Can someone smarter than me figure out the algorithm on what it would cost (theoretically) to take a territory that has 5 armies on it with the attacker having A60% D75% and explain how they came up with that number?

On the board, My Kingdom, we're debating the benefit of taking the castle territories around the 8 thrones.

Thanks!

Well, the idea of "cost" doesn't necessarily make sense in Simulgear. On average, 75% of those 5 neutral armies will kill a unit, so your "cost" is expected to be .75 * 5 = 3.75 units (averaged over a very large number of trials). Of course, that's the average, it could (and will) be anywhere between 0 and 5.

A more useful question might be, what's my chance of defeating X units given Y attackers with Z attacker percentage? (Note you can also reframe the question, what's the chance that X defenders kill Y of my attacking units given Z defender percentage?)

Such chances are calculated as cumulative binomial probabilities, and you can use a binomial calculator (e.g. this one) to find your answer.

So, using the calculator we can see that attacking 5 units with 10 units at 60%, you have about an 83% chance of succeeding (that is, killing at least 5 units, which is all there are!). Note that the defender has about a 90% chance of killing at least 3 of your units.

If you want high certainty of taking the territory (let's say 99%), you need to attack those 5 with at least 15 units.

Hope that helps!

Wow Kjeld, your idea of 'high certainty' is high indeed.  I would say high certainty is @80-85%.

Thingol wrote:

Wow Kjeld, your idea of 'high certainty' is high indeed.  I would say high certainty is @80-85%.

I was trying to demonstrate what it takes to get a level of "I'm going to take this territory barring some utter catastrophe of dice", something akin to attacking a singleton with 7 or 8 units with versus dice, which most players take for granted (though it can and does fail occasionally).

Note that with 10 units attacking you have an 83% chance of taking the territory, and with 11 you have a 90% chance. So somewhere in that range would be the amount that most players would probably attack with to have a reasonably assured success (assuming that any additional units are better deployed elsewhere past that point).

Yeah that calculator was in the FAQ and it doesn't make sense to me.  But thanks for your replies. I kinda get the idea.