All help compiled here
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cbt711 wrote:
The Basics and first reads should be the following:

The essence of a winning move and a bit of math. - Matty

All I know - Lionheart (Long, but very good).

First turn tactics - Vexer

Don't be desparate - Matty (and a lot of input from the community)

Some very detailed guides:
Deathmatch:
Deathmatch strategies
(read before capitals, especially for the math)

Capitals:
Captials strats, basic and advanced.

Team games:
Compiled by Beta from a ton of players

Same time games:
Why sametime is the best game type
Same time tips and tricks

Other FAQ:
What to do when heads up?
The extensive heads up (1v.1) guide and strats by TheChymera (links seem to be dead).

The mental game aspect - k_w_cheng (For advanced players, but also very good).

How to deal with bad luck / bad dice

What do you do when it's down to 3 players? How to end stalemates specifically?

Final thoughts: Practice on Turbo Risk if you're new.
When in doubt, listen to Vexer.

When REALLY in doubt, check the calculator (thanks to matty for linking me this)
Simple calculator
Advanced calculator (Note the (One less than in territory) for the attacker)
Fendi wrote:
I made this "sticky". Thank you cbt711 for finding those topics and gathering them all in one place.
elysium5 wrote:
Very helpful to have all the links here. Thank you.
Mike Donovan : How'd someone like that get to be your leader anyway?

Martin : Charisma. Circumstances, promises... Not enough of us spoke out to question him until it was too late. It happens on your planet, doesn't it?
TheChymera wrote:
The http://riskodds.com/ link is broken. Also, back when it was up I tried to double-check the results, and they weren't always correct.

For a basic overview of odds (broken down to the single-attack level) I would recommend the table at the end of my RISK odds article (also copied on wikipedia) - and for compound odds, I would recommend this research paper.