The Rally Point (discussion and questions)

[Athos1660]

I think my argument is probably misplaced, because it's not really the probability of an event occurring in isolation that bugs me, and I expect that might be true of others too, but the clustering of such events. If an event is very unlikely, then clearly it will still occur (hopefully rarely), but when there is a string of unlikely events, either occurring simultaneously (or nearly so) or over time but associated with an individual unit, that's what causes distress.

That's probably not very clear, so I'll try to illustrate the point.

Events over a period time, occurring to the same unit might include the situation where the unit which has a 58% chance of winning the melee fails to do so 18 melees in a row. The chance of that happening is a little less than 1 in 6 million (if I recall millennia ago maths lessons).

Event occurring simultaneously might be the situation I suffered recently, where a tight game, late on, with a small advantage to me, collapsed in a single turn because my opponent rallied almost all of his units eligible to rally. Not only those routing, but also those disrupted and fragmented, and then to add salt to the wound, he also won every single impact and melee on his turn, even those where the probability of that was highly unlikely. A tight game turned into a disastrous loss as a result of outlandish luck. Has that ever happened on a real battlefield? I’ll have to leave that question to the historians, but it certainly never happened in any of the limited number of battles I am aware of.

There often seems to be a disparity between the probabilities reported by the game and the results seen on the field of battle, but I say seems for good reason. I am beginning to suspect that the fault may lie not in the game mechanics (although we can still argue over the likelihood of any particular event occurring), so much as the fallibility of computers' random number generators hitting irregular patches.

I don’t know how this weakness can be overcome, unless there’s a way the game could create some novel technique to create a genuinely random number. I expect if that was possible whoever was responsible would become very rich. Beyond my ability, sadly.

So perhaps it’s not me who suffers ill fortune in war, perhaps it’s my computer. I’ve read many computer reviews, detailing many technical specifications, unfortunately luck has never been included amongst them.


Best Wishes

Mike

This is the concept of independence of the events in probability theory : if 12 planes are to crash throughout a year, the probability that they crash the same day is the same as any other order, such as one plane crashes each month or ten crash in June and two in December.

Yet ppl's mind often tends to link these independent events.

(edit)
I did not notice Richard replied before me...

[Tratmot]

Same impossible series happen to me too;
i think, after several try, disparity between the probability reported by game and real result, found is trouble in conversione from percentage number (58% ie), in d6 RNG simulation

Normal RNG system applied linear probability, BUT, when need to add 2 roll for result, and the second is dipendent for success from first, need to apply DIPENDENT Event Probability Formule.
Sorry, but my english is not good for this level of treath … but math works !

Tratmot (Cosimo)

[rbodleyscott]

Same impossible series happen to me too;
i think, after several try, disparity between the probability reported by game and real result, found is trouble in conversione from percentage number (58% ie), in d6 RNG simulation

Normal RNG system applied linear probability, BUT, when need to add 2 roll for result, and the second is dipendent for success from first, need to apply DIPENDENT Event Probability Formule.
Sorry, but my english is not good for this level of treath … but math works !

Tratmot (Cosimo)

The combat system is complex. The chances of a win, draw or loss is massively more complicated than the probability of a certain dice score. To avoid any possible miscalculations, the probabilities are not calculated mathematically at all. Instead the program runs the full combat calculation 1000 times, counts the number of wins, draws and losses, and reports the results as percentages.

[Tratmot]

ok, but … every cycle add a RNG value, right ? if yes, no matter how many time run calculation, have all time same deviance; it's no games issue, it's probability formule issue (imho)

[MikeMarchant]

There often seems to be a disparity between the probabilities reported by the game and the results seen on the field of battle, but I say seems for good reason. I am beginning to suspect that the fault may lie not in the game mechanics (although we can still argue over the likelihood of any particular event occurring), so much as the fallibility of computers' random number generators hitting irregular patches.

I don’t know how this weakness can be overcome, unless there’s a way the game could create some novel technique to create a genuinely random number. I expect if that was possible whoever was responsible would become very rich. Beyond my ability, sadly.

