A Probability Experiment (Using Star Wars: Imperial Assault)
Recently, a few mates and I attempted to defend the galaxy against the evil Empire regime, to destroy the Empire threat, and support the Rebel uprising. We failed…but we had a lot of fun doing so.
Imperial Assault is a fantastic game. It’s just incredible. If you haven’t played it yet, then I would recommend introducing it to your gaming group. If you like miniature games then you won’t regret it. We have had hours upon hours of fun – fun I will probably explore in a few additional blogs at a later date.
What I wanted to write about here though was one aspect of the game that came up during our third mission (which, looking back, was around eight months ago). One of the players, a guy in our gaming group, was playing as Mak Eshka’rey (the Bold Renegade) and needed to roll a couple of die to pass a strength test.
In Imperial Assault, the dice are entirely bespoke to the game, and this means they have custom faces, similar (but not identical) to those in Descent. Unlike normal dice, which are restricted to six numbers, the design is such that it allows for them to tell three different things at once within the context of the game. Firstly, they tell a number of hits the player gets when they attack. Secondly, they show the modifier for ranged weapons. This is to allow for close combat and missile weapons to be used within the game. Finally, they show surges.
Surges are an interesting addition to the Imperial Assault die, as they account for special abilities a weapon can implement. These can be anything from additional damage, to an additional range modifier, to specific effects like Bleed or Cleave.
Surges are also used for attribute tests, such as the aforementioned strength. To pass one of these tests, you need to roll a number of dice for different tests, and all you need is for one die to show a surge. The number of dice you roll differs per character, providing a really interesting asymmetry within the game. Some characters get more die than others. Sounds easy right?
The die come in a series of colours, each with different probabilities and faces on them. The blue, for instance, is more range focused. The green is used for most physical tests, and the red does a lot of damage.
So, back to the point at hand, my friend (Mak Eshka’rey) had to take a test. As statistics fans, rather than rolling the dice immediately we decided to work out the odds of passing the test without having to use Diala’s special ability for rerolls. Mak Eshka’rey rolls two dice for his strength tests – a green and a blue. These have six sides each, with three surges on the green and two surges on the blue.
Discovering the Odds
What we discovered was the series for some debate (a surprising amount actually) and we found it really interesting. The die look like this (S = Surge, H = Hit, # = Distance):
So, what was the immediate impression? You can probably see – 5/12 did not seem overly positive. It seemed, to be frank, under 50%, and immediately we were a bit demoralised. We needed to easily pass the test and didn’t want to rely on luck. Then it dawned on us.
We had been calculating the two odds separately, rather than exponentially. Yes, on either one die the odds were 50% or fewer; however, strangely (and this is a fantastic quirk of mathematics) together the odds far exceeded that. It’s actually really kind of cool.
As it can be seen, by looking at the problem exponentially, that just-under-fifty-percent chance has turned into 24/36 chance, or a 2/3 chance. This is a huge increase in the odds, and kind of refreshing. Suddenly, what seems like a difficult task becomes incredibly likely.
How Does This Work?
This notion of probability was actually brought to my attention when talking about standard die. There is an old bar bet, which says: “Let’s roll two dice. If the highest number is a 1, 2, 3 or 4 then you win the bet. If the highest number is 5 or 6 then I do”. Exploring this bet reveals a lot about probability.
Once again, the instinctive decision is to say no to the above notion; however, the odds are actually in my favour.
This is simply because there are 36 ways the dice could land when rolled, all of which are equiprobable (have an equal chance of appearing) of which more than 18 will show a five or a six on average and thus leverage the bet my favour. To be precise there should be the odds of 20/36, in my favour, if we took that bet. This is what the results table looks like:
The way this works is actually very simple. As people, we naturally assume we treat the two dice as just that – as two separate entities and two different events. If we were to roll the die separately this would present the original odds; however, in rolling them together we create a single event. It is in this event the odds change to be exponential instead.
It’s kind of cool as it’s so counterintuitive.
There is a really ace video, designed by Ted Ed, which covers these probabilities and it is well worth a watch.
One again, it is amazing how mathematics can play such a large part in the games that we play. Of course, we don’t have to pay attention to the maths, but if it adds to the enjoyment of the game then: why not?
Similar Blog: Exploring Game Theory (Using Catan)
I would like to finish this blog with a shout out to my mate over at Eyres.me.uk. He ran an amazing campaign, is one hell of a gamer, and his painting is absolutely fantastic. It really made the campaign as he put so much time and effort into each one to make the Imperial Assault world come to life. I would recommend checking out some of his articles on his blog.