Slitherine

stockwellpete wrote: ↑Mon Mar 18, 2019 6:57 pm

rbodleyscott wrote: ↑Mon Mar 18, 2019 6:52 pm
Yes, and it would be much more memorable than the larger number of occasions when this did not occur.

The nature of random events is that they are random - i.e. they are not evenly spread. Sometimes there will be more than the average number of fringe results, sometimes there will be less.

I know you know this already, but it needs to be said for anyone who is under the delusion that there is something wrong when fringe events clump.

Yes, OK. Accepted.

Is there any merit in the idea that when war bands fight other war bands that they should really cancel each other out rather than having a higher likelihood of double-dropping? How would making a change like this impact on the rest of the game? It would be negligible, wouldn't it?

Apart from being a (probably unwarranted) exception.

An alternative would be to change one's expectations.

Warbands are not supposed to behave like sturdy shieldwalls. These will come in the Dark Ages DLC, and they will have a much much lower chance of double dropping, because they will have +1 for being heavy foot, and no -1 for fighting impact foot.

From what you have previously told me, that is the style of warfare that you really wanted, and you only did the Warband vs Warband scenarios because the later period wasn't yet in the game.

you know guys, spreadsheets can calculators do exist....I feel like Commander Data......

Data! How long till Proxmia Centarui VII at Warp 9.32785498254987365486749847??? Well sir.....assuming no ....... gravimetric anomalies, subspace warp time rifts, spatial distortions and/or ROMULAN ATTACKS....

Anyways I misspoke for the Loose Order Warbands. It is ~4% chance (3.89% if want to be picky) to double drop for YOUR Warbands. The overall chance for SOMEONE's Warband (yours or your opponents') is double that at 7.78%. Sorry for any confusion.

Short answer for Heavy Foot Warbands head to head on Impact for your Warband to double drop - 14% x 16.67% (odds for an average unit testing at -2) = 2.33%. Double that for someone's Warband since they have an equal chance to lose combat.

Rember this is ON IMPACT and not subsequent melee rounds when the -1 from Impact Foot doesn't kick in. For any mirror match unit in melee, the odds of a double drop are 2.33% if not heavy foot (same as Heavy Foot + 1 is the same as taking away -1 from Impact), and Heavy Foot have like a 1% chance to double drop individually in melee.

Just so this isn't some sort of opaque MikeC magic math box, here is how you can very easily find out yourself.

Quick odds tables: Win/Draw/Loss for PoA differentials

0 PoA ~ 14/72/14
25 PoA ~ 20/70/10
50 PoA ~ 30/68/2
100 PoA ~ 49/50/1
150 PoA ~65/35/0
200 PoA ~ 80/20/0

A spreadsheet for odds can be found here:
https://ufile.io/1f0ii - Open office version
https://ufile.io/1ymw0 - Converted to Excel (no idea if anything breaks when I convert)

The odds to fail column represents the chance to fail on any given die roll requirement. To get the chance of a double drop, simply check the odds of failing on a 3 (and thus rolling 2) and then adjust down 1 row per -CT modifier.

The formula is very simple. %Chance to Lose x % Chance to double Drop = %chance for any given combat with those conditions producing a double drop for that unit. If it is a mirror match, simply multiply by 2. If you want to find out the total % chance to double drop for either side in asymmetric situations, simply add the two independent odds together (calculate each separately and add).

stockwellpete wrote: ↑Mon Mar 18, 2019 6:35 pm

MikeC_81 wrote: ↑Mon Mar 18, 2019 6:07 pm Loose Warbands going head to head will see one or the other double drop 4% of the time

Presumably the % is the same for close order war band units? So, on average, a double drop should happen once every 25 times in impacts between similar war band units?

In a 1200pts game between two war band armies you might expect there to be around 15 war bands on each side, which might result in around 20 or so impacts between them during the course of a battle. So, one such double drop in a battle would be about par for the course in this sort of match-up? And if a player suffered 3 or 4 double drops during the course of a battle, with a couple of them right at the start, then they might be entitled to feel that they are being a bit unlucky?

