A beginners guide to statistics in AA50.

Ive read so many horrible ways people judge theyre odds in this game lately so i will make a short guide to it so people hopefully can understand how it works.
First let us do a quick example.
If you throw a dice (1d6) you will get a number from 16, each of those have the odds 1/6 to appear or 16.67% chance.
Now what is the odds of getting a 1 in 2 throws in a row (Rolling 2d1:
(1, 1) )?
I have the feeling a lot in here would say 16.67%, this is ofcourse wrong.Reason is that first you throw one time, odds for it hitting a 1 is then 16.67%, but if you want it in the second throw aswell you have to make the assumption you also got it in the first. The way to calculate the odds for two throws in a row hitting a 1 would then be to multiply the odds from throw one, and throw two: 16.67% x 16.67% = (1/6) X (1/6) = 1/36 = 2.77%
Now over to AA50 odds:
A bit general odds:
Calculating odds of a battle with more units is highly complex as killed units are removed in every round someone score a hit. This makes it almost impossible to make a code that gives the exact odds for an attack. To counter this battlecalc constructors have used simulations of the actual combat you type in and give you an estimate for the odds. As you can see if you try the same battle in tripleA more times you will see a different result every time if the battle is semi complex like Karelia turn 1 attack of 3inf 1art 3fgt vs 5inf 1art. Also these battlecalcs only show the odds of winning the battle with 1 attacking unit surviving, it also says whats the most likely result of attacking units surviving but this is NOT what the odds are refering too. The odds stated refers to one unit surviving. The odds of more units surving will allways be lower then the odds of 1 unit survivng.
To calc the odds for 1 unit survivng the program runs the battle maybe 100 times. Then it adds up all the battles with 1, 2, 3…etc units survivng and dividing it by 100. And you then get an estimate for the odds that youre attack will survive.
Now over to more battles succeeding at once:
Sometimes in AA50 you are in the need off more then one attack succeeding at the same time, like if you hit the eastern front with Germany you want to take 3 territories for the bonus. So what you are interested in is the odds for ALL three attacks suceeding at the same time.
To calculate this you first need to determin the odds for each of the attacks individually, then as in the dice example over you need to multiply the odds for each off the three attacks to determin the attacks combined will succeed.
Now look on a German opening Turn 1.
Assault on Leningrad
 Take Karelia ( 3 infantry, 1 artillery, 3 fighters , cruiser/transport
Eastern front assault:  Take and Hold Baltic States ( 2 inf, 3 tanks )
 Take and Hold East Poland ( 1tank, 2 inf, 1 art )
 Take Ukraine ( 3inf, 1 art)
Navy assault  Sink UK battleship + transport ( 2 sub, 1 fighter )
Egypt assault  Attack Egypt with 1bmb, 2inf 1art 2arm
Odds for the attacks individual is then:
Assault on Leningrad 79.2% for wininng with at least 1unit surviving.
Assault on Baltic States 96.3% for at least 1 surving land unit a bit lower if you want odds for more to survive.
Assault on Eastern Poland 98.1% for at least 1 surving land unit a bit lower if you want odds for more to survive.
Assault on UKraine 94.4% for at least 1 surving land unit a bit lower if you want odds for more to survive.
Assault z2 84% for at least 1 surviving unit, dont care about the subs here so doesnt matter much
Assault on Egypt 75.3% for at least 1 surving land unit a bit lower if you want odds for more to survive.
Combined odds
Now to the interesting part, each of these attacks have no lower then 79.2%. Lets see what happens if we set as a demand that all 6 attacks have to suceed for us to have a successfull turn.Odds for all these 6 attacks will succeed in same game turn 1: 0.772 x 0.963 x 0.981 x 0.944 x 0.84 x 0.753 = 0.435 = 43.5%
As we can see we will only have a chance off 43.5% of these 6 attacks to succeed at the same time. If you are looking for a solid gameplan you would like to get the combined odds of MUST accomplish goals maybe up to 9095%. Though in some situations where the risk / reward ratio is great you might be willing to do an 20% individual odds attack, just becouse it wont hurt you much if you fail, but benefit you great if you succeed. In those cases you should NOT add that single attack into the multiplum you check to find if the must succeed attacks have high enough odds of succeeding for you to be willing to do it.
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Plz give me feedback on this guide, i would like to improve it so people wont start more threads based upon flawed statistics as im a geek who gets provoked by people using maths the wrong way to deffend theyre tactics or opinions. I might also add a paragraph about why this makes low luck a whole different game then dices in AA50 in the future, but that will have to wait.
Also english is not my native language so spelling errors do occur, and i would love if someone would help me correct it
 Take Karelia ( 3 infantry, 1 artillery, 3 fighters , cruiser/transport

