[OC] The battle probabilities for winning a fight in the game of Risk and the expected loss

Posted by Joghurt_06

9 comments
  1. Yes, this is a rempost because my last post didn’t clarify what this actually is (sorry about that)
    I made this using Google Sheets functions for a project I’m working on.

    The red numbers are the size of the attacking army and the blue numbers are the size of the defending army.

    For anyone wondering why the odds increase when both armies are the same size:

    The attacker has a slight advantage in a 3v2 (each unit defeats about 1.17 enemy units), which results in an almost guaranteed win for large army sizes (200v200) and a 50% chance for armies 17% larger (200v234).

  2. Interesting stuff. I have always figured that the attacker’s 3 to 2 dice advantage is much more meaningful than the fact that the defender can win ties, and that seems to be the case for a 5v5 and beyond. Interesting that the advantage is not quite there for 4v4, though.

  3. Winning should be colored red and losing should be blue, just to keep it accurate.

  4. I didn’t know 100% was possible because it’s a dice roll. I thought that there was always a chance (albeit small) that you can win a dice roll even with 1 unit.

  5. Why are the numbers different depending on which table I look at? Are the titles wrong?

  6. If you used odds instead of probabilities you could avoid the 0s and 100s. Though you would probably have to use exponential notation to fit the bigger numbers into the table.

  7. How is 2v1 75% chance for a win for the attacker? Isn’t it a 1v1 dice roll and the defender wins a tie? Am I reading the chart wrong?

Comments are closed.