The odds of 15 vs 15 Loose Warbands NOT creating a single double drop if they all were to charge each other simultaneously in one turn, on that turn is = (1-0.0778) = 92.22% (represents the odds of any one of the 15 individual Warband engagements not producing a double drop. Raise 92.22% to the power of 15 (to represent the odds of this occuring 15 times in a row) = 29.67% for no double drops. What this means is that if you were to smash 15 Warbands against each other, only 1 in 3 times will there NOT be a double drop.

Heavy Warband numbers = 48.8% for there to be no double drops. Keep in mind this is not YOUR ODDS of not suffering a double drop, just the odds of SOMEONE not suffering a double drop. Your own odds of suffering no double drops are much higher (not exactly x 2 but close).

This is why I always tell people to HOLD RESERVES. As for whether they are justified to feel unlucky, I am not going to get into this with you again. Keep in mind these are numbers cherry-picked from impact foot vs each other, the worst case scneario for letting RNG run wild.

Anyways I misspoke for the Loose Order Warbands. It is ~4% chance (3.89% if want to be picky) to double drop for YOUR Warbands. The overall chance for SOMEONE's Warband (yours or your opponents') is double that at 7.78%. Sorry for any confusion.

Short answer for Heavy Foot Warbands head to head on Impact for your Warband to double drop - 14% x 16.67% (odds for an average unit testing at -2) = 2.33%. Double that for someone's Warband since they have an equal chance to lose combat.

Close Order Warband vs Close Order Warband should be the same as Loose Warband vs Loose Warband, because as of v1.0.2 Warband do not get the +1 CT modifier for being Heavy Foot.

They are deliberately more volatile than other Heavy Foot.

Which makes a discussion of "too many double drops" based on some of the intentionally most double-drop prone troops in the game, as if they were typical of the game in general, a bit moot,

Oh I forgot about that little rule change you made.

MikeC_81 wrote: ↑Mon Mar 18, 2019 7:43 pm Oh I forgot about that little rule change you made.

Is there a current table showing troop type modifiers and combat characteristics?

Sorry, but I am totally bewildered now. Maths is not my strongest subject. I wrote this earlier, which I assume is now wrong . . .

"Presumably the % is the same for close order war band units? So, on average, a double drop should happen once every 25 times in impacts between similar war band units?

In a 1200pts game between two war band armies you might expect there to be around 15 war bands on each side, which might result in around 20 or so impacts between them during the course of a battle. So, one such double drop in a battle would be about par for the course in this sort of match-up? And if a player suffered 3 or 4 double drops during the course of a battle, with a couple of them right at the start, then they might be entitled to feel that they are being a bit unlucky?"

So the real likelihood of double drops happening between war bands is roughly twice more likely than this? So it is around an 8% chance that one of the 2 war band units in a melee will double-drop on impact, or about once every 12 or 13 times. And in a 1200pts game between 2 war band armies you might expect 2 double drops on average to occur during the course of the battle?

Cunningcairn wrote: ↑Mon Mar 18, 2019 8:20 pm

MikeC_81 wrote: ↑Mon Mar 18, 2019 7:43 pm Oh I forgot about that little rule change you made.

Is there a current table showing troop type modifiers and combat characteristics?

No, just the .pdf manual and the PatchNotes file, which shows all changes.

rbodleyscott wrote: ↑Mon Mar 18, 2019 8:27 pm

Cunningcairn wrote: ↑Mon Mar 18, 2019 8:20 pm

MikeC_81 wrote: ↑Mon Mar 18, 2019 7:43 pm Oh I forgot about that little rule change you made.

Is there a current table showing troop type modifiers and combat characteristics?

No, just the .pdf manual and the PatchNotes file, which shows all changes.

Is one in the pipeline?

Cunningcairn wrote: ↑Mon Mar 18, 2019 8:28 pm

rbodleyscott wrote: ↑Mon Mar 18, 2019 8:27 pm

Cunningcairn wrote: ↑Mon Mar 18, 2019 8:20 pm

Is there a current table showing troop type modifiers and combat characteristics?

