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Hello tacticians.
I have recently started collecting Orks, and I was going through the codex and analysing some units with a bit of quick mental mathhammer to assess their expected performance against GEQ, MEQ, TEQ, etc.
Obviously, when dealing with larger numbers of dice, you can reasonably expect to make closer to the expected average rolls. With fewer rolls, the likelihood of rolling terribly or excellently increases.

For example, unexpectedly fluffing a save for 3 terminators in round 1 is not outside the realms of possibility, and will probably deflate your overall strategy somewhat. On the other hand, rolling armour to save 30 orks, you are very likely to have 3-7 models left afterwards, and even when the result deviates more, it really isn't going to be different enough from the average to make a huge difference to the game.

The fewer dice you roll, the more likely the outcome will differ significantly from the expected outcome.

What I'm saying is, is that a hoard player can generally expect their rolls to conform to the expected result more, purely because they are rolling more dice. Therefore their tactical decisions based on those expectations should also be more sound. A hoarde player can play with more confidence that their realistic plan with come to fruition.

On the other hand, we've all seen that one monsterous creature who died feebly when stroked with a sharp stick, and we all know that one time when that monsterous creature just would not go down no matter what was thrown at it.

I'd wager that many, many games are decided on the lucky/unlucky rolls of an elite, low model count army player, rather than the skill and good decisions of both players.

This also makes the game more exciting and dramatic in the later rounds, as there are fewer models and dice involved, and you are more likely to see dramatically 'good' or 'bad' rolls.

This may all seem obvious, but only just occurred to me

Does anyone have any thoughts to add?

Yep, that's right - as the dice pool gets bigger, the closer you can expect it to be to the mean expected value. That means that things like resolving the shooting attacks of a horde of 30 shoota boyz is usually pretty "reliable".

You can still get screwed on single-source dice rolls, like assault distance (which doesn't have a big dice pool).

Hordes are not about rolls and kills. We're about board controle and area denial. Killin' is just some secondary stuff.

That is somewhat true but in return the basic assumption of your models being in range is less true. For example when looking at the damage a 10 model SM TAC unit does on various targets you can assume all 10 models will get within range to shoot and be right most of the time. However when you look at a 30+ model unit this assumption becomes much less true as you will almost certainly have 25% or more of a unit of 30 either out of range or dead. The same issues exist for claiming cover saves, melee piling in, etc.

Hmm some thought on your maths and so forth;

Your determination of poor rolls and excellent rolls is a little off, well maybe not off, but im having a hard time to put it into words what I want to say, so il try with the math

Yes 5 GKT's could all roll 1's and die, 30 boys could all roll 6's and live..........But the average says...... 1 GKT will fail and that 6 boys shall live.

However, by rolling more dice you aren't increasing the chance of rolling the statistical average per say, As a dice doesn't have an average roll. you roll a value between 1-6, and each has an equal chance to roll each value. To some extent you are removing the Extreme rolls, but only by the fact that the extreme rolls are covered by the other non-extreme rolls. umm let me give an example:

Rolling 2 dice, I get double 1's. Damn! just lost my 2 termies.
Rolling 4 dice, 1 get double 1's and then a 3 and a 6. Just lost 2 termies but I saved the other 2! technically you have still rolled those extremes, but they have been hidden by the fact you rolled 4 dice.

Another example:
30 boys roll 30 dice, now with 30 dice, each with 6 values, thats a stupidly large amount of different combinations possible, however, the chances of each and every combination is exactly the same. IE; the chance to roll 30 -1's, the chance to roll 30 -6's or the chance for 15 -2s and 15 -6's is the same. As each roll is indepedant with respect to each other roll.

But saying that; it is the fact that you reduce the chance of extreme rolls simply by increasing the number of rolls you make.As each roll is a chance to negate all the rolls being bad. You aren't statistically better off- but you are better off in the sense that your rolls mean less within the context of 40k. typically losing 6 boys =/= losing 1 GKT as other factors other than saves come into play with stat allocation and pts cost of each model.

So what I will say is; even with squads of 20 boys in wagons, I have seen some pretty extreme rolling Both ways.

