Probabilities, odds, expected value, etc

[barrycarter]

I'm sure someone's already worked out the probabilities of various
dice combinations (3-vs-2, 2-vs-2, 3-vs-1, etc), simplified the
mathematical graphs that constitute the maps, run expected value
calculations (how many troops do you need, on average, to assault a
region w n troops), done some probability distribution stuff, etc.

Where can I find this? If no one's done it, I'd be happy to do it myself.

[SirSebstar]

something like this?

Odds of winning various dice combinations in Risk

Attacker: one die; Defender: one die:

Attacker wins 15 out of 36 (41.67 %)
Defender wins 21 out of 36 (58.33 %)


Attacker: two dice; Defender: one die:

Attacker wins 125 out of 216 (57.87 %)
Defender wins 91 out of 216 (42.13 %)


Attacker: three dice; Defender: one die:

Attacker wins 855 out of 1296 (65.97 %)
Defender wins 441 out of 1296 (34.03 %)


Attacker: one die; Defender: two dice:

Attacker wins 55 out of 216 (25.46 %)
Defender wins 161 out of 216 (74.54 %)


Attacker: two dice; Defender: two dice:

Attacker wins both: 295 out of 1296 (22.76 %)
Defender wins both: 581 out of 1296 (44.83 %)
Both win one: 420 out of 1296 (32.41 %)


Attacker: three dice; Defender: two dice:

Attacker wins both: 2890 out of 7776 (37.17 %)
Defender wins both: 2275 out of 7776 (29.26 %)
Both win one: 2611 out of 7776 (33.58 %)

[barrycarter]

Yup! Also found it at competitor site: http://www.strategygamenetwork.com/statistics.html#q9

But more can be done: eg, digraphs of maps, expected gain/loss, and so on? Sort of a mathematical study of CC?

[sherkaner]

There is a plugin that can calculate some things for you, viewtopic.php?f=527&t=83451&start=0

I never tried it actually, if I feel the need I'll calculate things through at http://gamesbyemail.com/Games/Gambit/BattleOdds

digraph: A map is basically a directed graph, and some can get quite complicated.

[chipv]

Try it! It comes up with same numbers, is faster, more convenient, and does multiple calcs in one go.

[barrycarter]

It would be cool to use networkx or something to analyze the maps.

Are the maps available in "raw form" (not GIF) anywhere? Like nodes and edges?

[SirSebstar]

xml??
viewtopic.php?f=57&t=123370&p=2711926#p2711926

viewtopic.php?f=59&t=73696 see also

[sherkaner]

It's not XML any more, it's in the javascript now (json), but basically the variable map.countries is what you're looking for, every country has a list of id's of contries it borders and a list of countries it bombards. I guess you can transform that into the format you want.

[barrycarter]

Excellent, thanks! I assume that's the map you see when you're playing a game. The map browser just shows static GIFs, yes?

[sherkaner]

Excellent, thanks! I assume that's the map you see when you're playing a game. The map browser just shows static GIFs, yes?

Yeah, correct. That variable only exists on game pages.