No, just the .pdf manual and the PatchNotes file, which shows all changes.

Is one in the pipeline?

We curently plan to update the .pdf manual for the next dlc but one.

stockwellpete wrote: ↑Mon Mar 18, 2019 8:24 pm "Presumably the % is the same for close order war band units? So, on average, a double drop should happen once every 25 times in impacts between similar war band units?

You shouldn't think of it in those terms of averages. That implies regularity of evenly spaced events which is not the case here. This is why people think RNG should produce predictable evenly spaced out events. This is what causes the guy a poker table to lose tons of money thinking that after all the bad luck, he is "due" for some good luck.

Instead You should think of 15 warbands charging 15 opposing warbands with each combat being a separate, independent, and distinct event. Each Warband combat that occurs does not affect the others. That means even if you suffered 4 double drops in a row, it doesn't mean the next one will, or indeed should, have any lower chance of it happening yet again. Your only confidence is that in the long run, you will have very few games where there are large numbers of catastrophic events and that the distribution of games with good luck/bad luck/neutral luck will conform with Standard Deviation.

So instead of saying a double drop should happen once every 25 impacts, it is better to say that over the course of 100 times when we ram 15 Warbands against each other, we can expect 29% of those cases to produce no double drops for either player. Over 70% of the time, either player will experience at least one double drop! Which is what drives me nuts when people say that they can't deal with "bad luck" double drops ruining their plans. If you were to smash Warbands head to head, double drops occurring should be the expected norm! Not the exception! Do you now see why I view arguments that say luck "ruined" their strategies or plans with such skepticism?

When players are making strategies that involve 15 Warbands vs 15 Warbands that do not anticipate a double drop occurring somewhere along the way, what they are in effect saying is that they will choose to believe that this upcoming game will fall into the category of games which occur only 29% of the time. Would you make plans or strategies that work only 29% of the time??? Or would you make plans that will work for the games that occur 71% of the time???

rbodleyscott wrote: ↑Mon Mar 18, 2019 6:52 pm The nature of random events is that they are random - i.e. they are not evenly spread. Sometimes there will be more than the average number of fringe results, sometimes there will be less.

I know you know this already, but it needs to be said for anyone who is under the delusion that there is something wrong when fringe events clump.

While I'm well aware of the nature of random events, in this game (Very Large), I've now had eleven close order warbands double-break, and my opponent, well, zero, nada, zilch (presumably because when virtually every one of my units double-break, his do not have an opportunity to do so). There are all straight up fights in the open, generally with roughly even odds. It is really kind of unbelievable.

It also seems odd that all of the results in Pete's tournament were so lopsided--if the double-breaks were randomly distributed between both sides, you would expect the effect to be roughly the same, and therefore games to be closer, and yet they were not.

I'm not sure that I've ever played a game where only 4% of units (1 in 25!) double-broke; in most Very Large battles I'll have 3-5 units double-break (I'm ignoring double-breaks for skirmishers).

So feel free to call me delusional but in my view something does not seem right.

MikeC_81 wrote: ↑Mon Mar 18, 2019 8:55 pm If you were to smash Warbands head to head, double drops occurring should be the expected norm! Not the exception! Do you now see why I view arguments that say luck "ruined" their strategies or plans with such skepticism?

Of course some double-drops are to be expected, but shouldn't they happen to both sides? And isn't it a bit hard to anticipate that 11 of 15 units would double-break, and none of the opponents? Luck's not playing a significant role here?

MikeC_81 wrote: ↑Mon Mar 18, 2019 8:55 pm When players are making strategies that involve 15 Warbands vs 15 Warbands that do not anticipate a double drop occurring somewhere along the way, what they are in effect saying is that they will choose to believe that this upcoming game will fall into the category of games which occur only 29% of the time. Would you make plans or strategies that work only 29% of the time??? Or would you make plans that will work for the games that occur 71% of the time???

Um, but no one is expressing surprise that "double drops occur somewhere along the way"--what does seem odd is how often they seem to occur.

