Attacking - Gain in War and Offense to Send

[RiffArt]

Thanks for that pathetic sheep, you've given me a couple of ideas actually. I'm not a programmer so hadn't even considered a random function would provide a normal distribution but it looks like there are lots of distributions it's possible to use.

[pathetic sheep]

Pretty sure that bishop has stated that the Magic number is 104.04 on a hit not to fail.

that is to never fail. Like saying a die cannot roll less than 1. The uncertainty is whether a 104.0 fails is like rolling a double 1 on two dice or is it more like rolling 20 ones on 20 dice. And if you send 97% is that like a fail when rolling less than 7 on two dice or like totaling less than 70 on 20 dice. How does sending 90% compare with playing lottery?

[Verminator]

I send 101% offense every single time and have never failed. Over years and years. You guys are being duped with this 104% nonsense.

[noobium]

cue humiliating bounce when someone sends 101%

[Bishop]

I send 101% offense every single time and have never failed. Over years and years. You guys are being duped with this 104% nonsense.

That means nothing. Learn to statistics please.

[Clampy]

The formulae for nw effect on gains is about 25 ages old, and I haven't played much since then so it could have changed. Having said that, there are a lot of factors involved so forgive me if I am a little skeptical if someone suggests it's off from only anecdotal evidence.

You have a pretty high success rate if you send 101%, I used to send 100%, but it's still less than 100%. Personally I can spare sending another 4% if it means I'm not going to bounce and then get chained with no incoming acres.

For those getting 0-4 acres trad marches, can I ask roughly how much land the targets had? Less than 200?

[Bishop]

Formula is largly unchanged, except we modified min gains down from 3% a while back.

[JackRabbitSlim]

The magic number is 104.04% of the targets Defense. That is for a 100% win. As you lower that magic number, of course the % of times that you will win goes down.

But some people(101% man) seem to forget that even if you have only a 1% chance of winning, you can still win 10 times in a row. It is just well beyond realistic probability that you would.

So the statement about a 100% win needing 104.04% of the targets defense is totally correct. But if you use some common sense, you are going to know that anything over 100% of the targets Defense is going to win a majority of the time.

BUT at 104.039% you could still FAIL 10 times in a row. It is just way beyond realistic probability that you would.

Some of us are not math wizards and have trouble with probabilities. That is what most of the conversations above this post seems to be about. So if you are not a math wizard and you don't want to deal with any kind of Calculus, just send 104.04% of the targets Defense every time you make an attack. You will NEVER fail.

[Gidoza]

Allright, so the converse of a guaranteed success would then by 95.97% for a guaranteed fail with maximum kills?

[Ethan]

104.036269430053%, but the in game calc only goes to 2 decimal places. And normally this is all of a single unit, at most, difference.
If you are super worried use 104.05%, because maybe 104.035 is rounding up to 104.04 and is .01 too low... but you are much more likely to bounce because of a sol block or something. (Or bad intel)

The guaranteed fail level is all the way down at .97*.965/1.035 = 90.4396%.
And we can reasonably assume 97% is very close to 50/50. When I've tried to work out the whole curve assuming uniform distributions it has always come out wrong for some reason though - which is kinda depressing as I was in fact a math major and took grad level probability about 10 years ago... but continuous stuff drives me bonkers. (Part of the problem might have been insisting 97% precisely equals 50/50... which I'm not sure is true. It must be close... but it might not be exact.)

[RiffArt]

When I've tried to work out the whole curve assuming uniform distributions it has always come out wrong for some reason though

How are you checking it?

Assuming the random factor is distributed uniformly for both attacker and defender in [-3.5%, 3.5%] it's quite simple to work out. What I don't know is whether that assumption is correct. Given that so many people tell me "I've never failed at 102%" (~86% success rate) or similar, I must conclude that either the distribution isn't uniform, or else all of these people are unreliable.

Part of the problem might have been insisting 97% precisely equals 50/50... which I'm not sure is true. It must be close... but it might not be exact.

Assuming the random factors for both attacker and defender have the same distribution, then it must be exactly 50% (ignoring ties anyway).

[pathetic sheep]

Allright, so the converse of a guaranteed success would then by 95.97% for a guaranteed fail with maximum kills?

No.

Random factor is +-3.5% for offense and defense. Off/def ratio needed to win is 0.97. Thus in the worst case (-3.5% offense, +3.5% defense) the borderline winning situation is:

Thus in the best case (+3.5% offense, -3.5% defense) the borderline winning situation is:
0.9044

For guaranteed fail you need less than 90.439%.

[Bishop]

I haven't seen the distribution but mehul hated linear distributions.

[RiffArt]

I haven't seen the distribution but mehul hated linear distributions.

ToG is linear. Just saying ;-)

Thanks for the hint though.

[Ethan]

How are you checking it?

Assuming the random factor is distributed uniformly for both attacker and defender in [-3.5%, 3.5%] it's quite simple to work out. What I don't know is whether that assumption is correct. Given that so many people tell me "I've never failed at 102%" (~86% success rate) or similar, I must conclude that either the distribution isn't uniform, or else all of these people are unreliable.


Assuming the random factors for both attacker and defender have the same distribution, then it must be exactly 50% (ignoring ties anyway).

Firstly - assume people are quite unreliable. This is a very good assumption in most cases. I, for one, have failed hits above 100% before. (I think a fair fraction of the 101% type crowd are people still using angel, so they *really* have no clue what they are doing, as last I knew that have a 5% defaulted in)

Secondly - I was literally taking the uniform distribution as an assumption. I have no meaningful evidence for this, I just guessed it would be reasonable and would make a tractable math problem. (@Bishop - the combination of the two rands will be distinctly non-linear though, so I think it passes your recommended "Mehul likes" test".)

However, I was checking the resulting distribution for sanity checks after I tried the "quite simple to work out" calculus. If I stuck that .97 in there, I didn't even get a function that went to 1 at the end, instead stopping (I think) at .97, very clearly violating all sorts of requirements. Even if I threw a random adjustment in to rebalance back to unity, I still wasn't getting 50% at .97 off/def ratio, which (as you've reminded me to think though again) is a known datapoint without any calculus. (Although can the fact that one is devision and one multiplication perhaps mess that up?)

If you are up to it, a walkthrough of the derivation of the CDF (or PDF, or whatever the heck the things are called) would be very enlightening to me, as even the combination of my notes from grad level probability/stats and wikipedia were insufficient the last time I took a crack at it. To be fair, despite being a math major I probably couldn't get an A in basic calculus once we hit integrals - even though I could manage an A in Real Analysis, the *proof* of calculus. Unfortunately, composing this probability curve doesn't so much require proving anything about integrals - just getting answers them... which I can't seem to do right apparently. (The result being said grad level probability class was a C in the end - aced the discrete parts, and only just slightly failed the continuous parts. Was close but missed the comp there too - gotta retake if I even get serious about the PhD again.)