The other day I multicharged and needed 2 boys in B2B to keep me in combat for his turn while the others stayed out and I destroyed his tank with the nob, however, those 2 boys went a little overboard, each made 2-3 hits 2-3 wounds and killed like 4 or 5 of his dudes overall, he promptly fell back and shot me to pieces Or the opposite and by far the best; when your lootas pump out 3 shots each and you find that with a squad of 15 you managed something absurd like 30+ hits on a BS of 2

The problem with horde armies like Orks is that they reach the enemy front ranks in different waves, mostly three or so.
This especially holds if the enemy plays a refused flank.
Then you rolls much less dice. Some enemies can deal with Orks in this way.

All I'll say is that I see a great, great divide in this game between the models that are supposed to be crappy and the models that are supposed to be good. There are numerous ways to defeat the strengths of the higher quality models and cover up the weaknesses of the lesser quality ones (numerous ways to get Fearless, give ATSKNF to a blob squad, have good cover saves, etc). The orks probably have the least of this benefit, but the Green Tide is still a fairly unpleasant customer to deal with as far as pure model count goes.

A 4 point model can be as good as a 14 point model in many situations, but the same is not true the other way in practical play.

Something I just thought about:
An elitist list with say 6 models, invisibility, 2+,3++ or so forth... Vs say equal points in boys.

In terms of luck; it only requires the elitist list to make 1-2 rolls above average; lets say for example they took 12 wounds, technically 2 wounds should be applied by statistics, yet he saves all of them. In this case, he has already off-set himself by quite a margin, as in order for you to make that back you may need to make something along the lines of 12 saves on a 5+. Which is in reality much much much more unlikely.
Therefore, the elitist list has a much higher chance of securing the 'win' through the fact that 1-2 lucky turns results in an off-set the enemy simply cannot make back. However, in the same boat, they could roll those 1's and its all over.

But imo, if they were to lose, they would simply credit it down to bad luck, yet if they won it would be tactical prowess


Another analogy;
an elitist list is much more likely to go 5-1 in game wins, crediting the loss to when they just kept rolling ones - they have an extreme variation between win and lose that is down to a few dice rolling 'bad'.

Whereas, the horde is much more likely to go 1-5 in those loses, but to actually have stood a better chance of turning the game around - as a few bad rolls can be counteracted by slightly better than average rolls over more dice.

Solar Shock wrote:

However, by rolling more dice you aren't increasing the chance of rolling the statistical average per say, As a dice doesn't have an average roll. you roll a value between 1-6, and each has an equal chance to roll each value. To some extent you are removing the Extreme rolls, but only by the fact that the extreme rolls are covered by the other non-extreme rolls. umm let me give an example:

Rolling 2 dice, I get double 1's. Damn! just lost my 2 termies.
Rolling 4 dice, 1 get double 1's and then a 3 and a 6. Just lost 2 termies but I saved the other 2! technically you have still rolled those extremes, but they have been hidden by the fact you rolled 4 dice.

Gonna have to disagree with you based on sampling distributions. A die does not have an average roll when its outcome isn't applied to anything, but based on the game mechanics you will always have an average outcome when rolling wounds (or hits, whatever). A die may have equal chance of landing on 1-6, but you have a 2/3 chance of saving that marine's precious gene-seed.

Rolling 2 dice and getting double 1's is definitely one extreme. However, rolling 4 dice and still getting double ones (while the others are greater than 1) may have a similar outcome in the game, but statistically speaking these two rolls are significantly different.

The more dice you roll the closer you will be to the statistical average. This is fact. 30 saves on my marines should net 10 wounds and 20 armor saves. However, if you pick up 30 dice right now you will probably not get that same result. But statistically this is what will happen if you roll the that particular sample size over and over again, as opposed to a random number of marines dying/living each roll.

Yes, although there is an 'average' result, often your chance of hitting that average exactly is still pretty low.

Average total of one die is actually 3.5, but that is nonsense as you can't possibly get exactly that result, and all outcomes are equally as likely.

Average total on two dice is 7, and you have a 1/6 chance of getting that.

The chance of getting exactly the expected average roll increases with the number of dice rolled. (As someone else already pointed out)

The point I was making is that there's getting the expected average, there's deviating a nominal amount from the expected average, and then there's deviating hugely from the expected average to a degree that it affects the outcome of the game in a significant way.

When rolling few dice, you have a:
Low chance of getting exactly the expected average,
A large chance of deviating a nominal amount from the expected average,
A not-unlikely chance of deviating hugely from the expected average.

