Risk Legacy Odds – Basic Combat Math with a Twist, Part 3

Risk Legacy

As a wrap-up to my basic combat math series for Risk Legacy odds (see part 1 and part 2), I’m going to looking at the expected losses per attack for each side, as well as exactly how much a bunker makes a territory harder to take.

First, without a bunker.

Expected losses If the combat consists of the following…
1A 1D 2A 1D 2A 2D 3A 1D 3A 2D
Attacker losses .5834 .4211 1.2207 .3403 .9267
Defender losses .4167 .5785 .7793 .6597 1.0733

And now, with the bunker.

Expected losses If the combat consists of the following…
1A 1D 2A 1D 2A 2D 3A 1D 3A 2D
Attacker losses .7223 .5833 1.3866 .5062 1.1132
Defender losses .2778 .4167 .6136 .4938 .8740

Now, what exactly do those numbers mean? Expected losses are a way to estimate the results of a dice roll and can be thought of as a kind of average. In this case, it represents roughly how many armies you should expect to lose given a certain number of attackers and defenders.

Of course, you can’t lose a fraction of an army. So how can you use these numbers? Let’s say that you’re clearing out some thinly-defended (1 army per territory) enemy territories with overwhelming numbers. Since your expected losses are .3403, you should expect, on average, to lose about 1 army per 3 territories you take. Just realize the dice may say otherwise.

Now, more specifically, let’s look at how much of an effect the bunker has on the expected losses.

If the combat consists of the following…
1A 1D 2A 1D 2A 2D 3A 1D 3A 2D
Attacker losses w/o bunker .5834 .4211 1.2207 .3403 .9267
Attacker losses w/ bunker .7223 .5833 1.3866 .5062 1.1132
% change 23.98% 38.52% 13.59% 48.75% 20.12%
Defender losses .4167 .5785 .7793 .6597 1.0733
Defender losses w/ bunker .2778 .4167 .6136 .4938 .8740
% change -33.33% -27.97% -21.26% -25.15% -18.57%

So what does all this mean? Your dice probably hate you. Besides that, the actual effect of the bunker is highly variable in terms of expected losses. It makes a bigger difference in times where the defender already has bad odds (3v1, 2v1) than it does anywhere else.

Admittedly, at first glance it is a bit disappointing that it has such a small effect on the most common case (3v2). However, what is more important (in my opinion, at least, and that’s why you’re reading this) is that the 3v2 case switches to be in the defender’s favor.

I look forward to seeing what else this game has to offer.

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