Bingo!

That looks exactly like the game I'm thinking of, but it was not named that. What I played was in one of those books that came with checkers and had different board-game printed on each page, and I'm guessing "Asalto" is trademarked or something.

The Book of Classic Board Games called it "The Dalmatian Pirates and the Volga Bulgars."

https://boardgamegeek.com/image/926606/the-book-of-classic-b...

That image looks exactly like what I remember; thanks!