In game terms, the Ardennes offensive takes up about 2 turns, at this scale you could not replicate or define losses in any individual attack, IMVHO one of the great failings in this game. (Market-Garden = 1 turn, Op Cobra = 1 turn)
Overall US Losses
In late December German propagandists claimed that the object of the Ardennes offensive had been to cripple the attack capabilities of the Allied armies and chew up their divisions east of the Meuse. There also is considerable evidence that Model, and perhaps Rundstedt, accepted this as a reasonable tactical objective in the operations from Christmas onward. The attainment of this goal, to chew up Allied divisions and dull the cutting edge of the American armies, was achieved in only limited fashion. The attack of twenty-nine German divisions and brigades destroyed one American infantry division as a unit, badly crippled two infantry divisions, and cut one armored combat command to pieces. The total of American battle casualties reported for the period 16 December through 2 January (although these probably were incomplete returns) numbered 41,315 officers and men, of which 4,138 were known to be killed in action, 20,231 were wounded in action, and 16,946 were reported missing. During the same period the American formations in the Ardennes received 31,505 replacements, or "reinforcements" as these individual soldiers now were named. The matériel losses inflicted by German action represented only a temporary diminution in the fighting strength of a few of the American divisions and normally were replaced within a fortnight.
Interdum feror cupidine partium magnarum Europae vincendarum