A hole in the rules?

[marioslaz]

I have a doubt if a tactic I thinked it's legal. If it's so, it seems to me a hole in the rule, because it can product an advantage not historically justify. The tactic is about to reduce effect of impact troops against melee troops. For example, I will consider a type of troops who I know very well because it's my favourite historical era: Roman legions and Greek hoplites. In this example I will use for semplicity 2 BG of 6 bases each, both for hoplites and hastati/princeps; this is just for semplicity and I don't regard to real BG dimension in army list, also because you can think to this example as a portion of a larger clash (i.e. more BGs involved).

In historical battle each BG would deploy in a formation 2 bases deep and they clash at impact phase with 2 dice for each front base and with a POA for Roman player (impact foot), without regard to which is charging. Hoplites are likely to loose impact and this can produce a drop of 1 level in their cohesion due to the test. If they don't drop they will be STEADY in next melee and they will have a POA, otherwise hastati will have POA due to their ability of swordsmen. It's clear that the key is the impact phase and if hoplites can reduce the effect of it they will gain a benefit. So examine the effect of enter in melee in column formation (1 base width ans 6 bases deep). Romans and Greeks throw only 2 dice, Romans hit with 4 and Greeks with 5. Of course the chance Romans win the impact is still greater than Greeks one, but there is a difference in cohesion test. In fact the chance of "At least 2 or more hits received than inflicted" drop from 20% to only 10% (it's interesting that the chance is near the same for a 4 dice and 6 dice roll, so there is no difference to fight impact with 2 or 3 bases width).

I don't want to annoy you with tables of chances, but this is the tactic that, if legal, produce the better chance to hoplites:

• fight impact in column
• in next manoeuvre phase expand of 1 file
• in next turn manoeuvre phase expand of another file

I can assure that, if hoplites can pass first cohesion test, this tactic produce a better chance to hoplites. More, fighting impact with just 1 bases width reduces defeat chance from 53,7% to 44,4%; it reduces also the chance to win, from 27,2% to 19,4%, but improves chance of a tie from 19,1% to 35,8%, and if you follow my reasoning you can agree that a tie is an half win for hoplites. (I used comma to separate decimal because I'm Italian and we use so; sorry).

Mario

[SirGarnet]

I'm not up to working out the math at the moment, but consider this in the calculations . . .

If one-wide then only 3 bases (first 3 ranks) count for determining 1 hit per 3 bases from close combat, so any loss will be at a -1, and a 0-2 hit result will also be an additional -1 (not counting the penalty for losing to Impact Foot).

Unless obstructions interfere, the Romans will be 3-2 wide in melee after expansions and the extra dice.

[shall]

Has been studied to death and proved wrong.

You are right insofar as it goes but you need to run the full tree of CMTs and the game sequence to see what really happens. The less chance of 2 hits win drops but the -1 for 1 per 3 is automatic on any loss though.

You are only looking at the individual win lose odds at melee. Expecially you miss that the reason you want the hopites to survive is to win the melee but you commit them to a losing melee situation through overalps by doing so. The romans will be at a - but will have pehaps 2x ther dice. Note also it is very different if the Romans charge the hoplites in this formation due to the way the expansion rules. You are also very vulnerable to missile fire needing only 1 hit to create a CT. So any decent player will get some skirmsihers at you as you approach.

In FOG the bst formation for Spears is 3 deep to soak up casualties and shoulder to shoulder.

Trust me the hoplites get massacred if they try the above tactic - odds of winning drop from 55% to about 15% IIRC

Si

[marioslaz]

I'm not up to working out the math at the moment, but consider this in the calculations . . .

If one-wide then only 3 bases (first 3 ranks) count for determining 1 hit per 3 bases from close combat, so any loss will be at a -1, and a 0-2 hit result will also be an additional -1 (not counting the penalty for losing to Impact Foot).

Unless obstructions interfere, the Romans will be 3-2 wide in melee after expansions and the extra dice.

