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Thread: How Many Rams Make a Rammer?

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    How Many Rams Make a Rammer?

    This thread arises out of a post in a separate discussion. A player had split his WW ram hammer into two separate attacks, after realising that he had so many rams he could afford to knock down the opposition WW wall twice over. So I'd like to determine how many rams are enough to knock down a WW wall. If, for a given sized WW hammer and an assumed WW defence, you can build that many rams - well then, once you've got enough rams you can stop building them, build some catas instead, and do some extra damage. Of course, that's assuming you make the right guesses about your opposition's WW defence - but that's YOUR problem...........


    So, the variables to consider are:

    1. How big your hammer is
    2. How big the WW defence is
    3. What tribe is hosting the WW (determines the wall strength)
    4. Whether or not the WW account holds a Building-Strength artefact (modifies the wall strength).

    So what I've is run a preposterous number of simulations in Kirilloid, and posting the results in six separate tables - two for each tribe (i.e. one with no artefact, and one with the Unique Building-Strength artefact). Each table covers a range of hammer sizes and WW defences (hopefully covering both normal and speed servers), and provides how many rams are required to take down a L20 wall for that given hammer and WW defence size. Clicking on each result in the table should take you to the corresponding simulation, in case you want to play around with the numbers a little further.


    Simulation conditions are:

    1. Ram numbers are rounded up to the nearest 100 (otherwise it really WOULD be a preposterous number of simulations!).
    2. All troops (hammer and defence) are L20.
    3. Hammers are Roman, containing roughly 1:1 ratios of infantry to cavalry (by crop - i.e. 4:1 by absolute numbers).
    4. Hammer size is calculated by 'raw' crop - i.e. not discounting for Horse Drinking Trough.
    5. Rams are not included in the hammer sizes.
    6. A Hero with 20% Off-bonus and Long Sword of the Imperian leads the hammer.
    7. WW defences consist of roughly equal numbers (by crop) of Phalanges, Spearmen, Praetorians, Druidriders and Paladins.
    8. Three-fifths of defence players (i.e. 2 tribes out of 3) have Heroes (with 20% Def-bonus and no items) at the WW.
    9. Hammer and WW players have equal populations (arbitrarily set at 10 000).

    OK, here we go:
    Last edited by aesculapian; 20th November 2011 at 12:02 PM. Reason: Finished!

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    Roman WW, no artefact

    [IMPORTANT EDIT: Hmmm - interesting problem. Simulations that I draft as Roman defenders, and which run accurately as such, open from the links as Gaul defenders. I've tested this repeatedly and cannot find how to fix it. I've sent an email to Kirilloid to see whether he can either fix it or explain it to me. Meanwhile, I'll continue to post my numbers and links here; but if you want to run the Roman simulations for yourself, I'm afraid you'll have to manually change the defender from Gaul to Roman]

    Last edited by aesculapian; 20th November 2011 at 11:58 AM.

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    Roman WW, Unique Building-Strength artefact

    [IMPORTANT EDIT: Hmmm - interesting problem. Simulations that I draft as Roman defenders, and which run accurately as such, open from the links as Gaul defenders. I've tested this repeatedly and cannot find how to fix it. I've sent an email to Kirilloid to see whether he can either fix it or explain it to me. Meanwhile, I'll continue to post my numbers and links here; but if you want to run the Roman simulations for yourself, I'm afraid you'll have to manually change the defender from Gaul to Roman]

    Last edited by aesculapian; 20th November 2011 at 12:00 PM.

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    Gaul WW, no artefact

    Last edited by aesculapian; 20th November 2011 at 11:50 AM.

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    Last edited by aesculapian; 20th November 2011 at 11:51 AM.

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    Last edited by aesculapian; 20th November 2011 at 11:52 AM.

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    Last edited by aesculapian; 20th November 2011 at 11:53 AM.

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    Re: How Many Rams Make a Rammer?

    I just skimmed over your post Aesc, but I thought you might find this useful, it's written by kirilloid, with each of the combat formulas listed. I was actually looking at it the last couple of days thinking to do something similar regarding the most effective time to launch a WWK.

    Unfortunately, rams are far and above the most complicated combat thing to work with, still, since you're just looking at final wall level, it's not as bad as it could be...

    Assuming lvl 20 upgrades on rams:
    36 worked will destroy Roman
    108 will destroy Gaul
    180 will destroy Teuton

    With no defenders it's simple, as tribe variants have no effect, and "all" rams fire...

