Probabilities For AoW

[bddbrown]

I've just finished the first version of a program that calculates odds for AoW combats. It is pretty basic at the moment but I will make improvements.

Stuff It Does
* Melee
* Different Bases
* Different Frontage
* Different To-Hits
* Different Quality (re-rolls and cohesion)
* Different Starting Cohesion
* Cohesion Tests (all relevant reasons)
* Take Cohesion Into Account (dice in melee)

Stuff Not Taken Into Account
* Shooting or Impact
* Other Cohesion (say IC, rear support etc)
* Generals In Front Rank
* Usage Help
* Expansions and Contractions In Melee
* A Few Niggly Edge Cases

[bddbrown]

Initial results are kind of interesting:

8 bases of Superior/++ versus 8 bases of Average/-- with 100000 runs.
Running simulation 100000 times.
A won 99686 times (99%), B won 311 times (0%) and there were 3 draws.
Average bound length is 2.98074 bounds.
Running simulation 100000 times.
A won 99724 times (99%), B won 274 times (0%) and there were 2 draws.
Average bound length is 2.97771 bounds.
Running simulation 100000 times.
A won 99679 times (99%), B won 318 times (0%) and there were 3 draws.
Average bound length is 2.97999 bounds.

So, discounting impact Germans Foot versus Roman Legionaries, the Germans only have a 0.3% of winning.

Increasing the Germans to a BG of 12 but still on a frontage of 4.
Running simulation 100000 times.
A won 99626 times (99%), B won 374 times (0%) and there were 0 draws.
Average bound length is 3.07047 bounds.
Running simulation 100000 times.
A won 99673 times (99%), B won 326 times (0%) and there were 1 draws.
Average bound length is 3.07239 bounds.
Running simulation 100000 times.
A won 99649 times (99%), B won 349 times (0%) and there were 2 draws.
Average bound length is 3.07531 bounds.

A slight improvement for the Germans - but barely noticable.

Now a CT bonus for rear support - back to two units of 8.
Running simulation 100000 times.
A won 99535 times (99%), B won 462 times (0%) and there were 3 draws.
Average bound length is 3.48673 bounds.
Running simulation 100000 times.
A won 99546 times (99%), B won 444 times (0%) and there were 10 draws.
Average bound length is 3.48799 bounds.
Running simulation 100000 times.
A won 99579 times (99%), B won 418 times (0%) and there were 3 draws.
Average bound length is 3.48605 bounds.

Quite an improvement (about 33%) but overall still a one sided affair.

[bddbrown]

Some basic stuff to note:

Taking two BGs of 6 bases with a frontage of 3, no PoA and average.
Running simulation 100000 times.
A won 49809 times (49%), B won 49922 times (49%) and there were 269 draws.
Average bound length is 3.84047 bounds.

A is now Superior.
Running simulation 100000 times.
A won 70716 times (70%), B won 28896 times (28%) and there were 388 draws.
Average bound length is 3.82307 bounds.

A is now Elite.
Running simulation 100000 times.
A won 85678 times (85%), B won 13970 times (13%) and there were 352 draws.
Average bound length is 3.52199 bounds.

A is now Poor.
Running simulation 100000 times.
A won 28342 times (28%), B won 71550 times (71%) and there were 108 draws.
Average bound length is 3.5694 bounds.

Conclusions
Superior essentially (not quite) doubles your chances of winning.
Elite essentially (not quite) quadruples your chances of winning.
Poor eseentially (not quite) flaves your chances of winning.

I'll let people make their own conclusions regarding points costs - this simulation does not show how extra BGs affect a game.

[bddbrown]

BTW - I will release the program at some point when it is ready for general consumption. In the meantime if anyone wants me to run any specific simulations then please let me know.

[bddbrown]

Looking at a single PoA in combat for A:
Running simulation 100000 times.
A won 83302 times (83%), B won 16636 times (16%) and there were 62 draws.
Average bound length is 3.80799 bounds.

Seems like a single PoA (say armoured versus protected) is a massive advantage in combat - you are about 3 times as likely to win.

