As straight as a die
This is an odd simile when one considers that the die here is the singular of dice - hardly objects that appear straight. It makes more sense when we realize that straight means correct and true, rather than 'as the crow flies'.
The phrase originated as 'as smooth as a die', no doubt referring to the smoothness of the bone that dice were made from. This dates back to at least the 16th century; for example, Jehan Palsgrave's Lesclarcissement de la langue françoyse, 1530:
"Make this borde as smothe as a dyce"
It migrated to 'as true as a die' in the 18th century, as found in John Gay's Songs & Ball., New Song on New Similies, 1732:
"You'll know me truer than a die."
By the 19th century it had become as we know it now - 'as straight as a die'. The first known record of that form comes from the USA, in The Janesville Gazette, April 1871:
"I'm a racing man and up to a thing or two: but am as straight as a die for honesty."
Despite their reputation for smooth/true/straightness, dice weren't always straight. Modern dice are now almost always made so that the opposite faces add up to seven and of a material that is of even density throughout. Some earlier 'crooked' dice (or as they would then have been called, dies) were weighted to favour particular numbers or may have had more than one face that showed the same number.
See also - the die has been cast.
See other 'as x as y similes'.