Welcome to Librarium Online!
Join our community of 80,000+ members and take part in the number one resource for Warhammer and Warhammer 40K discussion!
Registering gives you full access to take part in discussions, upload pictures, contact other members and search everything!
Thanks to me having insomnia and a maths degree, I decided to find out the averages and odds on Swiftstride results...
You're most likely to roll.... 9"
Edit: In summary, a reliable range to allow for Swifstride models would be to leave 6" (~90% occurrence) or 7" (~80% occurrence) on top of your normal Movement in order to make a charge...
Mean: 8.44", Median: 9", Mode: 9"
Mean: the 'average' over all combinations and the number of times they occur
Median: if you lined all the combinations up in order, what number would be in the very middle*
Mode: the number that occurs most frequently (or 'happens' the most)*
*thanks curly
Percentage odds of occurrence:
2--------0.46%--------100.00%-----0.00%
3--------2.78%--------99.54%------0.46%
4--------1.85%--------96.76%------3.24%
5--------5.56%--------94.91%------5.09%
6--------8.80%--------89.35%------10.65%
7--------12.50%-------80.56%------19.44%
8--------15.74%-------68.06%------31.94%
9--------16.67%-------52.31%------47.69%
10-------15.74%-------35.65%------64.35%
11-------12.50%-------19.91%------80.09%
12-------7.41%--------7.41%--------92.59%
The first column is the Swiftstride result i.e. you roll 3D6 and the 2 highest dice = Swiftstride
The second column gives the percentage chance of that exact Swiftstride occuring
The third column gives the percentage chance of rolling equal to or greater than Swiftstride
The fourth column gives the percentage chance of rolling less than Swiftstride
To show my working...
3d6
3---1---111
------2
4---3---112---121---211
------3---3---3
5---6---113---131---311---122---212---221
------4---4---4---3---3---3
6---10---222---123---132---213---312---231---321---114---141---411
------4---5---5---5---5---5---5---5---5---5
7---15---133---313---331---124---142---214---412---241---421---223---232---322---115---151---511
------6---6---6---6---6---6---6---6---6---5---5---5---6---6---6
8---21---125---152---215---512---251---521---134---143---314---413---341---431---233---323---332---224---242---422---116---161---611
------7---7---7---7---7---7---7---7---7---7---7---7---6---6---6---6---6---6---7---7---7
9---25---144---414---441---135---153---315---513---351---531---126---162---216---612---261---621---225---252---522---234---243---324---423---342---432---333
------8---8---8---8---8---8---8---8---8---8---8---8---8---8---8---7---7---7---7---7---7---7---7---7---6
10---27---136---163---316---613---361---631---145---154---415---514---451---541---226---262---622---235---253---325---523---352---532---244---424---442---334---343---433
------9---9---9---9---9---9---9---9---9---9---9---9---8---8---8---8---8---8---8---8---8---8---8---8---7---7---7
11---27---146---164---416---614---461---641---155---515---551---236---263---326---623---362---632---245---254---425---524---452---542---344---434---443---533---353---335
------10---10---10---10---10---10---10---10---10---9---9---9---9---9---9---9---9---9---9---9---9---8---8---8---8---8---8
12---25---156---165---516---615---561---651---246---264---426---624---462---642---255---525---552---345---354---435---534---453---543---336---363---633---444
------11---11---11---11---11---11---10---10---10---10---10---10---10---10---10---9---9---9---9---9---9---9---9---9---8
13---21---166---616---661---256---265---526---625---562---652---346---364---436---634---463---643---355---535---553---445---454---544
------12---12---12---11---11---11---11---11---11---10---10---10---10---10---10---10---10---10---9---9---9
14---15---662---626---266---356---365---635---536---563---653---446---464---644---455---545---554
------12---12---12---11---11---11---11---11---11---10---10---10---10---10---10
15---10---555---456---465---564---546---654---645---366---636---663
------10---11---11---11---11---11---11---12---12---12
16---6---664---646---466---556---565---655
------12---12---12---11---11---11
17---3---665---656---566
------12---12---12
18---1---666
------12
To translate: the far left (under 3d6) is the total on 3d6... immediately right is the number of different combinations for that total... to the right of that are those combinations... below each combination is the swiftstride result (highest 2d6 of the 3d6)...
example:
17---3---665---656---566
------12---12---12
17 on a 3d6 can be rolled in 3 different ways, 665, 656 and 566 with Swiftstride results of 12, 12 and 12 respectively...
