Risk Board Game, World Domination Odds

Who has the advantage in a game of risk? The attacker or the defender ? The attacker gets an extra die, but the defender wins ties.
As it turns out, this is slightly better for the attacker, in the common 3 attacker vs 2 defender scenario. But in most of the other scenarios, the defender has the advantage.
Basically, if you're the attacker and you can't attack 3v2, 3v1, or 2v1 you will be at a disadvantage to the defender. Maybe you should still attack... but the odds won't be with you
Spreadsheet of results
docs.google.co...
Code calculating the risk odds
pastebin.com/3...
The Risk Board game is owned by Hasbro, who owns copyright to the Risk map I used in this video.

[@micahsilverman5284]

Excellent analysis! Very well spoken. Also thank you for including the spreadsheet! I'm going to turn the graphics into a handy little reference card:-)

[@mertaliozfidan3242]

See you in the future when your channel grows, I will be glad when you hit millions and I can I say "I knew it since he was 100 subscribers"

[@hubertperreault143]

Excellent video! Thank you, although, I wonder why on the table you got from the millions of simulations, for the first confrontations i.e. (2;1), (3; 1), where (num att; num def), we do not get the same results as the plots you got statistically? For example, from the middle-bottom plot shown at 2:21, 2 attackers and 1 defender should lead to a loss of 1 for the defender about 57,5% of the time (and so a win for the attacker seeing as there is only 1 defender). But the table from the simulations shows it leads to an attacker win 75,4% of the time. Any idea why your simulations does not represent the statistical values for the confrontations with 1 defender?

[@mrnoneofurbusiness7942]

the winrate of 41.7% of 1 attacker vs 1 defender is purely mathematical? or can you attack with 1 army in a specific scenario? i'm not that familiar with the game

[@xooox_1777]

It was information gathered from thousands to millions of dice rolls and comparing those dice and see who wins. it's just the average statistic that happened through-out a million dice rolls, so it should still be quite close to the actual percentage

[@mohammadjadallah9813]

Can someone please explain to me how 3v3 for attackers is a slight disadvantage for the attackers. I understand that they might lose one of their dies but isn't every battle that starts with 3v2 advantageous for the attackers slightly? So it should have a domino effect as the numbers get better on both sides??

[@zf2645]

You “ ran the simulation until either of the attacker or defender was completely wiped out”. The attacker can’t be completely wiped out, I assume you mean the attacker has one army left? And why would you run the sim with the presumption that an attacker with 1 die would attack a defender with 2 die or perhaps even 1 die? Cause you’d never make that attack in risk. It would be more informative to run your sim with the assumption that the attacker only attacks when it’s in his favour, which is anytime the attacker rolls more dice than the defender.

[@JeffreyMarciano]

No, the simulation would have been worthwhile if the decision to roll 1 die as is actually the case was incorperated