geometry - Putting the pips on a d6

Using a blank cube and a bunch of circular stickers, an average person constructs a d6. A d6 is also known as a six-sided die, or sometimes, a dice.

For the purpose of this puzzle, the average person

• knows the shape of the correct pip pattern for each number (as in "a 3 is three pips on a diagonal line" and "a 5 is like a 4 but with a pip in the middle")


• knows that the sum of two opposing sides is always 7


• doesn't know any more specifics on dice manufacturers' conventions (and doesn't have a reference handy)


• given options, chooses one randomly, as long as the things he knows will apply in the resulting die.

What is the probability for the resulting pip pattern being the exact same one that official casino dice always use? (Seen in both of the dice in the image below)

(There's no need to account for any minor inaccuracies in the pip positions, we are only interested in the overall pattern being the same.)

Answer

I make it

1 in 16.
There are two possible orientations of the Six and the One - Six horizontal and Six vertical - the One is symmetrical about all axes.

There are also two possible orientations of the Five and the Two - Two Up left to right, and Two down left to right - the Five is symmetrical about both axes.
There are also two possible orientations of the Four and the Three - Three Up left to right, and Three down left to right - the Four is symmetrical about both axes.
Finally there are two possible positions for the numbers around the middle faces of the cube - 5 4 2 3 or 5 3 2 4 (its mirror).
2 x 2 x 2 x 2 = 16.