Risk probabilities

[jedi1josh]

I mentioned on another thread that went off topic that the computer in Risk Factions seems to favor the defender more often than it should. Too many times I would have a territory of 8 men attacking a territory of just 1 man and I would lose 7 battles in a row, but I would also happen to win more often than I should if I controlled a territory with just 1 man and I was attacked by the computer's territory of 7 or 8 men. I eventually asked a Math teacher at the school where I'm employed if he could work out the probabilities for me. Here's what he came up with.

If the defender only has 1 man and the attacker has let's say 10 men and the attacker kept attacking and loosing until he was down to 3 men then stopped here's how the outcomes should be. (Even though the defender has a advantage with winning tie breakers he's at a huge disadvantage with only having one die versus the attackers 3 dice.)

For a lone defender to win a single battle against 3 dice, the odds are about 34% or 1 in 3.
For the lone defender to win two times in a row is 11.5% or 1 in 9
Three times in a row is 3.9% or 1 in 25
Four times in a row is 1.3% or 1 in 75
Five times in a row is .46% or 1 in 217
Six times in a row is .15% OR 1 in 625
Seven times in a row is .05% or 1 in 1887

So it's safe to say a defender with only 1 solider shouldn't win against a territory attacking him with 3 attackers very often, yet it happens all the time in this computerized version of the game.

[biocidej]

I'm not sure the odds are going to be quite that simple as there are other factors that could be at play (i.e. airports, extra dice, etc.), however, playing the classic Risk game I never noticed anything too out of the ordinary when I was fighting.

Also, the numbers for 5-7 are off because you can no longer roll 3 dice on rolls 5 and 6 you are rolling fewer die and on roll 7 you cannot roll at all.

1. Attacker 7: Defender 1 3 attack dice
2. Attacker 6: Defender 1 3 attack dice
3. Attacker 5: Defender 1 3 attack dice
4. Attacker 4: Defender 1 3 attack dice
5. Attacker 3: Defender 1 2 attack dice
6. Attacker 2: Defender 1 1 attack die
7. Attacker 1: Defender 1 can no longer attack

The odds are still rather low, however, not quite as bad as the number you posted. The odds for getting a single super-overkill (assuming no special rules) is about 1 in 271 so you will probably have a few instances of having a strongly defended single location before you get your 10 super overkills.

[biocidej]

Also, you can look in your stats and see the number of times each number was rolled. As long as all of the numbers are approximately the same (which I always saw that they were) than the die are coming up randomly.

[jedi1josh]

Originally Posted by biocidej

Also, the numbers for 5-7 are off because you can no longer roll 3 dice on rolls 5 and 6 you are rolling fewer die and on roll 7 you cannot roll at all.

I was basing it on a territory of 10 men, not 7 so you can roll three dice on turns 5-7, on turn 8 it would be only 2. I did it this way because I generally stop rolling if I lose all but 3 men. I chose the number 10 because it doesn't really matter what the total is as long as it's 10 or more and 10 is a nice round number to work with.

[Vastet]

It's still a bad equation. I rarely have only 1 battalion on a disputed territory. Having 3 scews the results exponentially over 1. If you're only defending with 1 then you're leaving yourself open.

I can't say the AI has raped me any more than I've raped it. Yeah, I lost 40 battalions to 5 once. But I also killed 30 with 2, so it all averages out in the end.