There are 6 sides on a die. The chances to roll any given number is 1/6. For each die you add, that number is squared. Hence to roll any given number on 2 dice is 1/36.

The way I see it, your chances of survival are 35/36 on any given roll.

The fact he brings in ten times more people every time means that there are 90% more people in the room each time. True, if he rolls double 6s, 90% of all people die, but the chances that'll happen are still 1/36.