Examples where one less pixel of available space changes it from 3 tiles to two.
Unscaled, 150px wide:
round(): browser-scaled down to fit in 375px wide box (17% tile size width reduction):
round(): browser-scaled up to fit in 374px wide box (26% tile size width increase):
Unscaled, 200px wide: 
round(): browser-scaled down to fit in 500px wide box (17% tile size width reduction):
round(): browser-scaled up to fit in 499px wide box (25% tile size width increase):
More distortion is created by only rounding in one direction. Shown along with very-little-distorted 'round()' also, for the same size box.
round(): browser-scaled down to fit in 447px wide box (1% tile size width reduction):
floor(): browser-scaled up to fit in 447px wide box (49% tile size width increase):
round(): browser-scaled up to fit in 302px wide box (1% tile size width increase):
ceil(): browser-scaled down to fit in 302px wide box (33% tile size width reduction):
round(): browser-scaled down to fit in 597px wide box (1% tile size width reduction):
floor(): browser-scaled up to fit in 597px wide box (49% tile size width increase):
round(): browser-scaled up to fit in 402px wide box (1% tile size width increase):
ceil(): browser-scaled down to fit in 402px wide box (33% tile size width reduction):