Excuse me, but I think that you are wrong.
Chance of 1HP3B with 2 dice: 75% (fight in column, so at least 1 hit)
Chance of 1HP3B with 6 dice: 89,1% (fight 3 bases width, so at least 2 hits)

I used the formula P(X=k) = (n/k) p^k × q^(n-k) = {n!/(k!×(n-k)!} × p^k × q^(n-k)
where:

• p = chance to hit (0,5 with no POA or POA+, 0,33 with POA-)
• q = chance to miss (equal to 1 - p)
• k = number of successes
• n = number of attempts

to determine the chance of "at least k successes on n attempts" that is called binomial distribution (http://en.wikipedia.org/wiki/Binomial_distribution to learn about)

I also considered the mid situation, Roman vs Greeks with 3-2 ratio in bases, but counting that Greeks have a POA positive if they pass cohesion test, this is better than fight with even number of bases but with a POA negative.

Nobody answer my question: it's legal this tactic?

Mario

[petedalby]

Nobody answer my question: it's legal this tactic?

Yes it is. But as Si notes - there are down sides.

Pete

[shall]

Chance of 1HP3B with 2 dice: 75% (fight in column, so at least 1 hit)
Chance of 1HP3B with 6 dice: 89,1% (fight 3 bases width, so at least 2 hits)

Yur stats are fine but amssively oversimplistic, and its legal, its just rubbish over all.

Calculate it for 2 wide...

Then run the tree out for how you do in a single element column hitting a line of romans. Don't do one do 3 next to each other. Then se what happens. Oddsof romans winning is much high then if you were simply 3 BGs wide 2 deep.

Basically the tree has to voer the sequential outcomes. As authors you may not be surprisred to know we built a multipoahse simulator for these types of things that covered the explicit tree.

But taken simplicilty....

If you pass ther first round 1 wide you expnad by 1 width. The Romans now have 6 dice vs 4 dice in melee. Your passing a CMT at impact only has value if it gets you into an advantage melee. Assuming you are not Sup Spartans you now have a seriusly disadvatnged melee round vs SUperoir Romans. On average they will beat you (3-2 being the median result), and you now have to take a second bad test. So on verage your plan swaps passing one reasonable to test for having to pass 2 of them. Not eaxctly a good swap. If you DIS you are dead meat. So risning additional lost combat rounds is the last thing you need to do.

Si

Si

[marioslaz]

Has been studied to death and proved wrong.

You are right insofar as it goes but you need to run the full tree of CMTs and the game sequence to see what really happens. The less chance of 2 hits win drops but the -1 for 1 per 3 is automatic on any loss though.

I already answered to this and it's wrong.

You are only looking at the individual win lose odds at melee. Expecially you miss that the reason you want the hopites to survive is to win the melee but you commit them to a losing melee situation through overalps by doing so. The romans will be at a - but will have pehaps 2x ther dice. Note also it is very different if the Romans charge the hoplites in this formation due to the way the expansion rules.

Not sure about what you are meaning. In impact Romans have POA+ anyway (I can find, in both situation ++ for impact foot and + for offensive spearmen)

You are also very vulnerable to missile fire needing only 1 hit to create a CT. So any decent player will get some skirmsihers at you as you approach.

Again, not sure what you are meaning. Hoplites can contract 2 file in a single move, so they can change from 3 wide to column in just a single move. It's a simple move if they make an advance of 3 MU, and so with a very simple calculation they must do just before to enter to charge reach, but anyway very close to the enemy formation, in this way they can prevent skirmish fire.

In FOG the bst formation for Spears is 3 deep to soak up casualties and shoulder to shoulder.

Trust me the hoplites get massacred if they try the above tactic - odds of winning drop from 55% to about 15% IIRC

Si

Do you mean that you consider all the cases that could arose? Like to pass or not first cohesion test and all subsequents or whatsoever? I hope you know that, because cohesion test use 2 dice and 2 dice have a Gaussian as distribution of the chance, a +1 or a -1 will have different weight on the overall chance. And this is just to make an example. You have to consider all the results of the impact, to cross them with all the chance of cohesion result, then to generate a lot of cases for the second melee, and so on. Trust me, I have a Master Degree in Engineering, I work as an Engineer since near 20 years, and I don't even think to start this calculation.

Mario

[stenic]

I'm confused. You say they'd be better in column for impact but in the same breath you say...

(it's interesting that the chance is near the same for a 4 dice and 6 dice roll, so there is no difference to fight impact with 2 or 3 bases width).