[madaxeman]

Those are pretty staggering odds.

Dont go into combat one POA down, and dont fight against Elite troops ever !

[rbodleyscott]

Those are pretty staggering odds.

Dont go into combat one POA down, and dont fight against Elite troops ever !

Agreed, unless you have overlaps on one or both sides and/or are higher quality and/or have a general fighting in the front rank and/or the enemy is already DISRupted or FRAGmented and/or the enemy is fighting to front and flank and/or you get extra impact dice for rear rank shooting support and/or you are a spawny git.

Well you get the idea.

Also Elite is almost but not quite enough to cancel 1 POA, so if you must fight your opponents Elite troops, do it with troops that are 1 POA up.

(We do, of course, have our own combat odds calculator).

[bddbrown]

Those are pretty staggering odds.

Dont go into combat one POA down, and dont fight against Elite troops ever !

Agreed, unless you have overlaps on one or both sides and/or are higher quality and/or have a general fighting in the front rank and/or the enemy is already DISRupted or FRAGmented and/or the enemy is fighting to front and flank and/or you get extra impact dice for rear rank shooting support and/or you are a spawny git.

Well you get the idea.

Also Elite is almost but not quite enough to cancel 1 POA, so if you must fight your opponents Elite troops, do it with troops that are 1 POA up.

(We do, of course, have our own combat odds calculator).

It would be interesting to see if the odds calculators are getting the same results as each other.

A single overlap
Running simulation 100000 times.
A won 58516 times (58%), B won 41413 times (41%) and there were 71 draws.
Average bound length is 4.07063 bounds.

Nearly evens things up.

A double overlap
Running simulation 100000 times.
A won 33108 times (33%), B won 66855 times (66%) and there were 37 draws.
Average bound length is 3.96845 bounds.

Yup, that definitely tips the scales nicely.

Superior troops
Running simulation 100000 times.
A won 70089 times (70%), B won 29757 times (29%) and there were 154 draws.
Average bound length is 4.27632 bounds.

Helps, but still a one sided fight.

Elite troops
Running simulation 100000 times.
A won 54102 times (54%), B won 45531 times (45%) and there were 367 draws.
Average bound length is 4.47653 bounds.

Yup, nearly but not quite - looks like the odds calculators are working right.

Spawny git.

The program broke with a divide by 0 error. Apparently there is no chance of this!

[terrys]

What do you mean by 'bound length'

[bddbrown]

The number of phases of melees fought. So 4 bounds would be side A, side B, side A and side B.

[terrys]

[/quote]The number of phases of melees fought. So 4 bounds would be side A, side B, side A and side B.

I'm impressed that your calculator goes into that level of detail over many bounds. We haven't done that with ours, because we don't expect the situation to remain the same for very long. There are too many 'ifs'. (if one side takes a casualty, if one side had a general, if that general dies, if it has rear support etc.) Players can choose to improve their chances in various ways.

Also, without including the impact phase in the calculations it does give an unbalanced view.
for example Warbands are on an equal POA to the Romans at impact, and could DISR them, and cuase a casualty etc.


Overall, I quite like the idea that Roman Legionaries are unbeatable, it makes you use them historically.
Of course you'll soon find that they are beatable, but not on a level playing field. You have to outnumber them, outflank them, surround them etc.

[bddbrown]

The number of phases of melees fought. So 4 bounds would be side A, side B, side A and side B.

I'm impressed that your calculator goes into that level of detail over many bounds. We haven't done that with ours, because we don't expect the situation to remain the same for very long. There are too many 'ifs'. (if one side takes a casualty, if one side had a general, if that general dies, if it has rear support etc.) Players can choose to improve their chances in various ways.

Also, without including the impact phase in the calculations it does give an unbalanced view.
for example Warbands are on an equal POA to the Romans at impact, and could DISR them, and cuase a casualty etc.


Overall, I quite like the idea that Roman Legionaries are unbeatable, it makes you use them historically.
Of course you'll soon find that they are beatable, but not on a level playing field. You have to outnumber them, outflank them, surround them etc.

