Dice probabilities (doubles, number over a certain value, etc)

Heya. I'm working on a game that uses 6-sided dice for conflict resolution. My probability class was about 12 years ago and I'm having a little trouble parsing the types of problem I'm having into the formulas I used to work with.

Here are the scenarios I'm trying to populate a spreadsheet with. I'd be grateful for any help.

1. Odds of getting higher than a [value] on N dice. I'm using: 1-(odds of not getting over that value)^(dice), but it's only giving me 66.5% chance of getting a 6 with 6 dice, and only 88.8% chance with 12 dice, which seems low.

2. Odds of getting various sets of doubles on N dice.

3. Odds of getting higher than a specific value with one result OR getting doubles of any kind

4. Odds of getting higher than [value] on N dice with two or more values.

5. Odds of getting higher than [value] on N dice with three or more values.

It occurs to me that the formulas for these might be complex enough that I'd save time by modeling the rolls a million times programmatically. I'll probably start on that and see if I get a reply here before I'm finished. :)

Essentially you have to work out all the possible totals and work out how many ways there are to make them. For a few dice, the easiest way is using a spreadsheet using brute force (and then answer the questions for each line). For more dice it's probably better to work out the combinations and how many ways there are to make them, then use the above method. For even more dice you probably need programming. When the numbers are excessive, then run simulations.