Code from Tutorial: Advanced Random Numbers (http://coronalabs.com/blog/2014/03/11/tutorial-advanced-random-numbers/)

dice.lua

math.randomseed( os.time() )

local function rollDice( dicePattern )
   -- Dice pattern 3d6+3k3
   -- First number : number of dice
   -- d : required string
   -- Second number : sides to the dice
   -- +/- : optional modifier
   -- ^/k : optional string; '^' keeps the high values, 'k' keeps the low values
   -- Third number : number of dice to keep, i.e. 4d6^3 keeps the best three numbers
   local dice = {}
   local random = math.random
   local total = 0
   -- Parse the string
   local count, sides, sign, modifier, keepHiLo, keep = string.match( dicePattern, "(%d+)[dD](%d+)([%+%-]*)(%d*)([%^k]*)(%d*)" )
   modifier = tonumber(modifier)
   keep = tonumber(keep)
   if ( modifier == nil ) then
      modifier = 0
   end
   if ( sign == "-" and modifier > 0 ) then
      modifier = modifier * -1
   end
   for i = 1, count do
      dice[i] = random( sides )
   end
   if ( keep ) then
      local function keepCompare( a, b )
         return a > b
      end
      if ( keepHiLo == "k" ) then
         table.sort( dice )
      else
         table.sort( dice, keepCompare )
      end
      for i = 1, keep do
         total = total + dice[i]
      end
   else
      for i = 1, count do
         total = total + dice[i]
      end
   end
   total = total + modifier
   return total, dice
end

local result, rolls = rollDice( "3d6" )
for i = 1, #rolls do
   print( i, rolls[i] )
end
print( result )
result, rolls = rollDice( "4d6+1^3" )
for i = 1, #rolls do
   print( i, rolls[i] )
end
print( result )