Hannibal's simpler Battle Calculator for WOK4

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Hannibal's simpler Battle Calculator for WOK4

Post by Hannibal » Wed Apr 13, 2005 2:27 pm

This might help the non-experts a bit (one or two vets probably have their own version). It would be a shame to just bin it, so I thought I'd "bequeathe" it the way that Thin King did his one of the times that he quit.

TK bequeathed a good, downloadable Battle Calculator Program. It's good, I tried it once or twice, but each iteration took my PC ages to work through .... and I wasn't always at my PC when I was making my attack plans (think garden, sunshine, staring at a map with a pen and a calculator just in case .....).

So, I am PRAISING TK's Battle Calculator, just offering my more rough-and-ready version, as an alternative, which I do just on the calculator, for speed and ease for a faster rougher answer .......

So, you've spied that your Enemy has 5 armies at lev 4.300, and you wonder whether your 31 armies at lev 1.700 can take them ...... or how many survivors you might have, after victory, to consider attacking on with ...... or, how many of your 31 armies to attack with leaving the rest to go plundering in another direction .....Or else, even, you just lost a big battle, and you wonder whether that was "normal" given the difference in lev, or whether you were very unlucky ....... (Happens to us all!).

The Hannibal formula uses a quick simple calculator rather than a program like TK's. What it does is work out a RATIO of your and their likely losses in the battle, on the average, so that you can see how many you "should" lose taking it, or that your numbers are too few to be likely to win. Once you have the RATIO, you can easily play around with different numbers attacking, without inputting the whole parameters to TK's program from the start all over again .....

That RATIO is (drum-roll) :
The lower of the two opposing PATT/PDEF, divided by [the higher of the two PATT/PDEF's PLUS TWICE THE DIFFERENCE BETWEEN THE TWO PATT/PDEF's ]. (same formula whether you're calculating as attacker or defender).

That gives you the likely RATIO of army-kills between you and your enemy; a number like 0.235; common sense reminds you whether it means YOU lose 1 army for every 0.235 armies of HIS, or HE loses 1 army for every 0.235 of yours ......don't get it the wrong way round! Whichever has the lower PATT/PDEF loses armies faster .....!

The logic (I'm only logical, not a mathematician), is as follows: (feel free to skip this paragraph ....) :

Let's say you're attacking, and your PATT is 16.000 (lev 1.7 X 10 X eff of .94), and your enemy's PDEF is, say, 42.000 (lev 4.400 X10 plus 4 X def of 0.7, all X eff of .90). Then, the game engine rolls 1-16 for you, and 1-42 for him. So, your enemy would win HALF the times he rolls 1-16, and ALL of the times he rolls 17-42, right? So, for calculation, allocating 2 outcomes for each of his dice rolls, he would win 1 out of 2 rolls whenever he rolls 1-16, but 2 out of 2 rolls whenever he rolls 17-42. So, on average, he would WIN 16 + 2X26 rolls/rounds, and lose 16 rolls/rounds .... That gives you a ratio : 68 : 16, or 0.235. Always divide the SMALLER by the larger to get a ratio (eg, 0.235), then common sense reminds you which way round it is, ie. which side loses armies faster. In THIS case, you should lose armies at a rate of 1: 0.235, ie., his 5 heavy armies "should" cost you 5 divided by 0.235 = 21.3 of your 31 armies, on average.

Note, beginners, that the ratio is definitely NOT simply the ratio of your PATT/PDEF to his ..... the DIFFERENCE in PATT/PDEF is effectively doubled .....twice as much effect as you "expect" till you get the hang of it (hence the success, usually, of sleeping strategies that allow time to build up LEV for armies .....!).

I keep saying "on average2, because luck makes the outcomes vary from the average .... your choice how much overkill to allow!.

And I say "rough and ready" because this formula takes no account of collateral damage on his (or your) DEF level for the prov, thus reducing DEF and therefore reducing PDEF during the rounds of fighting. It's not worth refining it that much since this is meant to be a quick ready-reckoner, and the LOWERING of a prov's DEF is a marginal effect in bigger battles anyway. Note that the DEF does matter, and the formula takes it into account - it's just the slight LOWERING of the def level during combat that the formula ignores ..... assume that the formula just slightly understates the attacker's odds, but not by enough to bother about.