Is it the same or not?

If it is the same then your arguement makes no sense as you will certainly more than likely suffer the Hits Per Base loss on the CMT and of course have been overlapped in the melee combat.

Steve P

[marioslaz]

Chance of 1HP3B with 2 dice: 75% (fight in column, so at least 1 hit)
Chance of 1HP3B with 6 dice: 89,1% (fight 3 bases width, so at least 2 hits)

Yur stats are fine but amssively oversimplistic, and its legal, its just rubbish over all.

Calculate it for 2 wide...

Then run the tree out for how you do in a single element column hitting a line of romans. Don't do one do 3 next to each other. Then se what happens. Oddsof romans winning is much high then if you were simply 3 BGs wide 2 deep.

Basically the tree has to voer the sequential outcomes. As authors you may not be surprisred to know we built a multipoahse simulator for these types of things that covered the explicit tree.

But taken simplicilty....

If you pass ther first round 1 wide you expnad by 1 width. The Romans now have 6 dice vs 4 dice in melee. Your passing a CMT at impact only has value if it gets you into an advantage melee. Assuming you are not Sup Spartans you now have a seriusly disadvatnged melee round vs SUperoir Romans. On average they will beat you (3-2 being the median result), and you now have to take a second bad test. So on verage your plan swaps passing one reasonable to test for having to pass 2 of them. Not eaxctly a good swap. If you DIS you are dead meat. So risning additional lost combat rounds is the last thing you need to do.

Si

Again, I'm not sure about your reasoning. I confront average vs average, because this is standard for Roman Legions and for Hoplites isn't it? It's pretty clear that if someone is better will have better chance. Anyway, I don't regard to your observation about morale, and I will confront the second combat, that is the first melee after impact. If I don't mistake hoplites can expand already one file, even if Romans charged. So chance for hoplites are these:
Win 38.5% Tie 25.5% Defeat 36.0%
This is for 4 bases against 6 bases with POA+ for Greeks. This because I suppose Greek passed cohesion test. If they don't pass cohesion test they are dead meat anyway, with 4 or 6 bases.

Mario

[marioslaz]

I'm confused. You say they'd be better in column for impact but in the same breath you say...

(it's interesting that the chance is near the same for a 4 dice and 6 dice roll, so there is no difference to fight impact with 2 or 3 bases width).

Is it the same or not?

If it is the same then your arguement makes no sense as you will certainly more than likely suffer the Hits Per Base loss on the CMT and of course have been overlapped in the melee combat.

Steve P

Sorry for the misunderstanding. I mean that chance of 2 or more hits drop from 20% to only 10% if you fight with 2 or 3 bases respect to fight in column (1 base width). That is, chance to suffer 2 or more hits than inflicted by Greeks:
in column: 10%
in a formation 2 o 3 bases width: 20%

I hope this clarify.

Mario

[shall]

I hope you know that, because cohesion test use 2 dice and 2 dice have a Gaussian as distribution of the chance, a +1 or a -1 will have different weight on the overall chance.

errrrrrr... yes I think we understand statistic 1.01 thank you

One of my slides used ot say ..."if you model sometihng statistically and the real world doesn't do it that way, its probably a problem with your stats, not a problem with the real worl".

The game has been going 2 years and people do not favour the Mario-Theory. Beleive me there are plenty of good statisticains and wargamers in the test group than have gone a lot further into the %es than you are doing here.

So maybe take a look at the statistics fully with SST statistical approaches and you will find a different answer. Oversimplification down to Binomial, Poisson, gausian, etc. npte the test is a twin threshold gaussian and this is important too. You need to cover the effect on both parts of the curve.

Now as a tabletop test the best test is Sup romans in 4s vs ave armoured hoplites in 6s as this is the most common one.

As for forming up into column it can be done with a 3MU move of course. If you do it that close to enemy then they'll charge you with overlaps. IF you do it far away they will comer and shoot you. A good player will make it much worse by coming up beside you so you can't even expand back out and then you are stuffed.