Honestly I dont get a grip on your math.
You say if I roll 1 dice I have 16 % odds of success, but if I roll one extra dice I only got 2 % odds of success. What if I roll 3 or 4 dice in a row ? That would be 100 % odds of no success ? And you get provoced by flawed statistics and people who use math the wrong way ? ( had to edit last sentence)

Maybe it was bad explained. I was not talking about getting ONE hit one two dices, was talking about getting TWO hit on two dices.
Thats 16% for 1 hit on 1 dice (assuming you need a 1)
So for 2hits out of two, its 2,77%.The example is applicable to cases where you need to win 2 out of 2 battles to be successfull.

No offence Adler, but it was pretty clear to me!

I feel it would be worth saying how to calculate the odds of getting x hits out of y dice. I’ll use 2 dice having to land at a one as an example.
There are 2 possible ways to have one 1 showing. Die A is a 1 and Die B is something 26 or Die A is something 26 and Die B is a 1.
You then find the odds of each event happening.
Die A is a 1: 1/6 x 5/6 = 5/36
Die B is a 1: 5/6 x 1/6 = 5/36And you then add the two probabilities to find the total.
5/36 + 5/36 = 10/36 = 5/18 = 27.8% chance that you will land one hit.I hope this helps.

I will add that to the article if you allow Butcher, also will add that thats the probablilty for exactly 1 hit with two dices, and not for 1 or 2 hits. (for the not math educated that might be a bit blurry, not sure though)

Yeah, I guess I should have elaborated. You would just add the probability of 1 hit to the probability of 2 hits to find the probability of 1 or 2 hits.
For attacks that you need at least one hit out of x dice, you should just subtract the probability that you will get no hits from 1. For example, let’s say that 2 inf and 1 fig are attacking 1 inf.
Odds that the attackers miss all hits in 1st round: 5/6 x 5/6 x 1/2 = 25/72
1  25/72 = 47/72 = 65.3% chance the battle is over after the first round.
Subracting the odds of a miss from 1 can help speed up a FTF game.
And Pin, you can put anything I post in this thread in an article. I posted in it because it reminded me of my Government teacher, “For all you mathletes out there…”

One question I have that would love to see added to this would be if I am making 6 attacks at various odds, what are the odds of each outcome, for example, 50% win all 6, 70% win atleast 5, 85% win atleast 4, etc, or 50% of the time I will win all 6, 10% of the time I will win 5, etc. I’m guessing its a bit complicated.

It is a more complicated process.
Say the six battles have odds of 95%, 83%, 89%, 97%, 92%, and 80%.
To find the odds of all six, multiply them together
0.95 x 0.83 x 0.89 x 0.97 x 0.92 x 0.80 = 0.501 = 50.1%To find the odds of say, five battles working, you find the odds for every way the set of battles could go (there are six ways to win 5 battles out of the six)
0.05 x 0.83 x 0.89 x 0.97 x 0.92 x 0.80 = 0.026 = 2.6%
0.95 x 0.17 x 0.89 x 0.97 x 0.92 x 0.80 = 0.103 = 10.3%
0.95 x 0.83 x 0.11 x 0.97 x 0.92 x 0.80 = 0.062 = 6.2%
0.95 x 0.83 x 0.89 x 0.03 x 0.92 x 0.80 = 0.015 = 1.5%
0.95 x 0.83 x 0.89 x 0.97 x 0.08 x 0.80 = 0.044 = 4.4%
0.95 x 0.83 x 0.89 x 0.97 x 0.92 x 0.20 = 0.125 = 12.5%
So now you add the probabilities together
2.6% + 10.3% + 6.2% + 1.5% + 4.4% + 12.5% = 37.5%
That is the probability that you will win exactly 5 of your attacks.
To find the probability that you will win 5 or 6, you must add the probability of winning 5 to the probability of winning 6.
50.1% + 37.5% = 87.6%
You have an 87.6% chance of winning 5 or 6 of your attacks.

