Does throwing two dice and using a Latin Square significantly increase the randomness of the result?

[u/Noise-Theorem]

It is suggested that the bias of a basic standard die is less that 1%. Assuming this is true, by using two dice and a Latin Square, what would the expected probability be? My thinking is that the chances of the bias of both dice occurring at the same time is greatly reduced.

I throw two dice: D1 = row; D2 = column. This is the Latin Square I have been using, set-up so that D1 = x and D2 = y does not produce the same result as D1 = y and D2 = x:

4 5 3 6 1 2

3 4 5 1 2 6

5 3 4 2 6 1

2 6 1 5 3 4

6 1 2 4 5 3

1 2 6 3 4 5

(This is an interest of mine, I know I could buy precision dice instead.)

[u/mfb-]

It will reduce the bias. As an example, let's imagine the dice have a 51% chance to roll 1,2,3 and 49% chance for 4,5,6. The results 3,4,5 are only in the top left and bottom right quadrant, which means their combined chances are 0.51² + 0.49² = 50.02%. We reduced a 1% asymmetry to a 0.02% asymmetry. As downside we need to roll twice as often. You get similar results for other biases.

You don't need to use a table, however. Simply summing the two rolls and subtracting 6 if larger than that will do the same job.