    I can't quite get the equations to work out at the moment, but I'll work on trying to get an equation which just lets you plug in values and pops out the number of rams.


    Great idea for the guide though, there are an awful lot of variables when it comes to rammers.





  9. #9

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    Re: How Many Rams Make a Rammer?

    Well, I've finished crunching all the numbers - now for some analysis!

    The advent first of the artefacts, and now of T4, has significantly broadened the variety of strategic options for the end-game; and this has implications for planning your rammer. Pre-T3.5, you could count on a Teuton WW holder, and a consistently large defence fuelled by the ubiquitous WW half-crop rate. Accordingly it became common practice for some (usually the smaller) WW hammers to specialise in rams, and others in catapults. Assaults would take place in pairs (or more), with a rammer taking down the tough Teuton wall, boosting the impact of the subsequent cata-hammer(s)

    Then, when artefacts were introduced to the game, new possibilities opened up. Monster defences could be created by supplementing the WW half-crop bonus with a Crop-sparing artefact. Alternatively, it became feasible for a Roman or Gaul to hold the WW, with their bigger wall (and other infrastructure) bolstered by a Building-strength artefact. Now, with T4, the automatic half-crop bonus for WWs has gone (will we ever see defences like this again?); and we have the ability to capture a WW village that much earlier. This ability may be a two-edged sword: it can remove the time pressure from building infrastructure, but it may also signal your WW strategy to your opponents, allowing them an early peek at which tribe will host the WW, and a guess at the likely supporting artefact.

    So, what do the tables above tell us about choice of WW defence strategy? Well, a few things are immediately apparent:

    Firstly, a Roman wall bolstered by the Unique Building-strength artefact is tougher than an ordinary Teuton wall. Not vastly tougher, but a fair bit. Add to that the 81% bonus (vs the Teuton 49% bonus), and the fact that your infrastructure (excluding the WW itself) is well-nigh undentable, and this combination becomes a very attractive option. (In T3.6 a Roman WW-builder had the fringe benefit of shaving a few hours off construction time by building crop fields concurrently with village infrastructure; in T4, this benefit is less significant).

    Secondly, a Teuton wall bolstered by the Unique Building-Strength artefact is a formidable challenge indeed. A respectable 200-300K hammer, going up against a respectable 3-5M defence (talking non-speed servers here), would require some 40 - 50K of rams to take down the wall. That's about a year of full-speed production: doable, perhaps, with a training artefact, but probably not more than once in a given end-game. An artefact-hardened Teuton wall has the potential to make most opposing WW-rammers asthenic, if not downright obsolete.

    Thirdly, of course, choosing a Building-strength artefact means passing up the option of a Crop-reduction artefact. A Unique Crop artefact could allow you to host twice as large a defence; which would, of course, bolster your wall, your infrastructure AND your WW itself. Most likely your choice will be determined by whichever artefact your alliance has in its possession; but if you could choose any artefact, which would be better? Looking at the tables above, we can compare how many rams will take down an Artefact-hardened wall, with the corresponding number required to take down an un-hardened wall with twice the defence. The answer is clear, across all ranges of hammer:defence ratios: the benefit from doubling your defence size is nowhere near as large as that of hardening your wall (and the same applies to infrastructure). The only real advantage of Crop-reduction over Building-hardening is that a larger defence will bolster the WW itself; and of course, that depends on you being really disciplined about taking double the defence, rather than letting the artefact take the pressure of feeding a 'normal-sized' defence.

    So, what are the implications for hammer planning?

    Firstly, as I mentioned at the outset, if you arrive at end-game and have a look at your opposition's WW tribe and artefact configuration, you should soon have a rough idea whether you have enough rams in your rammer(s) to take down the wall(s) - assuming a reasonable guess at how big a defence they will muster. If you already have enough rams, you may as well spend the last few months of the server building catapults. You should be able to muster enough to take levels off a GW, or at least a couple of crop fields; if you can secure the use of a training artefact, you could easily take levels off a WW directly.

    But secondly, might one guess in advance of end-game, which way to develop? Certainly if your opposition has no Account-scope Building-hardening artefacts (and if you can guarantee they won't capture one!), then by all means build rammers; they will likely take the conventional route of a Teuton WW-holder, and you can plan your rammer(s) accordingly. If they DO have a Building-hardening artefact, the guess becomes harder: if they use it with a Roman, rammers become even more important; if they use it with a Teuton, rammers are probably a waste of time; and if they use it with a Gaul - well, then the position is somewhere in-between.

