Shell script for rolling dice (#d#+#)

roll.sh

#! /bin/bash
if [[ $# -lt 1 ]]; then
  echo "missing argument"
  exit 1
fi
RANDOM=$$
roll=0
mod=0
while [[ $1 ]]
do
  if [[ $1 =~ ([0-9]+)d([0-9]+)\+?(\-?[0-9]+)? ]]; then
    i=0
    roll=0
    while [[ $i -lt ${BASH_REMATCH[1]} ]]
    do
      rand=$(($(($RANDOM%$((${BASH_REMATCH[2]}+1))))+1))
      roll=$(($roll+$rand))
      let i++
    done
    if [[ -z ${BASH_REMATCH[3]} ]]; then
      echo $roll
    else
      mod=$(($roll+${BASH_REMATCH[3]}))
      echo "$mod (roll: $roll)"
    fi
  else
    echo "invalid roll"
  fi
  shift
done