Optimal defense in risk

Optimal defense in risk

i play a lot of risk

online, offline, 3rd party variants (conquerclub.com)

in some variants or game states of risk, we're not trying to attack but rather hold objectives

the math says this

3v1 - attacker advantage of 66% win rate
3v2 - attacker advantage of 37.2% 2-0 (for attacker), 33.6% 1-1, & 29.3% 0-2

this is also well reflected in monte carlo sims


i'll probably be able to wrap my head around it later with some more thought when i have some time, but i'm trying to figure out the ideal distribution of armies

obviously you want to have large stacks ready to go but...

let's say it's the end of your turn
you have unlimited reinforcement moves
you have enough cards for a game breaking move if you survive
your opponents do not have a trade available
so you just need to survive the next turn and they know this

how do we go about it, lets say we have 20 armies and 4 connected territories

what is the ideal distribution?

17-1-1-1 is the norm
but would 14-2-2-2 be better enough to be worth having a weaker main stack from which you begin the assault should you survive

i think 14-2-2-2 would be far better than 17-1-1-1 but i'm unsure to what extent, furthermore, while i think 5-5-5-5 is probably the best way to ensure as many of your rolls as possible are 3v2 rather than 3v1, that leaves us with a much worse position to counter attack in the event we do survive

other practical applications for this would be a situation where you hold australia and have started extending into asia having taken hong kong and mumbai

you would often see people play it with one big stack in either bangkok or jakarta and then 1s elsewhere, but that big stack is "trapped" and can't be used for offense anyway, so would it not be better to then layer the defense, which also keeps more of our armies at the borders ready to go on the assault?


i'm sure i'll re-read this after some coffee and think what i wrote is dumb, but it's helpful to put these thoughts to paper in order to better think it through

and in the meantime, it wouldn't surprise me in the slightest if one of you reading this already knew the optimal approach and could save me from needing to construct the sims myself, which will require a lot of moving pieces

also wouldn't mind general thoughts on risk

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12 December 2024 at 05:59 PM
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i love risk

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