Single-attack Dice Odds

I have noticed there's quite a bit of resources out there dealing with RISK-like game probabilities. Some of these try to make predictions based on total army sizes (there's a much cited paper by Tan from 1998, and [url=http://www4.stat.ncsu.edu/~jaosborn/research/RISK.pdf]this comment[/url] by Osborne) - which are ultimately useless since no apt RISK player would ever auto-attack. Some others such as [url=http://riskodds.com/index.php]this "odds calculator"[/url] simply provide wrong values and do not account for "ties". I took the time to write a free/open source script which either uses fast formulaic contractions or an exhaustive lookup function to determine single-attack odds given the number of dice the defender and the attacker roll, [i]and even[/i] the number of sides on the dice! (which I think is interesting since I have always wondered whether the game could be improved by using a different number of dice faces or a different number of attacker/defender caps) [url=http://chymeric.eu/blog/2014/07/23/per-attack-risk-dice-odds/][b]Here's a tutorial article[/b][/url] about the script explaining among other things the formulae. There is also an odds table at the end showing you what kind of attacks are favourable (solely based on the number of troops, and not accounting for the strategic context - though I am also working on a tutorial which uses the odds info for strategy tips).

Isn't it much easier to just do 100.000 auto attack rolls and see how often you won? Alot of times when you start a big attack you are committed and you have to go on to the end, even if your chance at winning reduces because of initial bad dice, so I think attacking untill there is 1 army left is something a lot of ppl do. Apart from that, it is defenitely something I'd do in a 6v4 fight or something.

What you are referring to by "doing 100.000 auto attack rolls" is called a Monte Carlo simulation, and it's (in this case) computationally more intensive and less accurate than an exhaustive search of all possible outcomes - which is itself more computationally intensive than a formula. Attacking until you have 1 troop left is a very bad move. At the very least you should stop at 1 attacker (2 troops on the attacking territory), though if the opponent has 2 or more defenders, perhaps you should stop at 2 attackers (3 troops on the attacking territory) already - you can see that in the table at the end.