It is very unlikely that there is any such weakness in the random number generator algorithm.

The phenomenon you are seeing is called Poisson clumping, and is a feature of all random events, not just computer generated ones.

https://en.wikipedia.org/wiki/Poisson_c ... r%20bursts.

We're at the point now where I'm out of my depth with the mathematics. I am aware of Poisson clumping, but unable to apply the mathematics to draw any sensible conclusions.

I am also aware of confirmation bias, and this is something I have battled against most of my adult life. My obseravtions of the behaviour of the game are not significantly subejct to confirmation bias, I am sure, as I am as aware and as much irritated by the luck factor when it impedes my opponent as when it impedes me. I have often commented to my opponent when they have suffered bad luck, but have never once mentioned the fact when I have suffered similarly.

And yet, admittedly without the mathematical ability to understand it, my experience of the world informs me that these anomalies are not natural. They are too frequent to be ignored and if they are truly are a consequence of statistical clumping,then perhaps the game mechanics should rein them in.


Best Wishes

Mike

[MikeMarchant]

Same impossible series happen to me too;
i think, after several try, disparity between the probability reported by game and real result, found is trouble in conversione from percentage number (58% ie), in d6 RNG simulation

Normal RNG system applied linear probability, BUT, when need to add 2 roll for result, and the second is dipendent for success from first, need to apply DIPENDENT Event Probability Formule.
Sorry, but my english is not good for this level of treath … but math works !

Tratmot (Cosimo)

The combat system is complex. The chances of a win, draw or loss is massively more complicated than the probability of a certain dice score. To avoid any possible miscalculations, the probabilities are not calculated mathematically at all. Instead the program runs the full combat calculation 1000 times, counts the number of wins, draws and losses, and reports the results as percentages.

That's really interesting. An empirical method of determing the probabilities ought to be pretty accurate given enough calculations, and a thousand calculations ought to be enought to produce a faithful result.


Best Wishes

Mike

[MikeMarchant]

I think my argument is probably misplaced, because it's not really the probability of an event occurring in isolation that bugs me, and I expect that might be true of others too, but the clustering of such events. If an event is very unlikely, then clearly it will still occur (hopefully rarely), but when there is a string of unlikely events, either occurring simultaneously (or nearly so) or over time but associated with an individual unit, that's what causes distress.

That's probably not very clear, so I'll try to illustrate the point.

Events over a period time, occurring to the same unit might include the situation where the unit which has a 58% chance of winning the melee fails to do so 18 melees in a row. The chance of that happening is a little less than 1 in 6 million (if I recall millennia ago maths lessons).

Event occurring simultaneously might be the situation I suffered recently, where a tight game, late on, with a small advantage to me, collapsed in a single turn because my opponent rallied almost all of his units eligible to rally. Not only those routing, but also those disrupted and fragmented, and then to add salt to the wound, he also won every single impact and melee on his turn, even those where the probability of that was highly unlikely. A tight game turned into a disastrous loss as a result of outlandish luck. Has that ever happened on a real battlefield? I’ll have to leave that question to the historians, but it certainly never happened in any of the limited number of battles I am aware of.

There often seems to be a disparity between the probabilities reported by the game and the results seen on the field of battle, but I say seems for good reason. I am beginning to suspect that the fault may lie not in the game mechanics (although we can still argue over the likelihood of any particular event occurring), so much as the fallibility of computers' random number generators hitting irregular patches.

I don’t know how this weakness can be overcome, unless there’s a way the game could create some novel technique to create a genuinely random number. I expect if that was possible whoever was responsible would become very rich. Beyond my ability, sadly.

So perhaps it’s not me who suffers ill fortune in war, perhaps it’s my computer. I’ve read many computer reviews, detailing many technical specifications, unfortunately luck has never been included amongst them.


Best Wishes

Mike

This is the concept of independence of the events in probability theory : if 12 planes are to crash throughout a year, the probability that they crash the same day is the same as any other order, such as one plane crashes each month or ten crash in June and two in December.