    So thirdly, I'd like to pose the question "Should we give up differentiating WW-hammers into rammers and catters?". Or at least, should we make the choice much later in the game? In situations where the opposition might deploy a building-hardening artefact, I'd like to explore what would happen if WW hammers trained BOTH rams and catas (in judiciously-chosen ratios) prior to end-game; and then, once the WW race is underway and the disposition clearer, the choice of whether to boost ram numbers or cata numbers can be made more precisely - augmented (if need be) by a training artefact.

    Is such an approach likely to be harmful? Well, let's run some tests. Let's take two Roman WW hammers of, say 200K (excluding artillery). Let's say they've each had, say, 120 days of building artillery at full speed (no Training artefact) prior to end-game, and they'll get another 60 days of building artillery during end-game. Strategy A is the traditional specialist strategy - one hammer will build only rams, and one will build only catas. That'll make 16080 rams prior to end-game, plus another 8040 during end-game, for a total of 24120 rams; and 8280 catas prior to end-game, plus another 4140 during end-game, for a total of 12420 catas. Strategy B is the one I describe above: each hammer will spend (say) half its time building rams and half catas - i.e. 8040 rams and 4140 catas - prior to end-game; and then decide for the remaining 60 days which artillery to develop further. Let's see how each strategy stacks up in a range of scenarios, all hitting a L90 WW:

    Firstly, a traditional Teuton WW holder, with a Crop artefact enabling a 5M crop defence:

    Strategy A
    The rammer, with 24120 rams, takes the Wall from L20 to L0
    The catter, with 12420 catas, takes the WW from L90 to L84

    Strategy B
    Hammer 1 decides to spend end-game building rams only, realising that he may or may not (depending on defence size) get enough to kill the Teuton wall. He will have 16080 rams and 4140 catas by launch time.
    Hammer 2 focuses on catas; he will have 8040 rams and 8280 catas by launch time.
    Hammer 1 takes the Wall from L20 to L7, and the WW from L90 to L89
    Hammer 2 finishes off the Wall, but only brings the WW down from L89 to L86

    A slight but definite victory for the traditional strategy. Let's look at another scenario:


    Our Teuton instead takes the Unique Building-strength artefact (but can now only manage 3M defence)
    :

    Strategy A

    The rammer (24120 rams) takes the Wall from L20 to L15
    The catter (12420 catas) takes the WW from L90 to L82

    Strategy B

    Hammer 1 and Hammer 2 both decide that further rams are a waste of time against the hardened Teuton wall, and focus their remaining production time on catas. Both will have 8040 rams and 8280 catas at launch.

    Hammer 1 takes the Wall from L20 to L19, and the WW from L90 to L86
    Hammer 2 takes the Wall from L19 to L18, and the WW from L86 to L81

    A slight advantage this time to the new flexi-strategy.


    What if a Roman takes the Unique Building-strength artefact (managing 3M defence)?

    Strategy A

    The rammer (24120 rams) destroys the Wall, from L20 to L0
    The catter (12420 catas) takes the WW from L90 to L76

    Strategy B

    If we guess correctly at the 3M defence, then Hammer 1 might choose to spend half of end-game building rams and half catas: this will bring his total to 12060 rams and 6210 catas. Hammer 2 spends end-game building only catas, launching with 8040 rams and 8280 catas.

    Hammer 1 drops the Wall from L20 to L2, and takes the WW from L90 to L87
    Hammer 2 finishes off the Wall, and takes the WW from L87 to L78

    If we underestimate the defence, the results are even worse. Anticipating a defence of about 2M, Hammer 1 and Hammer 2 might both believe they have enough rams to take down the Roman Wall - if not individually, then certainly in combination. Accordingly, they both focus their end-game production on catas, resulting in 8040 rams and 8280 catas at launch.

    Hammer 1 drops the Wall from L20 to L13, and the WW from L90 to L87
    Hammer 2 finishes off the Wall, but can only bring the WW down from L87 to L81


    So on balance, the traditional strategy remains superior: early differentiation into WW-rammers and WW-catters seems to be the way to go - unless you have reason to be very sure your opponent will be a Teuton with a Building-strength artefact, in which case you may prefer to forget about rammers entirely.
    Last edited by aesculapian; 23rd November 2011 at 03:22 AM.

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