simple markov chain

grab a fair dice. start off with a number, 0, and we define the results of rolling the dice as:
1: +1 to your existing number
2: -3 to your existing number
3: +6 to your existing number
4: +6 to your existing number
5: multiply your existing number by 2
6: do nothing to your existing number.

roll the dice 30 times.

without doing calculations:
what number has the highest chance of turning up? why do you think so? is this likely to happen in a real experiment?
what if the dice was unfair, in that it favoured the number 2 to any other number by 2:1:1:1:1:1?

i got caught up in this for about half an hour, while doing some reading on genetic variation. it's not particularly hard, and if you do it superficially, you'll be done in 3 mins tops. but the concept just seemed to linger and i found myself thinking up more and more complicated scenarios based on the simple dice-toss + number-walk. i hope it screws up your day, too.