I realize that these sample sizes are rather small, but to just dismiss all this as several runs of bad luck seems a bit cavalier.

76mm wrote: ↑Mon Mar 18, 2019 9:02 pm

rbodleyscott wrote: ↑Mon Mar 18, 2019 6:52 pm The nature of random events is that they are random - i.e. they are not evenly spread. Sometimes there will be more than the average number of fringe results, sometimes there will be less.

I know you know this already, but it needs to be said for anyone who is under the delusion that there is something wrong when fringe events clump.

While I'm well aware of the nature of random events, in this game (Very Large), I've now had eleven close order warbands double-break, and my opponent, well, zero, nada, zilch (presumably because when virtually every one of my units double-break, his do not have an opportunity to do so). There are all straight up fights in the open, generally with roughly even odds. It is really kind of unbelievable.

It also seems odd that all of the results in Pete's tournament were so lopsided--if the double-breaks were randomly distributed between both sides, you would expect the effect to be roughly the same, and therefore games to be closer, and yet they were not.

I'm not sure that I've ever played a game where only 4% of units (1 in 25!) double-broke; in most Very Large battles I'll have 3-5 units double-break (I'm ignoring double-breaks for skirmishers).

So feel free to call me delusional but in my view something does not seem right.

I agree fully and I also understand probability! I regularly ( I'd venture always) when using warband have more than 4% with double drops. Has anyone tested the RNG? To say you should always have reserves is pretty obvious but what is also obvious is that when you use the warband armies against armies with vastly more units you have a choice of using your few units to fight or be a reserve or protect your flanks but you certainly don't have the numbers to do all of them. Very large battles however do negate the dominance of armies with mass of medium foot bulking units.

MikeC_81 wrote: ↑Mon Mar 18, 2019 8:55 pm You shouldn't think of it in those terms of averages. That implies regularity of evenly spaced events which is not the case here. This is why people think RNG should produce predictable evenly spaced out events. This is what causes the guy a poker table to lose tons of money thinking that after all the bad luck, he is "due" for some good luck.

I understand this. I am not expecting predictable evenly spaced results.

Instead You should think of 15 warbands charging 15 opposing warbands with each combat being a separate, independent, and distinct event. Each Warband combat that occurs does not affect the others. That means even if you suffered 4 double drops in a row, it doesn't mean the next one will, or indeed should, have any lower chance of it happening yet again. Your only confidence is that in the long run, you will have very few games where there are large numbers of catastrophic events and that the distribution of games with good luck/bad luck/neutral luck will conform with Standard Deviation.

Yes, I understand this.

So instead of saying a double drop should happen once every 25 impacts, it is better to say that over the course of 100 times when we ram 15 Warbands against each other, we can expect 29% of those cases to produce no double drops for either player. Over 70% of the time, either player will experience at least one double drop! Which is what drives me nuts when people say that they can't deal with "bad luck" double drops ruining their plans. If you were to smash Warbands head to head, double drops occurring should be the expected norm! Not the exception! Do you now see why I view arguments that say luck "ruined" their strategies or plans with such skepticism?

When players are making strategies that involve 15 Warbands vs 15 Warbands that do not anticipate a double drop occurring somewhere along the way, what they are in effect saying is that they will choose to believe that this upcoming game will fall into the category of games which occur only 29% of the time. Would you make plans or strategies that work only 29% of the time??? Or would you make plans that will work for the games that occur 71% of the time???

I understand this as well. But the point is that in many games I play one player gets all the double drops and the other player hardly gets any. Sometimes this works in my favour and sometimes it doesn't.

I have just down a test game against the AI on Legate difficulty - Anglo-Saxons versus Anglo-Saxons. Of the 10 impact combats between close order war bands, 3 resulted in a unit fragmenting and 2 resulted in disrupts. In the two impact combats between close order war bands with a general there was one fragmented unit. One of the frags was suffered by me and 3 were suffered by the AI. Not a single AI unit rallied throughout the game despite the fact I won the game 53-16 and was about 30-0 ahead at one stage.

