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<<script>>
document.getElementById("map_1").style.backgroundImage= "url(http://something.com/pics/race_" + state.active.variables["race"] + ".png)";
console.log("Javascript sucess. map_1.style.backgroundImage = " + document.getElementById("map_1").style.backgroundImage);
<</script>>
Comments
You could also try the jQuery way which seems to be the most accepted way around here.
I just saw that you said you don't want to change classes and want to confirm your div's ID is set to map_1, right? Not just it's class? I only ask because you're getting the element by its id which can make a world of difference.