But good luck with the real world testing

Si

[shall]

Again, I'm not sure about your reasoning. I confront average vs average, because this is standard for Roman Legions and for Hoplites isn't it? It's pretty clear that if someone is better will have better chance. Anyway, I don't regard to your observation about morale, and I will confront the second combat, that is the first melee after impact. If I don't mistake hoplites can expand already one file, even if Romans charged. So chance for hoplites are these:
Win 38.5% Tie 25.5% Defeat 36.0%
This is for 4 bases against 6 bases with POA+ for Greeks. This because I suppose Greek passed cohesion test. If they don't pass cohesion test they are dead meat anyway, with 4 or 6 bases.

A nice partial answer but aren't you going to do the comparison that therefore matters?

Keep your analysis going a little you are getting closer to the answer all the time

Si

[lawrenceg]

The tactic is legal.

It has been studied in depth (the authors used monte-carlo simulations) and IIC has been found not to offer much advantage in changing the probability of which BG will break first.

So yes, it is a loophole in the rules, but not worth closing.

[marioslaz]

I hope you know that, because cohesion test use 2 dice and 2 dice have a Gaussian as distribution of the chance, a +1 or a -1 will have different weight on the overall chance.

errrrrrr... yes I think we understand statistic 1.01 thank you

One of my slides used ot say ..."if you model sometihng statistically and the real world doesn't do it that way, its probably a problem with your stats, not a problem with the real worl".

The game has been going 2 years and people do not favour the Mario-Theory. Beleive me there are plenty of good statisticains and wargamers in the test group than have gone a lot further into the %es than you are doing here.

So maybe take a look at the statistics fully with SST statistical approaches and you will find a different answer. Oversimplification down to Binomial, Poisson, gausian, etc. npte the test is a twin threshold gaussian and this is important too. You need to cover the effect on both parts of the curve.

Now as a tabletop test the best test is Sup romans in 4s vs ave armoured hoplites in 6s as this is the most common one.

As for forming up into column it can be done with a 3MU move of course. If you do it that close to enemy then they'll charge you with overlaps. IF you do it far away they will comer and shoot you. A good player will make it much worse by coming up beside you so you can't even expand back out and then you are stuffed.

But good luck with the real world testing

Si

I'm Italian and perhaps, I hope, I don't understand english perfectly because your answer, at first glance, sounds like "I am more educated than you, so I don't reply to your argumentations because you must trust to my opinion". I can assure that in Italy we have very good University and to become an Engineer you need to study a lot of Math. It's true that now, after 20 years from my graduate I forget many formulas, and even many theorems, but I think I could understand also a little of your knowledge, and not only a "believe me, it works so..." (More, I'm Italian and I really don't know what SST is for).

Last, I'm an historical player and I really don't use this tactic even if proved good, because it's historically rubbish. I'm only concerned about game mechanisms.

Mario

[shall]

We tested it to depth and considered having aminimu 4 dice combat for smoothing effects but discovered it wasn't needed an it gave more tactically interesting situations allowing the 2 dice combats.

I did run a test of Romans in 4s and Greeks in 6s trying the column tactic and the Greeks got murdered. In straight line they won. Its about building all the correct factors into the stats:

Win lose odds split into several levels of win
Base loss odds
The double threshold CMT gausiian
3+ stages of combat
Use of generals to bolster

Remember winning or losing is actually an irrelevance. What matters is the odds of failing or badly failind a CMT and or los9ing bsaes.

In way what the Greeks need to do is to kncok bases off the romans so to do this they need maximum width melee advantages to get enough hits to force deathrolls. Also if the enemy is a bit clever then going in columns is a death trap against 4s of agile romans.

Si

[marioslaz]

The tactic is legal.

It has been studied in depth (the authors used monte-carlo simulations) and IIC has been found not to offer much advantage in changing the probability of which BG will break first.

So yes, it is a loophole in the rules, but not worth closing.

Ok, your answer it's still vague, but it seems more honest.

