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Risk Legacy» Forums » Strategy

Subject: Attacker's chances to win rss

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I wanted to know precisely what were the chances of winning a battle in this game. The tables below do not show how much casualties you will likely have, it just shows your chances of winning in the end (but you can win with only one troop left).

I found the results helped me quite a bit when choosing if I should attack or not, but these statistics obviously don't replace the choice itself. When fighting for breaking an opponent's continent bonus, many will choose to fight against all odds.

Single fight :


Ammo shortage :


Bunker :


Fortification :


For example, this last table shows that you should outnumber the defender at least two to one when attacking a fortified area.
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Would you be able to do one where the defender has both a Fortification and a Bunker?
 
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Finally, an answer to "oh man, what are the ODDS?"

Great work!
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Hound Archon wrote:
Would you be able to do one where the defender has both a Fortification and a Bunker?

You're right, I forgot the bonuses could stack!

Here they are, the little chances to win when attacking a fortified area including a bunker (click to enlarge):
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Craig Johnson
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Nice figures - do you have them in a spreadsheet or something, as a quick check on the first couple of figures shows a possible rounding error going on here?

For example, a quick excel spreadsheet gives 1 Att vs 1 Def 41.6r as the figure, rounding to 42 rather than 41. This is the simple one, as there are only 36 possible results when both roll one die, with 15 attacker wins vs 21 defender wins, 15/36 being 0.41666etc.

Following this with 2 Att vs 1 Def means the Def has to win two battles, firstly a 2v1 then a 1v1, but that seems to come out as 75.4% for an attacker win overall (57.87% for a win in one round, plus they will win 41.6r% of the subsequent 1v1 battles). Small differences indeed but maybe these could make significant differences later on?

 
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Actually, I started by calculating only the six "simple" cases (from 1x1 to 3x2) and rounding the results down. So you're right, there are rounding errors.

In a second time, I figured it was quite easy to calculate all the other cases. I let the spreadsheet round everything except for the "100%s" which I rounded down and the "0%s" which I rounded up, to reflect that you never are totally certain of winning or losing a battle.

I'll correct the tables anyway to make them clean. These first figures give a good idea of the odds, anyway.
 
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Mickey Sheu
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Eager to try my math abilities, I decided to try generating the tables myself. The numbers are a little different because of a lack of rounding until the end, but I think the numbers generally match the OP's.

here's a link to the excel sheet, in my dropbox:

http://dl.dropbox.com/u/689353/Risk%20Probabilities.xls
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Galgor I.
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if anybody is interested i've written a python program to calculate all probabilities up to any number of armies you are interested in and which can give also probabilities of who much armies are left after a battle. But i have not compared my numbers with your tables so perhaps there are mistakes in my program.
anyhow: why is there the rule that you can defend with only one dice? It makes never sense to do so?!
 
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When I'm down to only 2 defenders left in an area, and the attacker does not have very many guys left, I sometimes only defend with one dice. Not losing both guys at once can be a big change to a battle if you get lucky.
 
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Stephen Rochelle
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WhoLikesChicken wrote:
When I'm down to only 2 defenders left in an area, and the attacker does not have very many guys left, I sometimes only defend with one dice. Not losing both guys at once can be a big change to a battle if you get lucky.
As the defender, there is never a scenario where you improve your chances of winning by choosing to roll only one die.

Sure, you might lose your last two guys in one roll. The odds of that (37% for 3v2) are less likely than that of losing those two guys in consecutive single rolls (44% for 2x 3v1). The truism holds regardless of the numbers or modifiers in play.
 
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mar hawkman
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Yeah, one of the Leader powers in Risk: Transformers was to FORCE the defender to defend with one dice. It was BRUTAL to defend against. It also made the game take a lot longer, but I digress. The point is that after a few games playing with Barricade I ALWAYS used his power to force the defender to only roll one die, Why? I won more often.
 
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phil surette
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Another way to look at this is to consider the average number of attackers and defenders are lost per roll for a 3 on 2 attack with the various modifiers:



For more details, you can look at this spreadsheet https://docs.google.com/spreadsheets/d/1y6uB6sYfPhjGdny8F_iH....

Finally, there's a graphical web app that will show you the odds of a series of attacks succeeding, including the odds for every possible outcome - e.g. what chance you have of conquering a series of territories with different scars on them, and still having x number of units left over. I describe the app at http://grownmengaming.wordpress.com/odds-in-risk-legacy/. To give you an idea of what I mean:

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Anthony Williams
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I made a Spreadsheet that does a variety of odds related to this. It also accounts for attacker mods, like enclave of the bear, or the mutants.

http://boardgamegeek.com/filepage/107896/risklegacy-detailed...
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