Thanks mate, because I feel that atleast for axis turn 1, that some risks should be taken, and was wondering what type of risks exactly were being taken.

Say the six battles have odds of 95%, 83%, 89%, 97%, 92%, and 80%.
To find the odds of all six, multiply them together
0.95 x 0.83 x 0.89 x 0.97 x 0.92 x 0.80 = 0.501 = 50.1%I love this, man
Lets say this is the 6 standard battles in Germany Turn 1.
If I do all 6 battles in G1, I will only have 50 % odd of success, right ?
So I split them, 3 battles in G1 and the other 3 battles in G2, right ?
G1 0.95 x 0.83 x 0.89 = 70 % odd of success
and
G2 0.97 x 0.92 x 0.80 = 71 % odd of successSo obvious it pays off to split all the attacks out over multiple turns, right ?

no it doesnt, if you still have a goal of having all 6 to succeed, then the odds is still 50.1%, as you need to multiply 70% and 71% to make sure both T1 and T2 succeeds.
But if you succeeded with the 3first in turn 1, then you have 71% chance of getting all 6 done by attacking the last 3 in T2.

You must end with one number when finding the odds of one outcome.
I cannot stress this enough. Breaking the attacks into two sets does not change anything. You will still be multiplying the same numbers together.
What you are looking at, Adler, is one outcome because you want all six to succeed.
And there is absolutely no coincidence to this resembling G1 attacks… :roll:

I feel it would be worth saying how to calculate the odds of getting x hits out of y dice. I’ll use 2 dice having to land at a one as an example.
There are 2 possible ways to have one 1 showing. Die A is a 1 and Die B is something 26 or Die A is something 26 and Die B is a 1.
You then find the odds of each event happening.
Die A is a 1: 1/6 x 5/6 = 5/36
Die B is a 1: 5/6 x 1/6 = 5/36And you then add the two probabilities to find the total.
5/6 + 5/6 = 10/36 = 5/18 = 27.8% chance that you will land one hit.I hope this helps.
Hey Butcher, thanks to you and Pin for the explanations  I’m not great on maths and you both have a good way of explaining this stuff. Just one thing to point out though is the typo above, I guess the probabilities being added at the bottom are actually 5/36 + 5/36 as opposed to the 5/6 you typed.
Just thought I would point this out as it had me scratching my head for quite a while before digging out my calculator and before I realised it was typo! I may not be the only one!

Yeah, it is supposed to be 5/36 + 5/36, and I have fixed it. Sorry for any confusion.

Yeah, it is supposed to be 5/36 + 5/36, and I have fixed it. Sorry for any confusion.
Yeah, now you have fixed it, but after I got confused

Also consider for a moment you are really discussing probability instead of odds (which are often interchanged despite they are different).
Probaility will give you a percentage of how often the event will occur given infinite rolls (example 16.67%). Odds will deal with possible chances for an event happening versus changes against. (example 1 in 6).
If you have 6 infantry attacking, you can expect 1 to hit for the 6 rolls but only use it as a guide line for you are rolling 6 dice one, not infinite times.
Another point to consider is the possible deviation (something I call the “wild”). It is the possibility of how many additional hits you might achieve. Example: The odds of 6 infantry attacking 2 armor will yield the same odds however, it is far more likely for the infantry to score many (a max possibility of 6) hits versus the armor (a max possibility of 2). This becomes especially poignant in larger battles.
I have played long enough to see the craziest outcomes that could not be repeated in over 100,000 rolls. Also consider it is your roll against their roll so the outcomes increase dramatically.

