Can someone direct me to a site that can compute, or maybe just generates a table of Risk dice odds (e.g., for 3v2, 3v1, 2v2, etc..) with any number sided-dice combination (i.e., A = 5-sided, D = 7-sided)? I can't find one.

If one doesn't exist wouldn't it be cool to throw one onto a WG page, available to designers and players alike ..with a graphic inyourface?  Plug in a combination and the stats come up along with a bar-graph and/or a pie-chart, etc..

..a Premium Membership perk?

That would be cool, and it's been discussed before (I forget which thread) at some length.

However, in the meantime, I've found this simulator to be pretty useful and accurate, though it can occasionally crash the browser: http://prestopnik.com/warfish/rollSimulator/

M57 wrote:

Can someone direct me to a site that can compute, or maybe just generates a table of Risk dice odds (e.g., for 3v2, 3v1, 2v2, etc..) with any number sided-dice combination (i.e., A = 5-sided, D = 7-sided)? I can't find one.

If one doesn't exist wouldn't it be cool to throw one onto a WG page, available to designers and players alike ..with a graphic inyourface?  Plug in a combination and the stats come up along with a bar-graph and/or a pie-chart, etc..

..a Premium Membership perk?

 

Formulas submitted to tom. People use simulators, I don't know if those are home-cooked or online. Kjeld used something, but it calculated odds in the large and could be misleading for low unit games. There was also debate whether having conquer and capture odds would strip too much away from the game. But I think it would be a nice perk for designers.

Kjeld, Thanks -- that page is very helpful

Stripped from my WF interface script (used for the luck table) and put up as a separate script:

http://userscripts.org/scripts/show/67652

Requires FF and GM. Script will only run on the following page:

http://www.this-page-intentionally-left-blank.org/blankpage.html

NAN errors will not be fixed for 0-sided attacking or defending dice. I believe WG now allows this but you know the odds for those. Too lazy to go back and remove 0s as a drop-down option.

Algorithm used is deterministic and not a simulation. Results are expressed in table of attacking losses.

BTW, considering the number of math gurus lurking on WG I imagine saying "I know it's correct" is probably not enough. I could go into detail how this was achieved if you want a more formal proof.

Mongrel I'm interested in what you came up with to see whether you took the same approach.

To further clarify, the results are percentages, and of course are not valid for a small number of attacks. Since we're dealing with probability events I'm not sure any system can accurately predict the outcome of a single roll, much like you can't predict the result of a single coin toss other than to say 'heads or tails'.

Let's see.

My approach was nothing more than hard counting an bookkeeping.

It's best to do an example. Let's try to find the odds that in a 3v2 attack, with 6 sided dice, the attacker loses 2. The ideas outlined below are adapted for the other cases.

Step 0: The dice are 6 sided, so there are (6*6*6)*(6*6) = 7776 total 3-dice 2-dice
rolls possible. This will be the denominator.

Instead of counting triples of attacker rolls and pairs of defense dice one at a time, I instead look at triples of ordered rolls and pairs of ordered rolls, staying mindful that the number of triples that belong to an ordering changes with the number of distinct digits (In fact it was this difficulty that made me do it this way).

there are 6 ways of rolling an a b c type 1
3 ways of rolling an d d e type 2
1 way to roll an f f f. type 3

We've partitioned the space of attacker rolls into 3 types of ordered triples, so I will count over the three types taking into account the multiplicities.

So far,

Number of ways defense wins 2 = 6*(Number of ways defense wins 2, Attacker rolled a type 1) + 3*(Number of ways defense wins 2, Attack rolls a type 2) + 1*(Number of ways defense wins 2, Attacker rolls a type 3).

And then I continued on...

Sorry got some other pressing business.

Mongrel, you kill me..
You always post these fascinating tidbits, then.. Wait, the phone's ringing..

That was formatted WAY better when I was typing.

Sorry, still don't have time to elaborate.