The first part you can work out using binomial distribution. I posted a couple of links in another thread earlier. probability of DNA sequence errors
I'm not sure I understand the second part. This is the confusing part:
I'd guess you mean you win $1,$3 or $5 on those rolls and lose $2,$4 or $6 on those rolls, not sure though.If it lands on an odd number, you win an amount equal to that number and vice versa for odd number.
Assuming I'm right, the only precise ways of calculating this I can think of you really wouldn't want to do by hand. The easiest way I can think of will get you a decent estimate though.
If you calculate the average winning amount and the average losing amount ($3 and $4 respectively), you can calculate how many wins would be required on average to be that amount up. So for example wanting to be $20 up after 1000 trials would give the formulas:
Where x is the number of wins and y is the number of losses.
This gives the answers:
Now you can round x down to 574 and use it as the successful number of trials in the binomial distribution formula and get an estimate.
Hope this helps.