When rolling many dice, you have a:
Not-unlikely chance of getting exactly the expected average,
An excellent chance of deviating a nominal amount from the expected average,
A negligible chance of deviating hugely from the expected average.

Elite, low dice count armies are therefore more likely to swing a game based on lucky or unlucky rolls than a hoarde army.


As a separate point, this also got me thinking about being lucky or unlucky rolling saves.
Unlucky (single wound) models that fail saves and are removed from the game and obviously have no further effect on the game from that one unlucky roll onwards. Lucky models that make saves continue to be active and have the chance to be lucky again and again for the rest of the game.

I think this is part of what makes FNP, re-animation protocol, it will not die, etc. so crazy-good, because it gives you that second chance to negate an unlucky roll with more dice to try to bring you back to the statistical average.

If you're lucky and make all your saves, the story ends there and your models carry on as if nothing happened.
If you're unlucky and fail all your saves, you get a chance to adjust back towards the statistical average by rolling more dice with FNP.

So being especially lucky (deviating a lot from the expected average) doesn't get corrected with an additional roll.
Being especially unlucky (also deviating a lot from the expected average) gets corrected somewhat by the additional roll.

FNP is bad luck insurance.

I am now boring myself, so I'll stop.

 UnadoptedPuppy wrote:

Gonna have to disagree with you based on sampling distributions. A die does not have an average roll when its outcome isn't applied to anything, but based on the game mechanics you will always have an average outcome when rolling wounds (or hits, whatever). A die may have equal chance of landing on 1-6, but you have a 2/3 chance of saving that marine's precious gene-seed.

Rolling 2 dice and getting double 1's is definitely one extreme. However, rolling 4 dice and still getting double ones (while the others are greater than 1) may have a similar outcome in the game, but statistically speaking these two rolls are significantly different.

The more dice you roll the closer you will be to the statistical average. This is fact. 30 saves on my marines should net 10 wounds and 20 armor saves. However, if you pick up 30 dice right now you will probably not get that same result. But statistically this is what will happen if you roll the that particular sample size over and over again, as opposed to a random number of marines dying/living each roll.

Hmm i get what your saying, but im not convinced, lemme have a check, i was rushing it due to being at work.

Chance of rolling 1 on 1 dice = 1/6
Chance of rolling a 1 on 2 dice is 2/6 as each chance in this case is added, as your only looking to get a singular 1, if the first is a 1 you dont care about the second roll. However, in 40k you care about every individual dice. Therefore are they not independent?

So lets try a reasonable sample, 4 dice.
with a 4+ being what you want, that means each dice has a 50/50 chance.
first dice is 1/2,
second is 1/2
third is 1/2
fourth is 1/2.

On average you should get 2 4+'s. But your chance of getting a 4+ with each dice remains the same, you roll, you have 50/50, but you get a 1, you roll again, but you still get a 2, now at this point your saying it is statistically more likely that now you will get 4+? Why? when you roll that next dice its still 50/50, you get a 2, you roll again its 50/50 you get a 3. you've just rolled 4 dice of which your chances of getting what you needed we 50/50, but you didn't get anything.

Think of flipping a coin, you could flip it forever and only get heads, each time you get a heads it doesn't make it more likely to get a tails. Yes on average of 100 flips you 'should' get 50 heads and 50 tails, but thats statistics, not reality. Im not disagreeing that with a huge sample size you will roll statistically to the average; you will roll and even number of every side, but there isn't an average on a single dice. Yes with a marine you have 2/3rds chance to save him, so twice as likely to save, but rolling 6 individual dice will still have the same chance for each marine to die; 1/3.

However, if your rolling 2 dice to get a resultant thats different, as there are numbers more likely to come up due to more combinations that result in them.



Automatically Appended Next Post:

 pocketcanoe wrote:
Yes, although there is an 'average' result, often your chance of hitting that average exactly is still pretty low.

Average total of one die is actually 3.5, but that is nonsense as you can't possibly get exactly that result, and all outcomes are equally as likely.