And, before negative people chip in, I have to say that you need to be able to feed in both PATT and PDEF to use the formula ! You have to know, or spy, or best-guess the other guy's EFF level .... But that's equally true of TK's program, or any other battle-predictor! Of course, if you fought him last turn, you can easily calculate what his EFF was then, right? No need for me to tell you that calculation? Or just post and ask and I'll spell it out! ....Then add in effects of spying results, guess/know his WOK on EFF .... or just guess (me, I tend to guess, if I don't have other clues, 95% EFF if he's sleeping, or 90% if he's been active .....you can see afterwards how far off you were!).

This Battle-Calculator doesn't make you win. Other things matter more. It just sometimes help you plan .... or maybe helps beginners be amazed to realise how much effect LEV has, when their 25 trusted armies get slaughtered going up against 10 armies with higher LEV !!

As I'm no mathematician, I don't guarantee this formula, but I didn't want to just bin it. Stand by for two attack-vectors - mathematicians saying it is either rough or obvious, and the non-mathematicians saying it was too long and/or that they achieve the same by instinctive feel for the game! (On the other hand, I'd be gutted if no-one posted a reply at all!)

Cheers,
Han
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Re: Hannibal's simpler Battle Calculator for WOK4

Post by Hannibal » Wed Apr 13, 2005 2:34 pm

Hannibal wrote:
The Battle Calculator RATIO is (drum-roll) :
The lower of the two opposing PATT/PDEF, divided by [the higher of the two PATT/PDEF's PLUS TWICE THE DIFFERENCE BETWEEN THE TWO PATT/PDEF's ]. (same formula whether you're calculating as attacker or defender).

That gives you the likely RATIO of army-kills between you and your enemy; a number like 0.235; common sense reminds you whether it means YOU lose 1 army for every 0.235 armies of HIS, or HE loses 1 army for every 0.235 of yours ......don't get it the wrong way round! Whichever has the lower PATT/PDEF loses armies faster.
I think on the first post I did my usual of explaining too much. So this post, for those who don't like reading, reduces it to its mimimum !

Cheers,

Han
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Re: Hannibal's simpler Battle Calculator for WOK4

Post by Duke » Wed Apr 13, 2005 3:04 pm

Hannibal wrote: ......So, I am PRAISING TK's Battle Calculator, .
I lost you around this part. :wink:
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Post by Donut » Wed Apr 13, 2005 3:27 pm

So I see Han on the page and think, oh, he's just poppin in to see what's up.
Then I see he posted and think, oh, he's just poopin in to say hey.

Then in Han fashion... :P

I don't think you gave a link to the new calculator. Otherwise... just proof that you know you can't stay away from WOK. May as well join a game :P

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Re: Hannibal's simpler Battle Calculator for WOK4

Post by Brykovian » Wed Apr 13, 2005 3:35 pm

Hannibal wrote:(On the other hand, I'd be gutted if no-one posted a reply at all!)
We wouldn't want that ... who'd have to clean up that mess?! ;)

Thanks Han -- Nice little nugget burried in the middle of all that chatter! :)

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Post by Brykovian » Wed Apr 13, 2005 3:36 pm

Donut wrote:I don't think you gave a link to the new calculator.
LOL -- Donut didn't read it!! :D

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Post by Hannibal » Wed Apr 13, 2005 4:00 pm

Pearls before Swisconsinites. And Swedes. Just read the second short post!?

Han
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Post by TK » Wed Apr 13, 2005 4:20 pm

Nice one Han.

I used to use the same "ratio" technique in my WOK4 days. Thats right, I didnt even use my own battle calculator! Most of the time there is just no need...


WOK5 players should be aware that the varying PATT and PDEF means that this method will NOT work for WOK5.

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Post by korexus » Wed Apr 13, 2005 4:24 pm

In case you're having trouble with the ratios, try thinking of it this way;
The person with the higher power kills
(higher power) - (lower power) / 2 armies for every one army he loses.

Hans logic and figures lead there he just got caught up in expressing it as a ratio. :wink:

Also if you want a quicker version of the Battle Calculator, I believe Mullog put one up at www.kaomaris.com/AttCalc.php his programming's a bit sloppy* but it'll be about as accurate as you need for most battles and it is much faster :) .

Good to see you again, Han!

korexus.