Yet ppl's mind often tends to link these independent events.

(edit)
I did not notice Richard replied before me...

Most planes crashed occur in March and April, because they are not random events, there are other forces acting upon them. I'm not splitting hairs here, the point is that in FoG, these are not random events either, they are events generated with influences which should have a significant impact on the outcome. In either case, though, given all possible outcomes, the set of ordered outcomes is a very small subset of the total. People often tend to find patterns in these things because they are looking too hard.

If your coincidence is based on the fact all plane crashes involved aircraft where the integer of the square root of their registration numbers eqauled the cube root of the sum of the passengers ages, then you're probably looking too hard, and with that kind of effort will always find a pattern no matter how random the events. If on the other hand your coincidence is based on the fact all the pilots were alcoholics, you might be onto something.


Best Wishes

Mike

[Athos1660]

I think my argument is probably misplaced, because it's not really the probability of an event occurring in isolation that bugs me, and I expect that might be true of others too, but the clustering of such events. If an event is very unlikely, then clearly it will still occur (hopefully rarely), but when there is a string of unlikely events, either occurring simultaneously (or nearly so) or over time but associated with an individual unit, that's what causes distress.

That's probably not very clear, so I'll try to illustrate the point.

Events over a period time, occurring to the same unit might include the situation where the unit which has a 58% chance of winning the melee fails to do so 18 melees in a row. The chance of that happening is a little less than 1 in 6 million (if I recall millennia ago maths lessons).

Event occurring simultaneously might be the situation I suffered recently, where a tight game, late on, with a small advantage to me, collapsed in a single turn because my opponent rallied almost all of his units eligible to rally. Not only those routing, but also those disrupted and fragmented, and then to add salt to the wound, he also won every single impact and melee on his turn, even those where the probability of that was highly unlikely. A tight game turned into a disastrous loss as a result of outlandish luck. Has that ever happened on a real battlefield? I’ll have to leave that question to the historians, but it certainly never happened in any of the limited number of battles I am aware of.

There often seems to be a disparity between the probabilities reported by the game and the results seen on the field of battle, but I say seems for good reason. I am beginning to suspect that the fault may lie not in the game mechanics (although we can still argue over the likelihood of any particular event occurring), so much as the fallibility of computers' random number generators hitting irregular patches.

I don’t know how this weakness can be overcome, unless there’s a way the game could create some novel technique to create a genuinely random number. I expect if that was possible whoever was responsible would become very rich. Beyond my ability, sadly.

So perhaps it’s not me who suffers ill fortune in war, perhaps it’s my computer. I’ve read many computer reviews, detailing many technical specifications, unfortunately luck has never been included amongst them.


Best Wishes

Mike

This is the concept of independence of the events in probability theory : if 12 planes are to crash throughout a year, the probability that they crash the same day is the same as any other order, such as one plane crashes each month or ten crash in June and two in December.

Yet ppl's mind often tends to link these independent events.

(edit)
I did not notice Richard replied before me...

Most planes crashed occur in March and April, because they are not random events, there are other forces acting upon them. I'm not splitting hairs here, the point is that in FoG, these are not random events either, they are events generated with influences which should have a significant impact on the outcome. In either case, though, given all possible outcomes, the set of ordered outcomes is a very small subset of the total. People often tend to find patterns in these things because they are looking too hard.

If your coincidence is based on the fact all plane crashes involved aircraft where the integer of the square root of their registration numbers eqauled the cube root of the sum of the passengers ages, then you're probably looking too hard, and with that kind of effort will always find a pattern no matter how random the events. If on the other hand your coincidence is based on the fact all the pilots were alcoholics, you might be onto something.


Best Wishes

Mike

Events in FoG2 are independent. The events you are talking about in your post and that I commented (such as 'my opponent rallied almost all of his units eligible to rally.') are independent, ie the fact that unit 1 rallies has no effect on unit 2 rallying or not.