[/quote]

All very true. I think we all understand this is just a "dumb" simulation. And given it was so easy to calculate and display it adds a useful measure of how long a fight might last on average.

As for impact, well maybe. If the PoA etc are the same then it makes no difference to the overall results (apart from bounds). And the simulator is generic (no idea of troops, just bases, to hit numbers etc - so you could use it to calculate impacts, just not impacts followed by melees. Impacts and shooting are something I can easily add when I get a spare evening (as is multiple BGs - mostly to answer the 3x4 versus 2x6 which is best question). However, I am not sure that I put that much value on the numbers at the moment - getting yourself into the right position at the right time is a lot better!

I agree with Roman legionaries. But it does make it difficult to a) fight "historical" battles and b) encourage youngsters who want to see celtic hairy types rip into Roman authority figure legionaries. Maybe we should have a special teenager angst version of the rules?

[shall]

First it sounds a fabulous gadget and I look forward to the release of Deep Thought or of the creation fo the computer to come thereafter. Seriously it sounds excellent - we did a lot of combat simulations oursleves in the early stages. I like the numberof bounds part as well as it shows when it has been a tough fight. One thing I find about your Roman legionary smash is that it tends to take time to get a result and the Romans win aftera hard slog, which feels realistic.

The only comment I would make is beware the computer when it doesn't reflect the battle sitautions that occur in reality on the tabletop.......we found this with our simulator....in making judgement calls about what to do one is always trying to qualitatively merge the results of the simulations with what one expects to happen ont he table top.

Terry and I played Ancient Britons vs Elite Romans last week after the 0.3% odds statement. The game last about 10 bounds after which the results was indeed very one-sided as you predicted....but alas the wrong way round!!

Romans losses - 11 AP points army gone
Ancient Britons - O AP not a single BG down to FRAG

Hard to explain how and army of MF, Prot, IF, Sw can do this to a Legion with units of Sup, Arm, IF, Sk Sw. The luck went in favour of the Britons but not in extremis. A challenge for the simulator to explain perhaps..............

One detailed question on your model. Does the model include the death rolls and reduce the numbers as you go. the main advantage of, say, 8 bases on a 3 frontage is not the extra bases reducing the -1 for cohestin test but rather than fact that you can replace 2 lost bass in the battle withou dropping dice. 6 base Roman units often lose a base and are donw to 5 and the 4 dice and this is one of the most important effects. As you can see from your simulator numbers matter after a while - as you overap analysis shows. It makes abig difference to the results if the celts win the impact round - about 35% chance IIRC - as the Romans are almost always down a dice thereafter [to win the Brits have usually done 4/5 hits].

Great stuff and look forward to seeing more of it once fully developed.

Si

[bddbrown]

First it sounds a fabulous gadget and I look forward to the release of Deep Thought or of the creation fo the computer to come thereafter. Seriously it sounds excellent - we did a lot of combat simulations oursleves in the early stages. I like the numberof bounds part as well as it shows when it has been a tough fight. One thing I find about your Roman legionary smash is that it tends to take time to get a result and the Romans win aftera hard slog, which feels realistic.

Thanks. I wonder what people will think when the PocketPC version comes out and we start running the odds at the table...

The only comment I would make is beware the computer when it doesn't reflect the battle sitautions that occur in reality on the tabletop.......we found this with our simulator....in making judgement calls about what to do one is always trying to qualitatively merge the results of the simulations with what one expects to happen ont he table top.

Couldn't agree more.

Terry and I played Ancient Britons vs Elite Romans last week after the 0.3% odds statement. The game last about 10 bounds after which the results was indeed very one-sided as you predicted....but alas the wrong way round!!

Romans losses - 11 AP points army gone
Ancient Britons - O AP not a single BG down to FRAG

Hard to explain how and army of MF, Prot, IF, Sw can do this to a Legion with units of Sup, Arm, IF, Sk Sw. The luck went in favour of the Britons but not in extremis. A challenge for the simulator to explain perhaps..............