Anyone else get a big chuckle out of the fact that Pin’s example rolled two 1’s?! :lol: :lol:

Well, it is pretty likely given they were d1’s


I think this great for judging dices odds on ONE battle.
What is wrong with your strat exemple, or should I say MY strat, is that :
 It does not reflect in any way a lowluck setting in which context the strat was written
 It does not consider possibilities like straffing
 It does not consider the casulaties taken by the ennemy
 It does not consider the importance of each battle but rather try to multiply the sums of all moves as if each battles are equally important ( which is simply UNTRUE )
 It is based on triple A simulator
 It does not take in account the fact you CAN choose the order in which you do your battles. Calling off an attack after a failure somewhere else is possible. You can retreat when there is no point…
 Are you willin to take risks, if not, did you read the alternative plan?
My goal in that strat is simple, Take and Hold Karelia.
There is only 3 Battles in there that are MUST win and they must be resolved in THAT order.
Using low luck, I will use triple A calculator like you did. 1st : Sinking the BB/TR ( Pull out a sub, and send the bomber if you are too scared with 85%. It will be 100% )
 2nd: Taking Baltic States ( it’s 100% odds, not 96.3%… )
 3rd: Taking Leningrad 92% odds ( it’s not 79%, sim it again )
So anywhere between 78.2% to 92% odds of success…
Also let’s be clear, while you would try to round up your odds in thoses 3 battles to 92% by sending bomber on the BB, my bomber would go to Leningrad making it 100% instead and I’d risk the whole thing at 85% ( 100% x 100% x 85% ). Why? Because i’d resolve the sea battle first and already would have a clear idea either or not go the whole ten yards aka straffing or taking it.
Still, let’s take a look at WHY it is 100% win sending the bomber. Your Bomber, fighter and one sub fight against a BB. If we go by theses ‘‘statistics’’, the battle is at 9397% when in fact it’s 100% win Low luck. There is NO way around it.
Let’s do the “maths”: 4+3 = 7. That’s 1 automatic hit, and 1/6 for a possible second hit. PLUS 2/6 for the sub in yet another possible hit. Let’s say everything miss and the damaged BB hit back. The sub goes, another automatic hit goes in, the BB hit back again before sinking, the fighter goes. Worst case scenario, still 100% win.
Now, Why is Baltic States 100%? The fact is that in low luck you have a minimum and maximum number of hit you can do as well as the notion of automatic hits. 3 russian inf will invariably yield 1 hit vs the german 2 inf/3tanks. Even if you would not roll anything for germans and Russia would hit every round despite losses, it would go like this:
2inf/3tanks vs 3 inf
1inf/3tanks vs 2 inf
3tanks vs 1 inf
2 tanks win, worst case scenario.It’s not odds, it’s a SURE thing as far as winning. The odds are there to estimate how many losses you will sustain in the attack.
The strat was written in the context of low luck, so I will not debate it outside of the context.
Edited: typo and missed sentence.