(edit)
And the fact that plane number 1 crashes in Chile has no effect on the crash of plane number 2 in Spain, in this probability theory. Those 2 events (crashes) are independent. That's what 'independent events' means.

That's why the probability of their crashes the same day is the same as the probability of any other order.

And the probability that unit 1 and unit 2 rally at the same time in game is the same as unit 1 rallying during turn 3 and unit 2 during turn 8.

Likewise, the result of a roll of the dice has no effect on the following one.

Independent events means that two (or more) events are not dependent on one another. It does not mean that each event have no cause (such as "alcoholic pilots" as you wrote).

(edit 2)

Poisson, mentioned by Richard, is talking about the same thing as me, probability of independent events : "The Poisson process provides a description of random independent events occurring with uniform probability through time or space (or both). (Wiki)"

[Cunningcairn]

I know of two offhand.

Thanks for answering Mike. The Magnesia example isn't exactly what I was referring to as there was "friendly interference" in the rally. However that aside, it still only gives 2 examples over a period of approximately 1800 years. And that is the point. The probability of it happening was exceptionally low.

While I tend to agree, I think this is a bold statement just because Mike only listed 2 examples. I don't think Mike really was stating this was all, it was just 2 offhand, and I don't suppose all the examples in history are either documented (with accuracy) or that anyone would know of them all if they were documented.

You are correct my response wasn't well thought out. My thinking had been that no-one in the group has ever given an answer and yet are quick to reference things on other points hence it didn't happen that often. I still don't think it did and believe the issue is being avoided by distraction purely because the change isn't wanted.

[Cunningcairn]

I think my argument is probably misplaced, because it's not really the probability of an event occurring in isolation that bugs me, and I expect that might be true of others too, but the clustering of such events. If an event is very unlikely, then clearly it will still occur (hopefully rarely), but when there is a string of unlikely events, either occurring simultaneously (or nearly so) or over time but associated with an individual unit, that's what causes distress.

That's probably not very clear, so I'll try to illustrate the point.

Events over a period time, occurring to the same unit might include the situation where the unit which has a 58% chance of winning the melee fails to do so 18 melees in a row. The chance of that happening is a little less than 1 in 6 million (if I recall millennia ago maths lessons).

Event occurring simultaneously might be the situation I suffered recently, where a tight game, late on, with a small advantage to me, collapsed in a single turn because my opponent rallied almost all of his units eligible to rally. Not only those routing, but also those disrupted and fragmented, and then to add salt to the wound, he also won every single impact and melee on his turn, even those where the probability of that was highly unlikely. A tight game turned into a disastrous loss as a result of outlandish luck. Has that ever happened on a real battlefield? I’ll have to leave that question to the historians, but it certainly never happened in any of the limited number of battles I am aware of.

There often seems to be a disparity between the probabilities reported by the game and the results seen on the field of battle, but I say seems for good reason. I am beginning to suspect that the fault may lie not in the game mechanics (although we can still argue over the likelihood of any particular event occurring), so much as the fallibility of computers' random number generators hitting irregular patches.

I don’t know how this weakness can be overcome, unless there’s a way the game could create some novel technique to create a genuinely random number. I expect if that was possible whoever was responsible would become very rich. Beyond my ability, sadly.

So perhaps it’s not me who suffers ill fortune in war, perhaps it’s my computer. I’ve read many computer reviews, detailing many technical specifications, unfortunately luck has never been included amongst them.


Best Wishes

Mike

This is the concept of independence of the events in probability theory : if 12 planes are to crash throughout a year, the probability that they crash the same day is the same as any other order, such as one plane crashes each month or ten crash in June and two in December.

Yet ppl's mind often tends to link these independent events.

(edit)
I did not notice Richard replied before me...

Most planes crashed occur in March and April, because they are not random events, there are other forces acting upon them. I'm not splitting hairs here, the point is that in FoG, these are not random events either, they are events generated with influences which should have a significant impact on the outcome. In either case, though, given all possible outcomes, the set of ordered outcomes is a very small subset of the total. People often tend to find patterns in these things because they are looking too hard.