There were also 2 bizarre incidents - my close order war band unit with general routed a fragmented close order war band unit with a big win (numbers came up in red) but my general died in the melee. My unit passed its CT, but then pursued the routing unit and charged another enemy unit, a steady close order war band unit and was disrupted on impact. What are the odds on that happening?

Then, another of my close order war band units with general routed a fragmented enemy war band, pursued it, charged into the flank of a disrupted enemy war band unit, routed it, then pursued again and charged a third war band unit and disrupted it. This unit then fell back. What are the odds of that happening?

Overall, the RNG was very kind to me in this game - and if I had been playing instead of the AI against another player and had all this happen I would have felt very hard done by indeed.

stockwellpete wrote: ↑Mon Mar 18, 2019 9:35 pm I understand this as well. But the point is that in many games I play one player gets all the double drops and the other player hardly gets any. Sometimes this works in my favour and sometimes it doesn't.

That is not often is what gets complained about though. "Woe betides me, my master plan fell through when x event happened". I also don't know what "many" means. 1 in 10? 1 in 20? There is also the skill element to consider. You can actively make your opponent test more often, at worse odds. They can do the same to you. Their actions can shift the expected standard distribution of events in or against your favour.

Really the only argument to be made here is either:

a) RBS's code is bad and the RNG number generator is not working as intended and is creating far more edge case results than the Standard Distribution of the Cohesion Test function should produce.

b) RBS's code is working but you disagree with how the function is distributing luck-based events and is causing luck to drive events in the game rather than player action (skill).


My response to that is

a) This is a possibility and can be verified through rigorous testing in a sterile environment. Create a scenario with 15 warbands vs 15 warbands with nothing else. Then you and a friend start multiple PBEM games and only play the impact round (since maybe the PBEM uses a different RNG generator from single player) with this scenario and thoroughly catalogue the results and submit the results here. If the CT code is bad or the RNG code is bad, it will become apparent very quickly when you report back the results whether something is wrong or not.

b) This also a possibility but is exceedingly unlikely. If this was true it would be almost impossible for players like Pantherboy and Ruskicanuck among others to consistently post very good results. It would also be unlikely for individuals to have risen in the ranks from Div E in some cases to Div A or B play continuously like some have done throughout the 3 preceding and soon to be the 4th season. Instead, results would be scattered far more randomly.

76mm wrote: ↑Mon Mar 18, 2019 9:09 pm

MikeC_81 wrote: ↑Mon Mar 18, 2019 8:55 pm If you were to smash Warbands head to head, double drops occurring should be the expected norm! Not the exception! Do you now see why I view arguments that say luck "ruined" their strategies or plans with such skepticism?

Of course some double-drops are to be expected, but shouldn't they happen to both sides? And isn't it a bit hard to anticipate that 11 of 15 units would double-break, and none of the opponents? Luck's not playing a significant role here?

Once again, in any given game with RNG, nothing 'should' or 'shouldn't' happen. RNG only gives you the events that will/did happen. Within the realm of Standard Distribution of events, you will have some games where 11 of 15 units double break. If you play long enough, you will have some games where 15 of 15 units will double break. Conversely, you will at some point experience the walkover scenario where you do nothing and your opponent crumbles. But Standard Distribution says that those games are rare. In fact, they are exceedingly so. As I showed you, 4 of your units double dropping in a row with no outside factors, is roughly a 1 in 400,000 event. The vast majority of games will not have those extreme circumstances occurring.

rbodleyscott wrote: ↑Mon Mar 18, 2019 7:25 pm Warbands are not supposed to behave like sturdy shieldwalls. These will come in the Dark Ages DLC, and they will have a much much lower chance of double dropping, because they will have +1 for being heavy foot, and no -1 for fighting impact foot.

From what you have previously told me, that is the style of warfare that you really wanted, and you only did the Warband vs Warband scenarios because the later period wasn't yet in the game.

Hang on. Do different units have different penalties for fighting impact foot?

