Probability Calculation

[JohnD]

Hoping someone can help figure this out, my brain is more than a little sleep deprived.

If I have an event that has a 14% chance of occurring every time I generate a random result, then across 100 rolls, this event should occur 14 times. With a small sample size, maybe a few more or a few less. Correct?

Then what is the likelihood/probability of said event not occurring even once over said 100 random results?

[shadzar]

a 1 in 7 change of something happening not happening after 100 tries?

without the math, the chance of it not happening is very low says probability, however statistics is a different story. it could statistically happen 0 times or 100 times, which isnt very probable.

[Bidmaron]

2.82e-7. Highly unlikely

[dulux-oz]

The trouble is, 100 is a very small sample size (not withstanding previous posters calculations).

We were taught at University (3rd year Statistics) that while a truly random sample size of about 32 can give a statistical result with an error margin of only plus/minus 5%, you really need sample sizes in the 1,000s to 10,000s to generate statistically significant results with errors of only 1% or less.

So while Bidmaron is correct in saying its highly unlikely, its still possible for the result obtained to be correct.

However, I'd like to know more about how the 14% chance was determined in the first place, and how the 100 results were generated, and based on those two answers I'd be looking at some sort of biases, such as imperfect dice, bad maths, human error, or something similar.

John?

[damned]

Dice dont give a toss about history.
They dont care what the previous roll was.
They dont care what any of the previous rolls were.
When they roll they only worry about their own roll.

If you roll a d6 100x and dont get a single 6, the next time you roll a d6 there is still an 83% chance you wont get a 6.

[JohnD]

Yeah so, I'm leading towards a misrepresentation of the percentages.

All I have is a claim that probability of A is 14%. Not A is 86%. Either A or Not A happen on every generation of a result. There is no insight nor information on how the "random" outcomes are generated.

In response to inquiries I'm told the probability is actually just 2.8%, which is contradicted by the initial verbiage stating 14%, verbiage which is strangely no longer available (shocking). At the moved goalposts rate, it certainly is very believable that for example you could roll d100 100 times and not get any results of say 4, 29 or 85.

Going on history, I'm inclined to assume a willful misrepresentation of the odds, especially since the verbiage has been removed now.

Nothing to do with FG, just thought there are a lot of knowledgeable people here who probably unlike me have slept since Monday. Thanks guys. :)

[dulux-oz]

Yeah so, I'm leading towards a misrepresentation of the percentages.

All I have is a claim that probability of A is 14%. Not A is 86%. Either A or Not A happen on every generation of a result. There is no insight nor information on how the "random" outcomes are generated.

In response to inquiries I'm told the probability is actually just 2.8%, which is contradicted by the initial verbiage stating 14%, verbiage which is strangely no longer available (shocking). At the moved goalposts rate, it certainly is very believable that for example you could roll d100 100 times and not get any results of say 4, 29 or 85.

Going on history, I'm inclined to assume a willful misrepresentation of the odds, especially since the verbiage has been removed now.

Nothing to do with FG, just thought there are a lot of knowledgeable people here who probably unlike me have slept since Monday. Thanks guys. :)

Intriguing - I would love to know more, but its cool if nothing more could (or should) be said :)

Have a good one, John - and maybe get some sleep? :p

[shadzar]

Dice dont give a toss about history.

sounds like something Andrew Clay would have said during one of his shows. :D

[Bidmaron]

The probability in 100 rolls is .86 to the 100th power, which is how I arrived at that tiny *** number I previously posted.

[damned]

By my calculations not rolling 3 specific numbers out of 100 in 100 rolls is very close to 5%.
Not unreasonable odds.

[Bidmaron]

Sorry, damned but you are wrong. It is .0000282%. Fundamental probabaility. If the odds of an event are x then the odds of not having the event are 1-x. The odds of an event happening EVERY TIME (in this case the event not happening every time) is always x raised to the power of the number of iterations. Thus the answer is (1-x)^n. In this case, x is .14 and n is 100.

[damned]

lets keep it simple.
we have 100 possible numbers that could be rolled.
we have in this case 3 numbers that didnt get rolled.
there is a 97% chance that you wont roll those three numbers.

now before you argue you will see that my math is exactly the same as yours.

[Bidmaron]

Damned there is no context for that. What three numbers are you talking about? The OP said only 14%. There is nothing about 3 rolls. What am I missing? He asks what is the probability after 100 events of not once getting an event that has a 14% probability of occurring. You must be a mind reader or know some back context because my answer is math fact for what was originally asked.

[shadzar]

he is going off post 6 where the goalposts were moved.

[Bidmaron]

Oh, well, dropping it since it doesn't seem the poster can put together a cogent scenario he wants to examine. Sleep deprivation does funny things....

[Trenloe]

Sleep deprivation does funny things....
No, that's just John! ;)

[JohnD]

No, that's just John! ;)

Indeed. :)

[2bfjs]

On the subject of probability, what is the effect of Advantage and Disadvantage in D&D 5e? My calculations indicate when an 18 or greater is required to hit 15% probability of success, with Disadvantage 2.25% probability, and with Advantage 27.25%. What are your opinions on how best to handle converting adventures from previous editions to 5e with regard to game balance and Advantage/Disadvantage or is it not a factor to consider?

[Trenloe]

What are your opinions on how best to handle converting adventures from previous editions to 5e with regard to game balance and Advantage/Disadvantage or is it not a factor to consider?
It's part of the 5E rules used for playing 5E, I wouldn't consider it too much of a factor when converting from older systems. The main thing to consider is that 5E (mostly) uses the advantage/disadvantage mechanic instead of specific numerical modifiers ) there are some exceptions, but in general adv/dis is used instead of a specific modifier to d20 rolls. If you feel some previous version ability would be better served rolling with advantage or disadvantage, then go with that. Otherwise, I'd recommend not spending to much time converting old ruleset "stuff" - find an equivalent 5E NPC, ability, etc. and use that - with appropriate modification to fit the aim and flavour of the original.

[shadzar]

also, none of the old SoD will work with 5e due to death saves.
there is tons more that 5e doesn't account for that can be seen in Tales From the Yawning Portal, where the adventures just don't work with 5e since 5e is designed around being super heroes of the world to begin with, rather than being common-folk that just happen to be adventuring.

You basically have to consider that 5e is D&D in name only. Tomb of Horrors can still be deadly due to insta-death things like Petrification that bypasses Death Saves. So the odds of converting would be like said during 3.0, you just recreate things with the closest approximation to what you had with 2nd and just go with it.

Better to rewrite the whole adventure for 5e than to just try to convert a few things due to the assumptions of older editions and newer editions.

think about things that didn't exist:
perception checks
all the other skills
any feats

then find out what the older edition adventure was trying to do and emulate that with NPCs, monsters, traps, environs, etc as best you can with 5e.

there is 100% chance, that just plugging in the same named things between 5e and an older edition will yield less than wanted results.

[2bfjs]

Thank you both. Shadzar's words, "find out what the older edition adventure was trying to do" describes my current approach. I have to also agree playing 5e lacks the edge. I made death saves in all 3 latest sessions as PC and still alive (not a very good player). As GM my players expect a high-risk tension and I haven't moved to 5e.

[LordEntrails]

Agreed, convert by feel/intent/etc. There are numerous blogs that agree with this approach and give even more details. The Angry GM is one that comes to mind, but the "GM Advice" thread has more as well.

As for tension and high-risk, such is easily achieved in 5E by simple using many of the optional rules that are in the DMG.