The chance of getting exactly the expected average roll increases with the number of dice rolled. (As someone else already pointed out)

why does the chance of getting the average increase with each roll? how are your dice affecting each other?
and agree about your lucky unlucky stuff
was thinking bout that today also, which was your fault btw

Lists that contain deathstars basically rely on this 'lucky' to remain in game,and therefore do more idea. for example imagine a 6+ warboss who just saved like 8 AP2 attacks through them rolling 1's to wound. Technically he should be dead, but his PK just removed half your deathstar. In that instance of luck he has not only avoided losing X amount of points (his worth), but he has also returned the amount of points he killed and those points now cant make any more points back either.

basically they use luck to boost themselves ahead in the game and then continue to hold that lead, which increases the more times they get lucky and kill more than they should have been able to.

Yes, dice rolls are independent of each other, but if you roll 4 dice, you are more likely to roll 2 between 1-3 and 2 between 4-6 than you are to roll all 4 between 1-3.

It's to do with the number of possible combinations that the dice can come up with together.

When you roll 4 dice, getting 4 ones is unlikely because there is only one combination which could give this result (rolling a one on every die)

1111

Getting three 1s and a 2 is four times more likely because there are 4 different combinations that can give this result:
2111
1211
1121
1112

So it doesn't matter which die shows the 2 as long as the end result is three 1s and one 2.

When throwing four 4+ armour saves, the most likely result (because it is the result with the most possible combinations) is to pass 2 and fail 2.

The individual dice rolls are independent, but what matters is the number of possible combinations they can show after they have all been rolled.

As I said above, if you roll to charge on 2 dice, 7" is the result with the most possible combinations, and therefore it is the most likely result. Being the most likely result doesn't mean you are likely to get it though, as there is still only a1/6 chance of rolling exactly 7" to charge. You are much more likely to manage a 10-11" charge on 3 dice and even more likely to roll a 14" charge on 4 dice (not that that is likely to come up )




Regarding luck, how about this:

I roll a d6, passing on a 4+. If I pass, I get to roll again.
I have a 50-50 chance to stop after one roll, but if I pass the first roll, I'm back to 50-50 to continue even further.
It would not be outside the realms of possibility to go on for 5-6 rounds, but not if I don't pass that first roll.
(If I was passing on a 2+, I might get lucky and get to 18 rounds)

Then I roll 100 dice simultaneously, passing on a 4+.
I'm very likely to lose around half in round one, be down to around a quarter in round two and I'll be very likely down to a single die after 5-7 rounds. That single final die might stop there, or it might go on alone for an additional 4-5 rounds! So that one lucky die could conceivably pass a 50-50 test 10 times in a row! (If passing on a 2+, this could go on for a very long time )

 pocketcanoe wrote:


Snip

You are certainly correct I thought hard about it and the difference is how we are considering each roll and to some extent I think both apply. I certainly got what you were saying and i hope i wasnt coming across like i was trying to prove you wrong, I just like to get to the bottom of things Returning to your original topic

Reliability - are you interested in game winning reliability? or overall reliability?

As for me, I am starting to think that deathstars are more reliable at 'winning' games but overall are less reliable.
Whereas; hordes are less reliable at winning but more reliable overall.

So with a deathstar, you reduce the amount of dice rolling normally to a few dice that seem to do alot with each roll. Therefore each roll is more heavily weighted. Il try a math example.
*generic deathstar* is rolling 10 dice, each dice is worth a value of 4. they hit on 4+, so average would be they get 5 hits, so a value of 20. But for every one that is above average thet get +4.
*generic horde* is rolling 40 dice, each value worth 1. they hit on a 4+ so average of 20 again but for everyone above average its only +1, so they need 4 above average to match a deathstar 1 above average.

To me, in terms of game winning ability,the deathstar seems more reliable, as lets say we have an invisible 2+ dude whom you wound on a 4+. So you need 6's to hit, so 6 dice to get 1 hit. 4+ to wound so 2 hits to get 1 wound, thats then 12 dice. Then you need a 1 to kill, so thats 6 wounds; which is 12 hits which is 72 dice.
With those 72 dice you should statisitcally kill him, but you've only forced him to take 6 saves, to me it seems much more reliable that he will roll better than statistical average due to rolling so few dice. Compared with a horde who would often be rolling lots of saves and therefore even when they roll better than statistical average it has less of an impact.
- So to me the deathstar here seems more reliable at using the advantage it gets from 'good' rolls.

whereas, the horde is more reliable overall, as its likely over the course of a game that you will have balanced out any bad rolls with good rolls. Something that is much harder in a deathstar, your either wrecking face, or being tabled

But im not too sure, as like with what you said before, each one saved from a death he should have statistically got is then technically making an impact on the game still, even though he should be dead Which is definitely the strength of FNP and RP.

what ya think?