Edit:
In conclusion, a reliable range to allow for Swifstride models would be to leave 6" (~90%) or 7" (~80%) on top of your normal Movement in order to make a charge...
Last edited by thetopcat84; March 20th, 2011 at 18:06. Reason: corrections... conclusion...
Rep for all of the work!!
Those of us NOT math majors appreciate the breakdown, but I will raise my hand to ask for a slightly simpler clarification - you clearly show that you have the highest likelyhood of rolling an average of 9 when rolling three dice and picking the highest two, so add that to the typical cavalry base movement of 8 for a total distance of 17 and that is where we should base our strategy assumptions? At least from a standpoint of playing the odds...
From those numbers you have a 52.81% chance of rolling 9 or higher, which is only slighty better than having a 1 in 2 chance of making a 17 inch charge from movement 8. I would personally not, unless it was last ditch, count on getting more than 6 as then you have 9 in 10 chance of making it.
Dunno about rep, maybe some sleeping tablets or something!!
Winginson is right though, the odds of rolling 9" or higher is only 52.31%... so over time you will roll 9 or higher more often than you won't, but it's not a reliable figure...
Alternatively, looking at 7", you'll make 7" or greater 80.56% of the time (roughly 4 in every 5 rolls)... a much more reliable figure to go by...
Really, the best way to draw conclusions would be to compare to the average charge range that infantry troop-types are likely to roll... that way you could find an optimum distance (especially with pre-measuring) that you could set up your knights/cav to make it most likely that you'll be the one charging into combat... vitally important for cavalry armed with spears/lances for their charge bonuses and the +1CR too...
I'll do that the next time I'm not sleeping...
Edit: So to answer your question MDSW, wait and see!
Last edited by thetopcat84; August 5th, 2010 at 21:11. Reason: Answering MDSW
Moved, since this is not a rules question.
Having an army and not owning a rulebook is like owning a car with no steering wheel.Originally Posted by amishcellphone
Apologies, Rork...
Just trying to get the scene right here, so going to be spouting a few thoughts... interrupt me at any point!
The swiftstride 'scenarios' have loads of variables... your M, enemy M, will enemy charge, will enemy reverse at half M, will enemy even take the charge?
Obviously, you want to position your cavalry close enough to be able to successfully charge in your next turn regardless of what the enemy does... and the perfect scenario would be to get close enough to entice a failed charge, moving the enemy comes closer to you, making it more likely that you'll make your charge...
Example: M4 Inf are being lined up by your M7 Cav... to have ~80% chance of successfully charging, you place your Cav 14" away... Inf now have to roll a 10 to successfully charge, with 83.33% chance of failing... your opponent will realistically choose a) CHARGE! or b) Reverse 2"... b is the savvy choice... cos now you need to roll a 9... ~52% chance of success...
It ain't easy...
As a theory, I would say that M8 Cav would be best placed 14"/15" from target depending on targets M... M7 Cav should probably be 14"...
All things considered, it has put a huge new wrinkle into the game with variable charge distances. Infantry charge distances are now only slightly less than cavalry. The closer you move your cavalry to the infantry to raise the odds of charging, you also increase their odds of the infantry charging you. Before, you could simply stay out of range and charge the infantry at your whim.
Personally, I like the change from a game standpoint, but my poor Bretonnians are simply devastated - they seem very reluctant to venture too far from the castle (however, some of the other changes have helped them - i.e. I love my trebuchets!!!
Also, Topcat - Anyone putting in that much work deserves rep!!!!
considering you have a maths degree i'm impressed you have the median and mode mixed up.
Also very useful, thanks.