Hannibal's simpler Battle Calculator for WOK4
Posted: 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
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
