the movie dares to have a character so selfish and downright greedy that he is willing to purloin charitable dollars for a relief effort—he might be more sympathetic if he was just stealing candy from babies. The screenplay is credited to Adrian Scott, but to perform this tightrope act five other writers contributed to the script—probably just to keep the lead actor from being so hissably evil. Sure, he's a charmer, but if he carries out the plan, he's a snake and so much of one, you'd suspect even Cary Grant couldn't pull it off.
Fortunately, there's enough contrivance of plot that the character has a bit of a change of heart (it's 1943, after all, and nobody was ready for something along the lines of the cynical The Third Man—that would be in 1949—yet), apart from the fact that another character actually does want to steal the money, setting up Adams as his antagonist. But, the character's actions are close to his gambling instincts and so the transition is not so much of a stretch.
But, the title is what made me want to see this. Back when I was a youngster, there was a replacement television series on CBS called "Mr. Lucky," developed by Blake Edwards in the same spartan style—the production company was called Spartan Productions—as his hit series "Peter Gunn." "Lucky" told the story of a gambler who, in the series pilot episode, was run out of favor of the Latin American country that tolerated his gambling ship, "The Fortuna," from making its trade off its shores. "Lucky" had to come to America...or in international waters off-shore of America...in order to run his ship and partake in the many adventures that the operation caused him to cross paths with. The series was fun (at least to the four year old me) until sponsor interference forced the gambling theme to be dispensed with and "The Fortuna" became a floating restaurant. The series folded soon after that. The series isn't based on the film although it shared the same title...and its source, the original Milton Holmes story.