In the game "Settlers of Catan", there is a stack of fourteen tiles, four of which are "water", two "gold", and the other eight an arbitrary mixture of "sheep", "wheat", "ore", "brick", and "lumber".
I shuffled these tiles, and then placed the tiles to create one to four islands.
I thought about this as a loop:
1. I pulled the top tile and placed it in the first spot.
2. Then I took the new top tile and placed it on the bottom of the pile.
3. Repeat until all tiles placed.
The other players argued that my moving the top tile after every draw affected the randomness of the placement -- of the water tiles specifically -- and created a unrandom setup. They thought the usual procedure of placing the top one into the first spot, then the next tile into the second slot, and so on, would be better.
It seemed to me that my procedure was completely random and would not affect the location of the four water tiles in any way, as I had no knowledge of their location in the stack.
How do I prove to my friends that I didn't affect the outcome of the tiles other than to be completely random?