RvW, I specified standard kill rates.
As for not being greater, that is also assumed.

I make my statements giving sufficient credit to my audience to make the most basic of assumptions. Apparently I should change that for your sake...

If 100% goes over the number of attackers, slightly lower settings (in this case as low as 67%) will still go over the number of attackers (your formula, using 8 attackers, 75% luck): "8 * 0.60 * (1 + 0.75) = 8.4". However, as I showed on the previous page, the maximum is actually 7.

I don't so much mind implicitly capping at the number of armies, my problem was that it's a clear sign your formula must be wrong. Same thing with assuming standard kill rates: if it doesn't work for non-standard kill rates, it's actually rather unlikely to work for standard kill rates.

Correct formula:

    Killrate + Luck * ( 1 - Killrate )

In light of your statement quoted below I'll forego explaining the colour-coding.

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I make my statements giving sufficient credit to my audience to make the most basic of assumptions. Apparently I should change that for your sake...

Before typing such a statement, you might want to double-check being right yourself. Then, after making sure you indeed are, you should still phrase it more politely.

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To your credit, your formula for minimum number of armies killed:

    ( 1 - Luck ) * Killrate

does seem to check out.

Ska, although your settings and requirements will eliminate a good number of players, I don't think that they are too high. That is, unless you are looking for real time games? Multi-day it would take about 6-12 hours to fill a large FFA (9+ players) with similar settings to that. A 2v2 or 3v3 game would probably fill up in a couple of hours, maybe as little as 30 minutes. For a real time game, I can imagine that being a problem, and you'd be limited to playing during a major country's primetime (8pm EST perhaps?).

Your settings are absolutely not the problem here, as 16% luck and such are by far the most preferred. Many people go so far as to seek out member created games specifically for the lower luck settings. Your requirements are the reason that it takes longer to fill games, but that's due to the fact that most people who play do not win too many games (especially in each of three different categories at the same time) and quite a few get booted rather than surrender (again, especially true for real time games). For every person with a 60% win rate, there's one or more people with 40%. A HHH has enough games played and won to reduce 100 people to below 45% win rate.

I think the easiest thing you can do to get more people in your games would be to either invite them straight up, or to lower the number of games required to 100 or something. Personally, I end up inviting people to my games anymore, to avoid the lottery.

I make my statements giving sufficient credit to my audience to make the most basic of assumptions. Apparently I should change that for your sake...

Richard, RvW is obviously an engineer and therefore will never make any assumptions about anything ever. I always give credit to articulate people that they can see patterns of behavior and make the most basic of adjustments based on that. Apparently, I should change that for your sake...

JRuss,
If I am not mistaken, RvW is a HS student in the Netherlands (correct me if I am wrong)

Ironically, it is I who is the engineer. We constantly are making assumptions and only a bad engineer refuses to do so.

University student actually, doing a computer science studies. I did my first year in a combined mathematics and computer science programme though and in my university computer science branched of from mathematics (not electrical engineering, as in most other universities). Also, I simply happen to like mathematics. So if my posts seem a little math-heavy, that might explain it.

Assumptions are okay, but subconscious assumptions (or misunderstandings about which assumptions were made) can cause all kinds of trouble, don't you agree? (Famous example: "this value represents a number of centimetres" vs. "this value represents a number of inches" on a particular Mars probe...)

ps. Give me half a year or so and I'll be an engineer too. ;)