Mario

[marioslaz]

I did run a test of Romans in 4s and Greeks in 6s trying the column tactic and the Greeks got murdered. In straight line they won. Its about building all the correct factors into the stats:

This is a completely different situation. As I said a lot of time I'm an historical player, so I don't think to tournament situations, but to historical ones. Anyway, in a fight between a single 4 Romans BG and another single 6 Greeks BG, the better situation is still column. In fact, chance to loose impact now is 58.9% in line and 46.5% in column. In this calculation I considered the effect of superior troops and also the rule (that at first I forgot) that in impact you roll the same number of dice. To calculate this I used binomial distribution with a formula of Open Office "calc". For example, to calculate chance Greeks loose fight making 1 hit, I multiply chance of making exactly 1 hit on 4 attempts (chance of hit 33.3%), with the sum of the chance enemy makes at least 2 hits (chance 50%) on 4 attempts, the chance enemy makes exactly 1 hit and at least 1 failure produce a re-roll with 1 hit, the chance enemy makes no hit and at least 2 failure produce re-rolls with then give at least 2 hits.

The outcome is what I just said: a slight difference (not much over 10%). Other considerations. Less dice less chance to loose a base if you lost impact (you cannot get more than 2 hits). Less dice less chance to get -1 for "at least 2 more hits received than inflicted". Not a great advantage, as Lawrence wrote, but still an advantage. My reasoning stop here, because this it is only a curiosity for me, since I'm not interested in unhistorical tactic

Mario.

[lawrenceg]

I did run a test of Romans in 4s and Greeks in 6s trying the column tactic and the Greeks got murdered. In straight line they won. Its about building all the correct factors into the stats:

This is a completely different situation. As I said a lot of time I'm an historical player, so I don't think to tournament situations, but to historical ones. Anyway, in a fight between a single 4 Romans BG and another single 6 Greeks BG, the better situation is still column. In fact, chance to loose impact now is 58.9% in line and 46.5% in column. In this calculation I considered the effect of superior troops and also the rule (that at first I forgot) that in impact you roll the same number of dice. To calculate this I used binomial distribution with a formula of Open Office "calc". For example, to calculate chance Greeks loose fight making 1 hit, I multiply chance of making exactly 1 hit on 4 attempts (chance of hit 33.3%), with the sum of the chance enemy makes at least 2 hits (chance 50%) on 4 attempts, the chance enemy makes exactly 1 hit and at least 1 failure produce a re-roll with 1 hit, the chance enemy makes no hit and at least 2 failure produce re-rolls with then give at least 2 hits.

The outcome is what I just said: a slight difference (not much over 10%). Other considerations. Less dice less chance to loose a base if you lost impact (you cannot get more than 2 hits). Less dice less chance to get -1 for "at least 2 more hits received than inflicted". Not a great advantage, as Lawrence wrote, but still an advantage. My reasoning stop here, because this it is only a curiosity for me, since I'm not interested in unhistorical tactic

Mario.

I think Simon was probably thinking about a long line of BG, perhaps 6 BG of 4 legionaries versus 4 BG of 6 hoplites.

One thing I think you could look at in your simple example is the state of the legionaries after the melee.

So take 6 IF swordsmen versus 6 spearmen, all average, no generals, no rear supports etc.

At the end of 1 impact plus 1 melee, you could have:

spearmen broken, swordsmen steady
spearmen fragmented, swordsmen steady
spearmen disrupted, swordsmen steady
both steady

... etc ...

spearmen steady, swordsmen broken


altogether 16 combinations.

Then look at how the probabilities of various results depend on the initial spear formation.

This is a lot of calculations, but not impossible by hand.

My feeling is that approaching in column reduces the probability of a bad result for the spearmen, but also reduces the probability of a bad result for the swordsmen.

[Redpossum]

Unlike the rest of you folks, I am rather poorly educated, and have no impressive credentials at all

But if I really wanted to know whether this worked or not, I would just try it. After all, theory is at best an approximation of reality, and what matters is not whether it works in theory, but whether or not it works in the real world.

So sit down with two BG's and some dice and a cold beer, (or other recreational substance of your choice), and run through it 100 times.

[marioslaz]

Unlike the rest of you folks, I am rather poorly educated, and have no impressive credentials at all

But if I really wanted to know whether this worked or not, I would just try it. After all, theory is at best an approximation of reality, and what matters is not whether it works in theory, but whether or not it works in the real world.

So sit down with two BG's and some dice and a cold beer, (or other recreational substance of your choice), and run through it 100 times.

I really like your solutions Specially about cold beer

Mario.