When calculating probability for two standard die, 4,2 and 2,4 are treated as two separate outcomes. By that logic, why aren’t doubles treated the same way? One outcome for die A and B rolling 3,3 and another for die B and A rolling 3,3.
In: 5
Imagine the dice are actually laying out on the table: die A shows four pips and die B shows two. You could physically pick up A and turn it into a two, and physically pick up die B and turn it into a four.
Now do the same with a pair of threes: You cannot change either of them from a three to a different three. There is only one three on each die, and so there is only one actual result out of 36 potential ones where both roll a three.
**Edit:** If it helps to have a visual, [here](https://www.edcollins.com/backgammon/diceposs.gif) is an image showing every possible result to rolling two six-sided dice.
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