If your coincidence is based on the fact all plane crashes involved aircraft where the integer of the square root of their registration numbers eqauled the cube root of the sum of the passengers ages, then you're probably looking too hard, and with that kind of effort will always find a pattern no matter how random the events. If on the other hand your coincidence is based on the fact all the pilots were alcoholics, you might be onto something.


Best Wishes

Mike

Mike all that has been said is obviously true with regards statistical phenomena. The phenomena that you experience would not be that noticeable if the probability of the events occurring was lower. (oops) The underlying problem remains that the probability attributed to certain events is too high. Play the mod as the clumping phenomena has not occurred but in saying that I don't believe enough games have been played to be certain.

[desicat]

3) Lack of tactical steps to prevent rallying, or re-rout the Fragmented enemy if it occurs. (Skirmishers. Light Horse!)

I will stick a post-it with this tip on my screen.
Always saying to myself : don't let the routed enemy at ease.
Yet always keeping my light troops near the main melee.

Always chase and harass Broken Elephant units - always!

[MikeC_81]

Mike all that has been said is obviously true with regards statistical phenomena. The phenomena that you experience would not be that noticeable if the probability of the events occurring was higher. The underlying problem remains that the probability attributed to certain events is too high. Play the mod as the clumping phenomena has not occurred but in saying that I don't believe enough games have been played to be certain.

Let's be more precise in our wording so we don't keep talking past each other, yes? Why is this an "underlying problem"? No one has yet managed to make the case that it is a "problem".

If it isn't a problem then you have a game mechanic preference issue which isn't so much a problem as you want the game to do something else due to taste. This isn't a concrete issue like a clear mathematical discrepancy in point costing or closing up ZoC loopholes in existing rules. This is a game design issue and if RBS is firm on this, you should respect that and stop making it out like it is anything other what it is. We all have things we don't like about the game. Schweet and Pete are making a cool mod and you seem to have played it quite a bit and enjoy it. That is cool too and when the Mod tournament starts, if everyone flocks to that instead of Vanilla then great. If not, then oh well.

[paulmcneil]

Same impossible series happen to me too;
i think, after several try, disparity between the probability reported by game and real result, found is trouble in conversione from percentage number (58% ie), in d6 RNG simulation

Normal RNG system applied linear probability, BUT, when need to add 2 roll for result, and the second is dipendent for success from first, need to apply DIPENDENT Event Probability Formule.
Sorry, but my english is not good for this level of treath … but math works !

Tratmot (Cosimo)

I've found that paying much notice to the predictions of combat outcome is very similar to someone telling a six foot man that it's safe to wade across a river because it's only four feet deep on average. (Metric measurements are also available).

[Cunningcairn]

Mike all that has been said is obviously true with regards statistical phenomena. The phenomena that you experience would not be that noticeable if the probability of the events occurring was higher. The underlying problem remains that the probability attributed to certain events is too high. Play the mod as the clumping phenomena has not occurred but in saying that I don't believe enough games have been played to be certain.

Let's be more precise in our wording so we don't keep talking past each other, yes? Why is this an "underlying problem"? No one has yet managed to make the case that it is a "problem".

If it isn't a problem then you have a game mechanic preference issue which isn't so much a problem as you want the game to do something else due to taste. This isn't a concrete issue like a clear mathematical discrepancy in point costing or closing up ZoC loopholes in existing rules. This is a game design issue and if RBS is firm on this, you should respect that and stop making it out like it is anything other what it is. We all have things we don't like about the game. Schweet and Pete are making a cool mod and you seem to have played it quite a bit and enjoy it. That is cool too and when the Mod tournament starts, if everyone flocks to that instead of Vanilla then great. If not, then oh well.