Larger sample sizes do actually make it "more likely to get approximately average rolls". But it's way more complicated than that.

I think the issue is that probability is really hard for us to understand. So we do things like "if I have make 6 saves for terminators, on average one of them should die". However, exactly one of them will die only 26.8% of the time. The other nearly 3/4 of the time, something other than exactly one of them dying will occur. More over, approximately 2/3 (66.5%) of the time, ONE OR MORE of them will bite it.

My favorite example of this break down of understanding came from explaining why the advanced targeting array is totally worth it on a dual plasma crisis suit. Every time it's in double tap range, it actually has a 1/2 (51.8%) chance of scoring a precision shot. IMHO, totally worth 3 points to drop in the back field and target heavy weapon squads.

You can give a set of rolls maximum reliability by avoiding having to roll altogether. Hitting automatically or negating cover or armour saves removes good and bad luck.

Having said that, you are then relying on fewer dice rolls to give you a result, so again, potential deviation from what is expected increases.

My head hurts.

As a wise man once said, "30 Orks might beat 10 Marines. 100 Orks almost guarantee it."

I would state that the math of the game will always be there to impress some players in to some form of play style or another.

Luck being what it is, some folks can roll their dice really well when it is 1 die at a time. Whether it is from skill of dropping the die from the right height, at the right spin, to get the desired result. This is a main concern for folks who like to run "low dice count" armies. Whether it is called luck, proper dice rolling techniques, or blatant cheating in certain situations. One can not ignore how a person throws their die/dice into the equation.

Life is never lived inside a vaccum environment.

 DarknessEternal wrote:
As a wise man once said, "30 Orks might beat 10 Marines. 100 Orks almost guarantee it."

This is sadly, very true. :p There have been times a 20 Boy squad can wipe out a 10 Marine squad even after loses. Other times, it takes two waves to do it. Damn dice. :p


Automatically Appended Next Post:

SYKOJAK wrote:
I would state that the math of the game will always be there to impress some players in to some form of play style or another.

Luck being what it is, some folks can roll their dice really well when it is 1 die at a time. Whether it is from skill of dropping the die from the right height, at the right spin, to get the desired result. This is a main concern for folks who like to run "low dice count" armies. Whether it is called luck, proper dice rolling techniques, or blatant cheating in certain situations. One can not ignore how a person throws their die/dice into the equation.

Life is never lived inside a vaccum environment.

Pro Ork Dice Rolling

1. Get a bucket.
2. Put dice in bucket.
3. Shake violently while shouting.
4. Dump dice into a kiddie pool.
5. Be sad/excited at the results.

:p

Solar Shock wrote:

Chance of rolling a 1 on 2 dice is 2/6 as each chance in this case is added, as your only looking to get a singular 1, if the first is a 1 you dont care about the second roll. However, in 40k you care about every individual dice. Therefore are they not independent?

Your math is incorrect. The chance of rolling snake eyes is 1/36.
You are correct, the two saves are independent of each other (your first save does not effect your second save) as all dice rolls are, which is why the probabilities are multiplied together.
(1/6)*(1/6) = 1/36

As for the '4 dice, 4+' example you are again correct. The chance of each individual die is 50/50. The total outcome is also 50/50. As before, each roll is independent of each other. Failing a save does not increase the chances of passing a save. That being said, on average you will save 2 and fail 2. So after failing the first two you can expect to pass the second two based on your statistical average, but the 50/50 probability remains.

why does the chance of getting the average increase with each roll? how are your dice affecting each other?

The chance of getting the average does not increase with each roll. The average is, technically, the most common roll. Therefore, the more you roll a particular sample size, the more you will see results close to the average.

Think about rolling two dice (and adding the sum).
7 is the most common roll, while double 1's/12's is the least common.
If you roll two dice a bunch of times how often do you think double 1's/12's will occur compared to 7's?

I hope this is somewhat clear (or not redundant from other posts), finals are numbing my brain a bit.