Back to my comment - what you can do on the table is not necessarily a good guide for the rest of us.

One detailed question on your model. Does the model include the death rolls and reduce the numbers as you go. the main advantage of, say, 8 bases on a 3 frontage is not the extra bases reducing the -1 for cohestin test but rather than fact that you can replace 2 lost bass in the battle withou dropping dice. 6 base Roman units often lose a base and are donw to 5 and the 4 dice and this is one of the most important effects. As you can see from your simulator numbers matter after a while - as you overap analysis shows. It makes abig difference to the results if the celts win the impact round - about 35% chance IIRC - as the Romans are almost always down a dice thereafter [to win the Brits have usually done 4/5 hits].

Yes. It includes death rolls. It also the CT rolls correctly for all the factors such as 25% losses, 1HP3E (only in the first 3 ranks), lost combats by 2 etc. Also now has re-rolls for CTs and combats (but not death rolls). It does do overlaps (well actually it just fights the whole frontage versus the whole frontage which is not necessarily right, but works if you enter the numbers right).

Great stuff and look forward to seeing more of it once fully developed.

Si

I did some work on it the other night, so if I can make it available in its current form, including source code if people want it? At least it know has usage help.

Now if only I could find a way to make money out of this...

[shall]

I would keep it to yourself for now - might be an excellent 10 pound AOW Bruce Brown accesory in due course.............of course just like in a Casino, users may be thrown out.....or shot by the annoyted opponents across the card table for counting!

I think the challenge with it all of it is to model multiple BG combats rather than a single head to head. This, rather than skill, was the main thing in the game with Terry in truth.

If you want to look at an open table simulation for Ancient Britons vs Legionaries I would suggest trying the following as a tabletop version of a historical head on charge.....

4 units of 6 Roman legionaries laid out so they are 12 bases wide and 2 deep at the start. These are 14 points each IIRC - so 24 bases = 336 points. So half and AOW army.

Set the Britons fighting them to be 6 units of 8 Warriors, Prot, IF, Sw, MF. Same points. Put them with 4 units at the front with 2 overlaps at each end and spare rear elements for the 2 centre unit. Put 2 units behind so that they are way behind each front unit and therefore give rear support to all of the them.

Now add an FC to the Roman line and 2 TCs to the British line. Put both British TCs into the front line of the centre units. Keep the Roman FC out until an emergency happens as they can't afford to lose them - he simply cannot afford the 1 in 12 chance of losing him when he is likely to win anyway. Very realistic as the Britons risk all to the charge.

This is a roughly equal points head-on smash that the Roman should win in most cases after a very hard struggle. It is a reasonable battlefield test of a straightforward charge set up properly in the rules. My guts tell me its about 75/25 in favour of the Romans but it would be great to simlulate if possible.

The reasons it deviates from one-to-one simulations is mainly that with 40% chance of winning round 1 on average 1 or 2 of these Roman units will need to test with 2-s. That means they need a 9 to pass IIRC - which even with re-rolls isn't easy. The Brits get slowly hammeded elsewhere but the generals and rear support slow it down a lot.

It would be great to have some simulated answer to sucha smash if it can be done...but apprciate that might be for the 20 pound systems upgrade.

Cheers

Si

PS a test I would also do is to start the Romans DISR and see what happens. Lots of charges will come after loads of missile fire and some Roman units should be DISR when hit.

[bddbrown]

The core methods are in place to run this combat. I'll take a look and see how long it will take.

On a similar topic are you planning on a battle report for the AB versus Roman fight? I think we are all dying to know how you managed this victory.

[shall]

Great Bruce.

We'll see what we can do on the battle report. As a minimum we'll post up an outline of what happened later in the week.

Si

[bddbrown]

Apologies Simon, Richard posted a battle report on behalf of Terry!

[shall]

Yes an all pretty accurate - except my LH BGs were 4 bases not 6 - see posting. Terry is a bit poorly at present so impressive that he managed to get it done.

Si