*I don't get to say that very often! :D
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Post by Brykovian » Wed Apr 13, 2005 4:36 pm

Hannibal wrote:Pearls before Swisconsinites.
And I get this after a nice compliment? Sheesh ... why, I never! ;)

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Post by TK » Wed Apr 13, 2005 4:53 pm

korexus wrote:In case you're having trouble with the ratios, try thinking of it this way;
The person with the higher power kills
(higher power) - (lower power) / 2 armies for every one army he loses.

LOL. I thought korexus might try to "correct" Hannibal... but...


PATT 10

PDEF 8


The attackers kills 10-8/2 = 6 armies for every 1 lost?

Or did you mean (10-8)/2 = 1 army for every 1 lost?

The answer is more like 1.5.


Let P be the higher power, and Q be the lower. 1 army belonging to P will kill (on average) 2*P/Q - 1 armies belonging to Q.

P = 10, Q = 8.

2*10/8 - 1 = 1.5

So 1 army belonging to P kills 1.5 belonging to Q.




Excises to follow....? :roll:
Last edited by TK on Wed Apr 13, 2005 5:15 pm, edited 1 time in total.

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Post by korexus » Wed Apr 13, 2005 5:09 pm

Wouldn't say I was trying to correct, just simplify a bit...

However it seems I went to far in one go. Maybe I should have written it down or put some numbers in or something.

What I was getting at was the higher powered player will win

(higher power) - (lower power)/2 out of every (higher power) kills - you can just ignore draws - I must have jumped a line somewhere.


How lucky we are to have you constantly on the prowl, TK.
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Post by Raw » Wed Apr 13, 2005 6:46 pm

Why did you have to introduce letters into this, that got me all confused :p.

They all seem to work about same, but can you please figure out the "luck" factor?

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Post by Hannibal » Wed Apr 13, 2005 6:55 pm

korexus wrote:Wouldn't say I was trying to correct, just simplify a bit...

What I was getting at was the higher powered player will win
Yep, saying "the higher powered player will win" is CERTAINLY simplifying it a fair bit, thanks from us all, Kor. ........er, but we were stupidly struggling towards, er, .... by how much! You weren't targettng the Wisconsin/Sweden market, were you?

Just teasing,
Han
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Post by korexus » Wed Apr 13, 2005 6:59 pm

Raw wrote:They all seem to work about same, but can you please figure out the "luck" factor?
It's quite simple. How lucky you are is inversely proportional to how much you've pissed the GM off recently. :P
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Post by Hannibal » Wed Apr 13, 2005 7:08 pm

Brykovian wrote:
Hannibal wrote:Pearls before Swisconsinites.
And I get this after a nice compliment? Sheesh ... why, I never! ;)

-Bryk
Hmmm, that tag to the left of your posts, Bryk, has you as from Minnesota, so I THOUGHT I was just insulting Donut. After all, you got what Do-ball missed. Or do Minnesotans see themselves as in a sort of "Greater Wisconsin", such that they can take umbrage if they really try?!

Just teasing,

Han
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Post by Hannibal » Wed Apr 13, 2005 7:22 pm

TK wrote:

LOL. I thought korexus might try to "correct" Hannibal... but...
Might as well tease everyone now I'm started. Hey, TK/PS (Bryk will get that one), are you saying Han was right and Kor was wrong? Or can you manage to find a way that we both were wrong?

Playing,
Han
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Post by Raw » Wed Apr 13, 2005 7:29 pm

Hannibal wrote:
Brykovian wrote:
Hannibal wrote:Pearls before Swisconsinites.
And I get this after a nice compliment? Sheesh ... why, I never! ;)

-Bryk
Hmmm, that tag to the left of your posts, Bryk, has you as from Minnesota, so I THOUGHT I was just insulting Donut. After all, you got what Do-ball missed. Or do Minnesotans see themselves as in a sort of "Greater Wisconsin", such that they can take umbrage if they really try?!

Just teasing,

Han

Mr Brykovian is from WI orignally.
It's not fast unless its got a fart can.

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Post by Hannibal » Wed Apr 13, 2005 7:41 pm

Raw wrote:

Mr Brykovian is from WI orignally.
I didn't know that. I thought Bryk was from Minnesota. No offence intended. And my respect for having mostly overcome it, Bryk!

Kidding,
Han
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Post by korexus » Wed Apr 13, 2005 7:43 pm

Han, you're clearly bored without WoK. Why don't you head on over to the Lobby and sign up for Josh's WoK-On game? :wink:
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