Now, let’s not talk about low luck and especially NOT about my strat.
Let’s talk about dices:
Your overall multiplying odds method is still facing the following flaws:
 It consider all battles as equally important when they are not.
6 battles, one of these is really minor but at 50% , 2 are average ones you can lose at 75%, 3 are major ones in which one cannot be lost, all at 90%. If we take this method, we are at an overall 41%. Yet, the very word OVERALL does not makes any sense here.
 It does not consider possibilities like straffing or special stuff
Straffing is self explanatory, this is 0% odds to win, yet it’s a battle and an objective in itself to kill x ennemy units. Also, do your odds consider how a Battleship, a destroyer or sub abilities can mess a fight?. Does it consider both planes can be lost at sea on a sinking carrier? I don’t even scratch the surface here.
 It does not take in account the fact you CAN choose the order in which you do your battles.
When you are gambling on holding a territory but must cut down ennemy transport or possible counters, you resolve cutting the ennemy line to your objective first. Once you won that battle, you know what to do in your main battle. Even if that Main battle is at 90% odds and the sea battle at 85%, it becomes a whole 0% because even that sure win is a loss. So you can’t say bluntly it’s 76.5% odds. Also you can minimise your losses in that main battle since there is no point on taking it after losing sea battle.
 It’s based on triple A simulator.
We talking about dices here. Your odds are fine but the human factor cannot be factored in theses sims. In low luck, it does not really matter, but with dices comes the mythic word: Luck. Statistics or not, there is hardly anyone reckless enough to send several planes over an AA gun even if odds tell him only 1 plane should be lost… Octopus refers to it as the ‘‘Wild’’ and he is right, you CAN get several 1s. I seen 5 of theses once. The only roof to maximum hits is the number of dices rolled and that’s another story even if that Triple A simulator tells me it’s 100% win, you can still lose… You can miss all your attack regardless of number of dices and the ennemy can hit on all his own… That Triple A simulator does not factor theses remote things, 100% odds does not exist with dices, yet that sim gives you that.
All in all, my point is to take each battle separately. Multiplying odds of several battles with different importance, conducted in a different order and based upon a simulator that gives you 100% odds for dices roll without considering special factors is simply
wrong.

first of all this guide to statistics was NOT written for low luck, only reason i used youre attacks in it (and reason i didnt refere to youre strat) was that i couldnt be arsed to come up with a G1, calculate all the odds for it under dices to succeed and then use those numbers.
All the maths in this thread is correct, thats simply HOW maths works, no way getting around that fact. Its like claiming the world is round etc.

It consider all battles as equally important when they are not.

It does not consider possibilities like straffing or special stuff
Maths are just a tool to show you how to calculate the odds of whatever problem you are pondering about the odds for. IF you want to know what the odds on a combat round is combined you now have the tools for that. You also have the tools neccesary to calculate youre “main” attack, and youre “strafe” or high variance attacks individually.
Multiplying it all together just give you an indication of how how many times ALL attacks that YOU DECIDE to add into the equation will succeed. So for youre strategy you will only succeed with all the attacks in 45 of 100 German turn 1s. Other solid openings have a success rate off 90%. Again, this all demand that you play the game oob with regular dices.
 It does not take in account the fact you CAN choose the order in which you do your battles.
It is irrelevant to calculate odds AFTER the battle have occured. As you cant change the combat moves after the first dice have been thrown. Maths here is for learning the people who dont know how to use it to calculate theyre odds BEFORE they attack. Then they can split it up as listed earlier in this thread so they can see what theyre odds are AFTER 1st battle succeed, so they have a backup plan IF that first battle fails.
 It’s based on triple A simulator.
Its the best estimate for how dices will roll, as it would be much to time consuming to manually calculate every battles, would take hours for every battle bigger then 1unit vs 1unit.
 It does not consider the casulaties taken by the ennemy
It assume you take the worst deffensive units first as casualties and the worst attacking units as casualties, so it actually gives you an worst case scenario unless youre up against a retard that sack his best deffensive units in a battle thats not huge in his favor.
 It does not take in account the fact you CAN choose the order in which you do your battles. Calling off an attack after a failure somewhere else is possible. You can retreat when there is no point…
You have to do 1 battleround as long as the combat move have been declared. Its beside the point though, as you then will have failed the overall strategy as lined out above and havent reached the goals.
Its REACHING those goals you use Maths for. You use it to determin the odds reaching the goals YOU set youreself, if you feel a battle is of minor importance you skip the battle in the calculation as that would be a battle thats not crucial for the overall strategy to be successfull. For instance you could have a lone sub vs 3loaded cvs at sea, that would be a +ev attack, but it still wont have good odds, so i would not add it in my calculations for odds for that combat round.
Still, let’s take a look at WHY it is 100% win sending the bomber. Your Bomber, fighter and one sub fight against a BB. If we go by theses ‘‘statistics’’, the battle is at 9397% when in fact it’s 100% win Low luck. There is NO way around it.
Let’s do the “maths”: 4+3 = 7. That’s 1 automatic hit, and 1/6 for a possible second hit. PLUS 2/6 for the sub in yet another possible hit. Let’s say everything miss and the damaged BB hit back. The sub goes, another automatic hit goes in, the BB hit back again before sinking, the fighter goes. Worst case scenario, still 100% win.
In a oob setup with dices this is just utterly blatenly false, and just completely stupid. Again read the topic, this discussion is about using DICES
Thats the reason why playing LL and dices this game becomes two different games. Those attacks that might have 100% in low luck becomes lower with dices. So useing the odds from low luck to determin a winning strategy in a dice enviroment is just completely stupid, you have to use the odds the dices actually have to find it.
For a quick example go check out my tourney game in the tech tourney vs DemolitionMan. German 1 i failed BSt eventhough i had 100% in LL and 92% in dices. Thats what this guide is all about, understanding the differences between LL and dices AND learn how to calculate the true odds for an attack or a group of attacks in dice enviroment.
Now this thread have been derailed enough, start a new thread and i will answer you there if you still want to discuss things on the side of this topic.


