Attacking - Gain in War and Offense to Send

Forgive me if I'm misunderstanding, but I think you're trying to make things too complicated. What we want to know is "if I send x% off:def ratio, what is the probability the attack will succeed?", or vice versa "if I want a 95% success rate, what off:def ratio do I need to succeed?", i.e. our x-axis would be "offence/defence" and our y-axis is "% victory". That is quite simple to work out once you've made your assumptions about the distribution. For a uniform distribution anyway, I haven't yet tried any others simply because I'm unsure how to test which is accurate.

As for using a CDF, I'm not sure what you're trying to use as your random variable. Maybe I'm being dense, but I don't see how CDF/PDF helps us here.

Holy Crap. The OP didn't ask anything about a "Guaranteed Fail". I think this has went off onto a tangent that it wasn't meant to even get close to. It might be a good idea for folks to go back an re-read the OP. Maybe then you will realize that this thread is finished and we should move on to the next random question. LOL! "Guaranteed Fail". Where in the world did that even come from? I am only thinking out loud. I am not really looking for an answer to that. OMG. Here comes another 30 posts about a "Guaranteed Fail" now.

Just to refresh:
What are the diffs in Gains from In War to NOT In War?
What is the % of Off to Def needed to guarantee a Win?(I am taking a little liberty with this. It's not the exact question he asked.)

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Originally Posted by JackRabbitSlim

Holy Crap. The OP didn't ask anything about a "Guaranteed Fail". I think this has went off onto a tangent that it wasn't meant to even get close to. It might be a good idea for folks to go back an re-read the OP. Maybe then you will realize that this thread is finished and we should move on to the next random question. LOL! "Guaranteed Fail". Where in the world did that even come from? I am only thinking out loud. I am not really looking for an answer to that. OMG. Here comes another 30 posts about a "Guaranteed Fail" now.

Just to refresh:
What are the diffs in Gains from In War to NOT In War?
What is the % of Off to Def needed to guarantee a Win?(I am taking a little liberty with this. It's not the exact question he asked.)

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Originally Posted by RiffArt

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Question 2: If I send 97% of the target's defense, will I win as the guide suggests?

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You took a lot of liberty. The question is "will I win" the answer is "sometimes". The original question said nothing about any sort of guarantee.

Riffart could be a turtle worried about a crack in his shell. Or trying to calculate how many failed hits it would take to crack his shell. 104.04% is useful if you are an attacker trying to decide how many troops to leave home.

Knowing exact odds for an outcome is a much better answer than "sometimes". Sometimes people win lotteries. Sometimes people get hit by lightning. Sometimes sink holes swallow houses. If you check the odds your best bet is to play a free online game inside your house.

It is a safe bet that someone asking about winning at 97% is not looking for "% of Off to Def needed to guarantee a Win". The guide says quite clearly:

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Mod Off = Mod Def * 1.040362694

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A logical follow up question is "If I can win at 97% how low might I be able to win". Or maybe "how low can my ratio be and still have better odds than winning poker with a pair of jacks?"

Well originally I was under the impression that the random factor was no longer involved (as some people have suggested, e.g. when they say 101% never fail). If you re-read the entire first post I do state this. That's why the question wasn't worded with "guarantee" - I thought it was a simple yes/no as to whether you'd win.

What motivated the question is situations such as if you've got double your opponents defence, how is it best to split your troops to hit twice? And is the chance of two successes sufficiently high, or are you better just hitting once? What about attacking a province that's nearly UB and you've not got enough offence - even with mercs - to reach 104.04%. Or suppose you're in war, are UB with elites home and want to attack, how much defence do you leave at home? Enough so that the enemy can't reach 104.04% or do you want to make sure that they can't even hit you at 97% [i.e. higher defence at home] (now we've stablished that at 97% the odds to win are 50-50). To be truly UB (from a single attack anyway, ignoring OPs etc.) you need to know what the "guaranteed fail" ratio is.

Where did you establish the 50/50 win chance?

1 person out of 2 1/2 pages said there was no random factor ,everyone else has said what the number is.Id stick with the majority.I dont see where the 50/50 odd work at 97%.Maybe im missing something.