Mike I realise I can create a bit of confusion with my wording. I am not driven by frustration but rather a desire to improve a situation that no-one has been able to convince me is not without flaw and that can be corrected. I have the utmost respect for RBS and what he has created. I have been a faithful follower of his work from the beginning of my time as a wargamer. However that will not stop me saying something when I think it isn't quite kosher. You understand that what is being discussed here is more complex than the posts make it out to be. That is one of the reasons I have focused mainly on discussing feel rather than the mechanics of what is happening with respect to accepted understandings of ancient combat. When statistics are brought into the discussion we all tend to drift off what the issue actually is. It does become tiresome to hear the same old responses regurgitated every time anything that might change the rules is brought up when it is absolutely not relevant. Snugglebunny, and this not an attack on him in any way, posted a few posts saying that he had just finished playing X number of games and that he had only had Y number of rallies. At the same time he posted this I was recording an average of 3 rallies per turn in the 4 games I was playing and logging. To be more accurate these rallies were logged in the end phase of battles where I had routed large number of troops. In one of these games my opponent had conceded yet 5 turns later won the game. There is a greater frustration out there than is realised because a lot of players cannot be bothered even visiting the forum let alone commenting. The mods do remove a lot of the perceived issues being discussed at the moment. I don't want to argue about this as there is no need. The proof is there for everyone to try. Finally I don't think anyone wants this to be a competition between the vanilla and the mod and if push came to shove I would support vanilla if I thought it was splitting the community.

[Cunningcairn]

Mike all that has been said is obviously true with regards statistical phenomena. The phenomena that you experience would not be that noticeable if the probability of the events occurring was higher. The underlying problem remains that the probability attributed to certain events is too high. Play the mod as the clumping phenomena has not occurred but in saying that I don't believe enough games have been played to be certain.

Let's be more precise in our wording so we don't keep talking past each other, yes? Why is this an "underlying problem"? No one has yet managed to make the case that it is a "problem".

If it isn't a problem then you have a game mechanic preference issue which isn't so much a problem as you want the game to do something else due to taste. This isn't a concrete issue like a clear mathematical discrepancy in point costing or closing up ZoC loopholes in existing rules. This is a game design issue and if RBS is firm on this, you should respect that and stop making it out like it is anything other what it is. We all have things we don't like about the game. Schweet and Pete are making a cool mod and you seem to have played it quite a bit and enjoy it. That is cool too and when the Mod tournament starts, if everyone flocks to that instead of Vanilla then great. If not, then oh well.

Now to answer your question. The underlying problem is the problem that events that should be extremely rare are occurring very frequently. Making the case for stating a fact? What has been said is what has happened. The standard answer after the initial derogatory remarks implying the complainant is fabricating the story is that it is statistical clumping or some other statistical phenomena. That is extremely rude and uncalled for. There are many here that understand statistics, maths and many other things. Yes I fully understand that these events have not been experienced by everyone as yet but it is happening to many players. None of us know how many games are being played by players complaining or defending the issue so to argue about it is a statistical nonsense. What is real is a number of players who play a lot of games are experiencing these issues. If nothing is going to be done about that is fine until a new player raises the issue again. We then go through the same cycle again and again and again. I am now tired of it and Mike I really don't have anything against you and don't want to argue with you. You have done great things for the game and I have much respect for that. Join the league again and let's leave the conflict for the FOG battlefield.

[stockwellpete]

. . . and when the Mod tournament starts, if everyone flocks to that instead of Vanilla then great. If not, then oh well.

That's not going to happen. The mod is not being set up to challenge the vanilla game, it is just offering an alternative for those who are ready to try something a bit different every now and then. I will not be organising any separate tournaments with the mod and all my focus will be on running the vanilla FOG2DL and KO Tournaments. Hopefully, anyone who decides to set up a small tournament using the mod will time it so that it mostly takes place in the gaps between the FOG2DL seasons (i.e. in January, May and September).

[Swuul]

What is real is a number of players who play a lot of games are experiencing these issues.