Derailing your thread… wow…Then WHY the hell did you come yapping about your dices and statistics when you knew it was a low luck based strat? And THEN starts another thread STILL using my strat as an exemple and try prove it wrong, AGAIN talking about dices when it’s a low luck strat?
Let me tell it to you short, with dices you don’t say a 100% attack move on Caucasus and a 20% attack on Congo is an OVERALL strat of 20% odds… it’s two different battles with way different importance, one is at 100% and the other 20%. Caucasus WILL 100% likely get trough ( if we beleive what that triple A sim says) despite you multiplying by Congo’s 20% odds…
I’m not saying your odds per territory are wrong, I’m saying multiplying odds of different battles is WRONG and gives no relevent idindication whatsoever. Geez!? Multiply the odds of eating apples by the odds of eating oranges all you want, it will still be the same separate number of apples and oranges eaten at the end until you eatablish a common denominator, ex saying they are fruits.
You assume all battle worth the same, that a battle is a fixed value when it’s a different variable for each battle. Taking X and Y are different battles , you can’t determine odds until you determine X and Y value even if you know the odds.
How do you determine the value and importance of a battle? Thats up to you, let’s say for exemple sake you would do it on territory value as that common denominator and want to know how many ipcs you are likely to hold in the end of turn. It’s basic maths, (4 100%) * (120%) would at least tell you you have 100% chances to achieve 4.5 ipc of your objectives. Which means 4ipc sure and 20% chance for 1 more ipc. Now that’s a bit more relevant as an overall turn overview…
You could do that with units involved, how many you destroy or lose, and other variety of values for each battle but bluntly saying you just multiply all battle odds equally without considering the battles worth themselves makes no sense at all. Going around saying its ''how maths work ‘’ won’t change that fact.
P.S: Quoting: “a retard that sack his best deffensive units in a battle thats not huge in his favor”. I think you really need to lose a game against me, I’ll see if I can make the time…

up for a pbf game anytime with dices.
And the maths still stands, you just dont get the concept behind probability, and thats what this thread is about, not low luck, wich is designed to partially remove probability. Example would be 2arms attacking a territory, with LL youre 100% sure to take it vs 1inf. With dices youre not 100% anymore, and you dont have to play many games to actually experience that.
In a turn in AA you have a goal you want to achive, by adding the probabilities of the different battles you are doing you get the odds for the goal to be achieved. If the goal is to get the 3rd NO with a nation, you multiply the different attacks related to that and you get the odds you will have the 3rd NO after the turn. All the others reading this thread is grasping this concept, so it might be about time you get ure head out of the sand and read it again til you actually understand the concept of probability.