I was rolling stats for a set of characters (main + backup) with my DM, and he told me I could choose between 3 sets of two rolls. One rolled by him, one rolled by another player, and one rolled by me. Him and the other player use physical dice, rolling three dice, then rerolling the lowest value twice. Myself, I roll electronic dice, and I used a 5d6d2
command.
When the three of us came up with sets of rolls, the results were very different, to the point that you could easily guess which one was mine (the only that was done using electronic dice):
DM's rolls: {14, 17, 14, 15, 15, 18} & {17, 16, 16, 16, 16, 14}
Player's rolls: {15, 17, 17, 16, 18, 17} & {17, 15, 16, 16, 18, 16}
My rolls: {7, 12, 15, 13, 16, 11} & {16, 16, 10, 14, 14, 17}
This isn't that surprising: in my experience, physical dice have a tendency to roll higher (just by comparing what I roll against them, this is far from the first time when this happens). However, we started a friendly argument regarding the statistics we were using for the rolls, and whether we were actually rolling the same/equivalent thing.
My belief is that the two different roll scenarios are equivalent, while my DM believes it's a situation similar to the three doors problem, as he calls it.
My scenario/rolls
Rolling 5 six-sided dice and taking the three largest values. The 5d6D2
roll, which using this page we can get a neat graph of the possibilities for each roll.
Example roll: {3, 2, 2, 1, 1} Result: 7
My DM's/fellow player's scenario/rolls
Rolling 3 six-sided dice, then rerolling the lowest value twice.
Example roll: Roll: {6, 4, 1} Result: 11
Reroll the 1. Roll: {4} Result: 4
Reroll either 4. Roll: {1} Result: 1
Final roll: {6, 4, 4} Result: 14
Is there a statistical distribution difference between these two scenarios?