What units currently are the best at resisting Impact Foot? I feel like my list has been Elephants and Lancers on the defense. I used to think pikes had a decent chance until some lowly Loose Order Warbands frontally routed two average pikes in an impact + melee, during my current game with devoncop. Having two cheaper units easily rout two expensive units in the terrain that naturally suits the pikes is.........concerning. Sure, other impacts + melee went alright for other average pikes (better cohesion rolls), but I'm now fairly spooked about losing my expensive pikes to cheaper warbands.

stockwellpete wrote: ↑Mon Mar 18, 2019 8:24 pm Sorry, but I am totally bewildered now. Maths is not my strongest subject. I wrote this earlier, which I assume is now wrong . . .

"Presumably the % is the same for close order war band units? So, on average, a double drop should happen once every 25 times in impacts between similar war band units?

Probability should not be interpreted like this.

If you say 4% is something once every 25 times, how about changing it to twice every 50 trials, or four times every 100 trials? They all give you the same probability.

Using "four times every 100 trials" case, you may have 4 "bad events" at the very start of these 100, i.e., 4 in your first 25. But you can't say "oh it shouldn't happen that a lot" because if you play 100 turns, none "bad events" may come out after that 4 "bad events". It also could be that you have none "bad events" in your first 25 trials, when you expect it "should" happen once. We all need to think twice on our intuition.

Probability distribution tells you the odds in the long run. Same as expectation. It is also an average on the long run. In math, we shall say that long run means t -> infinity.

The relatively high odds of untouched warbands double dropping cohesion on first impact sounds a bit rough for multiplayer but other than that I don't think reducing the probability of double cohesion drops would be beneficial to the game. Skill is still by far bigger factor than RNG in FoG2 battles (and ultimately RNG is equally unfair to everyone).

If you look at historical battles, some "unpredictable" pursuits and cohesion losses are nothing out of ordinary. Ancient and medieval warfare (or any warfare really) wasn't predictable or micro-managed by the commander most of the time. Reducing the range or deviation of the random element would not improve the authenticity of the game. For almost every "unlikely" outcome you have in game there is an even more unbelievable historical example.

Countless important battles through history have been won or lost due to half of the army chasing after a fleeing enemy while the rest of the battle was still in progress, only to be routed as they were looting the enemy camp; or when the entire cavalry element of the army under general decides to completely ignore their direct orders and attack the enemy unsupported. Sometimes the morale of the army could be crushed by a false rumours of general having died or the battle going badly. FoG2 doesn't even begin to model stuff like half of the army deserting because they already got enough loot or don't feel like attacking a well positioned enemy; or simply marching off the field in the middle of the most important battle of the century because the "sub-general" had some family grudge with the "C-in-C". It's definitely not a game of chess.

melm wrote: ↑Mon Mar 18, 2019 11:23 pm

stockwellpete wrote: ↑Mon Mar 18, 2019 8:24 pm Sorry, but I am totally bewildered now. Maths is not my strongest subject. I wrote this earlier, which I assume is now wrong . . .

"Presumably the % is the same for close order war band units? So, on average, a double drop should happen once every 25 times in impacts between similar war band units?

Probability should not be interpreted like this.

If you say 4% is something once every 25 times, how about changing it to twice every 50 trials, or four times every 100 trials? They all give you the same probability.

Using "four times every 100 trials" case, you may have 4 "bad events" at the very start of these 100, i.e., 4 in your first 25. But you can't say "oh it shouldn't happen that a lot" because if you play 100 turns, none "bad events" may come out after that 4 "bad events". It also could be that you have none "bad events" in your first 25 trials, when you expect it "should" happen once. We all need to think twice on our intuition.

Probability distribution tells you the odds in the long run. Same as expectation. It is also an average on the long run. In math, we shall say that long run means t -> infinity.

I think that most players understand probability ratios. A number of players including myself are getting numbers far greater than 4% though. I'm not bemoaning bad luck as the percentage of double drops is a percentage of double drops for the number of combats for both sides and should not be counted for just one side. In an earlier post someone, I don't remember who, got about 30% during testing. If this the case then either their is a bug in the combat resolution code or the RNG is not functioning correctly.