How much is a lot of games? I don't know how many games I've played, but according to Steam I have played 333 hours. Probably not a lot then, as to the best of my knowledge, I have never witnessed 3 or 4 broken units rally on same turn. I can not even remember any game where 4 broken units would have rallied during the whole game. Statistically, if none of the four units are low strength and they each have 3 rounds to attempt to rally and they all are average or better quality and none of them are a general, that should happen in aprox 0.4% of the games, ie once in 250 games you should expect to see it about once. Doesn't mean it doesn't happen, it is bound to happen in some of the thousands of matches played.

And in the tens of thousands of matches played, there are going to be matches were four broken units rally on same turn, even though the possibility for that gets astronomically low. But to have it happen twice in row in two games, well, the odds for that is something that would fuel the infinite improbability drive for quite the leaps.

[Cunningcairn]

What is real is a number of players who play a lot of games are experiencing these issues.

How much is a lot of games? I don't know how many games I've played, but according to Steam I have played 333 hours. Probably not a lot then, as to the best of my knowledge, I have never witnessed 3 or 4 broken units rally on same turn. I can not even remember any game where 4 broken units would have rallied during the whole game. Statistically, if none of the four units are low strength and they each have 3 rounds to attempt to rally and they all are average or better quality and none of them are a general, that should happen in aprox 0.4% of the games, ie once in 250 games you should expect to see it about once. Doesn't mean it doesn't happen, it is bound to happen in some of the thousands of matches played.

And in the tens of thousands of matches played, there are going to be matches were four broken units rally on same turn, even though the possibility for that gets astronomically low. But to have it happen twice in row in two games, well, the odds for that is something that would fuel the infinite improbability drive for quite the leaps.

Embarrassingly according to Steam I've played 6,647 hours I think I need a break LOL! I don't ever switch the game off when I'm not playing so maybe that isn't game time. I don't know how they measure time played.

[rbodleyscott]

What is real is a number of players who play a lot of games are experiencing these issues.

How much is a lot of games? I don't know how many games I've played, but according to Steam I have played 333 hours. Probably not a lot then, as to the best of my knowledge, I have never witnessed 3 or 4 broken units rally on same turn. I can not even remember any game where 4 broken units would have rallied during the whole game. Statistically, if none of the four units are low strength and they each have 3 rounds to attempt to rally and they all are average or better quality and none of them are a general, that should happen in aprox 0.4% of the games, ie once in 250 games you should expect to see it about once. Doesn't mean it doesn't happen, it is bound to happen in some of the thousands of matches played.

And in the tens of thousands of matches played, there are going to be matches were four broken units rally on same turn, even though the possibility for that gets astronomically low. But to have it happen twice in row in two games, well, the odds for that is something that would fuel the infinite improbability drive for quite the leaps.

Embarrassingly according to Steam I've played 6,647 hours I think I need a break LOL! I don't ever switch the game off when I'm not playing so maybe that isn't game time. I don't know how they measure time played.

I don't think they do. I am fairly sure they just record the time the game is open in STEAM. Much of my 2,000 hours on Skyrim was down to leaving the game on when I was AFK/asleep. (Or so I tell my wife).

[Athos1660]

3) Lack of tactical steps to prevent rallying, or re-rout the Fragmented enemy if it occurs. (Skirmishers. Light Horse!)

I will stick a post-it with this tip on my screen.
Always saying to myself : don't let the routed enemy at ease.
Yet always keeping my light troops near the main melee.

Always chase and harass Broken Elephant units - always!

Yes, you won’t want to see them coming back

In Pike and shot, ammunition are unlimited (no ‘5 turns’) and light troop shooting is quite powerful, so I’m used to supporting my non-light troops in melee with their shooting at unengaged enemy non-light troops and of course also to using them to re-rout the Fragmented enemy (which is something artillery can also handle).

In FoG2, light foot have limited ammunition, are often more numerous and artillery is rarer in the currently implemented armies. So, indeed, it makes even more sense to use (some or all your) Light troops to harass routed enemy units.

The FoG/P&S series offers interesting variations in tactical uses of the same unit type, depending on the period. So each period has its own flavour.