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Originally Posted by Bishop

Where did you establish the 50/50 win chance?

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50/50 @ 97% target's MD is *ONLY* if we assume a symmetrical (composite) distribution.

{Asside}
Uh - I think symmetrical (around +0) and identical distros for the two +-3.5% random factors suffices, but wouldn't bet the house on it. I can imagine a way in which both the attackers and defenders +-3.5% are symmetrical, but different from each-other (thus violating identical above), which produces odds <50% at 97% send.
{End Asside}

While the symmetrical distribution is an assumption, I argue it is a reasonable good bet to be true. Firstly, humans like symmetry, and both find it nicer and easier to think about.
Secondly, we *know* an explicit asymmetric "skew" already - the .97 factor. If asymmetric distributions were being used we could find a way to produce much the same impact just from skews of various sorts, and the .97 wouldn't really even need to be there.

What good 50/50 is is unclear to me, since cases where you come up short would seem to be high impact, and thus risk a catastrophic bounce. But knowing what say, +3% is might be useful for getting that 2x in that otherwise is out of reach. But anything other than .97 is far more conjecture than the assumption about the 50/50 point.

If anyone with nothing better to do wants to test 97% sends and report on the success, that'd be pretty cool, but that's some pretty serious spading since it should involve a good number of bounces.

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Originally Posted by Ethan

If anyone with nothing better to do wants to test 97% sends and report on the success, that'd be pretty cool, but that's some pretty serious spading since it should involve a good number of bounces.

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Find province with 0 military. Then you only need 97% of the land. Bounce razes.

I failed one on an inactive. Sent 100.3%.

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Originally Posted by Thunder TA

1 person out of 2 1/2 pages said there was no random factor ,everyone else has said what the number is.Id stick with the majority.I dont see where the 50/50 odd work at 97%.Maybe im missing something.

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There is definitely a random factor. Has been for years bit people didn't understand how it worked and claimed there wasn't one.

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Originally Posted by Bishop

Where did you establish the 50/50 win chance?

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I believe this is correct based on what Mehul had posted about this before he sold the game. Feel free to update us on the formula used ;)

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Originally Posted by Ethan

If anyone with nothing better to do wants to test 97% sends and report on the success, that'd be pretty cool, but that's some pretty serious spading since it should involve a good number of bounces.

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Testing equal off to def sends would be of more interest to me.

It's not clear if 2 or 4 random numbers are used (I believe Mehul once said it was 4). It'd be 50-50 at 97% either way assuming this part is still correct. But at an even send, 2 variables would give you 84% success while 4 variables would give you 93% success. This should be enough difference to be able to tell which it is with enough careful attacks.

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Originally Posted by AquaSeaFoam

I believe this is correct based on what Mehul had posted about this before he sold the game. Feel free to update us on the formula used ;)

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What did he post? He was always very vague about the random factor.

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Originally Posted by AquaSeaFoam

Testing equal off to def sends would be of more interest to me.

It's not clear if 2 or 4 random numbers are used (I believe Mehul once said it was 4). It'd be 50-50 at 97% either way assuming this part is still correct. But at an even send, 2 variables would give you 84% success while 4 variables would give you 93% success. This should be enough difference to be able to tell which it is with enough careful attacks.

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Yes, 4

To answer some of the questions in the previous Attack Gains Clarification post...

* There is no penalty for sending overkill

* The "random factor" simply adds and subtracts a small percentage from both the attacker and defender points. By doing it to both, it means that most likely random factor is no-change, and larger changes occur less often. For example, if the random factor was 100%, then we'd basically modify the formulas as such:

Offense = Offense * (1 + random-number-between-0-and-0.5 - random-number-between-0-and-0.5)

Same for defense.

Worst case, Offense would get a -50% disadvantage and a Defense would get a +50% advantage, meaning the random factor is 100%. However, the likelihood of this extraordinarily small as 4 random numbers are involved.

NOTE: THE RANDOM FACTOR IS NOT 100%

Mehul

dig dig dig

FWIW, the probability distribution of the random factor isn't flat, or
even a normal/bell curve distribution. It's triangular, resulting from
statement like "points = points - random(0.035) + random(0.035)".