Author Topic: The definitive guide to Iterative Probability and IP Proofing Comments thread  (Read 8390 times)

Offline Zionpopsickle

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I'm sorry if I step on any toes but as a person with a physics, mathematics and philosophy background I wish to make some commentary upon this guide in the hopes of making the guide as effective as possible since I think the idea of how to handle Iterative Probability is very important in a game that is so reliant upon repetitious rolls of a dice.

1) I think a valuable inclusion would be a discussion about probability especially how to calculate probability and a chart that shows the long term probability of common iterative states.

This can be calculated via:  [Desired threshold = Chance success ^ #effects]   or via [Log (Desired threshold)/Log (Chance Success) = # effects]

Here is a quick little table I whipped up in Excel in a couple of minutes to give a basic idea (Sorry for the fugly formatting)
Quote
                       Desired Threshold of Failure (%chance to have rolled a failure)               
                              0.75          0.5     0.25        0.1       0.01     0.001
Chance    0.05|          1         1      1             1         2       3
of            0.1|          1         1      1             1         2       3
Success   0.15|          1         1      1             2         3       4
            0.2|          1         1      1             2         3       5
            0.25|          1         1      1             2         4       5
            0.3|          1         1      2             2         4       6
            0.35|          1         1      2             3         5       7
            0.4|          1         1      2             3         6       8
            0.45|          1         1      2             3         6       9
            0.5|          1         1      2             4         7     10
            0.55|          1         2      3             4         8     12
            0.6|          1         2      3             5        10     14
            0.65|          1         2      4             6        11     17
            0.7|          1         2      4             7        13     20
            0.75|          1         3      5             9        17     25
            0.8|          2         4      7            11        21     31
            0.85|          2         5      9            15        29     43
            0.9|          3         7    14            22        44     66
            0.95|          6        14   28            45        90   135

We have threshold across the top and chance of success going vertically with the numbers that correspond being the number of iterative attempts that it takes for the probability of failure to cross that threshold.

I think this is very illustrative of why Immunities and rerolls become increasingly important over higher levels because even with a high threshold of 75% and a high success rate of 95% (aka anything but 1) it only takes an average of 6 save or lose effects to cross that threshold.  At higher level play one can expect said number of save or lose effects in every combat and thus ways to avoid them become increasingly important.

2) While you did talk about it a bit I think it is important to note the fact that while over the course of a long term of play the chance of failure approaches unity that each individual roll is made in vacuum and is completely discrete from any other roll.  Thus while a chart like the one posted above serves as a nice guide it does not in any way mean that if you are making your xth roll that the chance to fail is any different than it has been in any of the previous rolls.  This is a common misconception about probability and any post seeking to discuss probability fully should address this, if only for completeness sake.

3) A discussion of the complexity of calculating full-attack schemes versus AC should probably be included.  The full-attack schemes of monsters with various natural weapons that all have different attack bonus and damage amounts can become very mathematically tedious to calculate and are extremely unintuitive to nearly anyone who doesn't deal with statistics on a regular basis.  This can lead to a real difficulty in properly valuating AC boosts which is a major threshold for players going from the intermediate levels of skill mastery to the more advanced.  This is probably most important for DMs who are attempting to gauge monster strength against party defense as monsters with large numbers of inaccurate attacks and monsters with small number of high accuracy attacks deal damage in very different ways which interact with the parties defenses (AC, Miss chance, etc.) in ways that are far more complicated than initial perception. 

4) A reiteration of the previous points but I think it really should be included:  More maths!  You are writing a guide about iterative probability and yet do not include a single formula for calculating probability or any other rigorous mathematical treatment of a subject that is by its very nature defined by such things.  Illustrative examples would be really appreciated because while I agree with the basic conclusions of your arguments the logical train used to go from the premises to said conclusions are largely absent.  Without the mathematics and other premises to go by it is not possible to evaluate if what you are saying is truly valid or if it just agrees with my own biases.  If this is to be a comprehensive guide to IP Proofing then one needs to be able to see the entirety of the thought process for why such a thing is relevant.  Otherwise the guide consists entirely of "do as I say because I am right" as opposed to showing the audience why you are correct and thus allowing them to naturally come to agreement.  Plus inclusion of further premises and mathematical foundation allows for a better understanding of the nuances of your views and can allow for important corollaries and caveats to arise, which in any subject as complex as CharOp are nearly as important as the basics.

Offline RobbyPants

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Here's a somewhat better formatted version of your table. To do this, you either need to separate your columns with spaces instead of tabs, or you actually need to use the bbcode version of the HTML <td>, <tr>, and <td> tags.

                  Desired Threshold of Failure (%chance to have rolled a failure)               
                             0.75   0.5     0.25   0.1     0.01    0.001
Chance            0.05 |     1      1       1      1       2       3
of                0.1  |     1      1       1      1       2       3
Success           0.15 |     1      1       1      2       3       4
                  0.2  |     1      1       1      2       3       5
                  0.25 |     1      1       1      2       4       5
                  0.3  |     1      1       2      2       4       6
                  0.35 |     1      1       2      3       5       7
                  0.4  |     1      1       2      3       6       8
                  0.45 |     1      1       2      3       6       9
                  0.5  |     1      1       2      4       7       10
                  0.55 |     1      2       3      4       8       12
                  0.6  |     1      2       3      5       10      14
                  0.65 |     1      2       4      6       11      17
                  0.7  |     1      2       4      7       13      20
                  0.75 |     1      3       5      9       17      25
                  0.8  |     2      4       7      11      21      31
                  0.85 |     2      5       9      15      29      43
                  0.9  |     3      7       14     22      44      66
                  0.95 |     6      14      28     45      90      135


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Offline awaken_D_M_golem

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Slight tangent ... this is almost too easy in 4e.
(yeah yeah I know this isn't a 4e thread)

Take a Companion Character at +1 level to the party.
55/55 vs PCs 60/50 vs monster's 50/50, is the basic game maths.

Human As Monster can have the normal monster attack and damage.
So it keeps up on ranged basic attacks and melee basic attack.
Monsters get better attack powers than PCs. Humans can cherry pick the best.
The 1 item is Neck Slot with a gentlemen's agreement to keep it maxed.
Reassign the defenses ala the CC entry, to AC so it is better.

Still can pick 1 or 2 or 3 (maybe more) utility powers. 
Re-roll on saves is the obvious 1st choice.
Then Raise Dead rituals up the wazoo, via the mysterious 4e source of all monster rituals.

A little boring for my tastes, but does this concept easily.
Your codpiece is a mimic.

Offline lans

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I think I'm reading this wrong.

For the 5% chance of success, you have a .1% chance of getting a failure after 3 attempts? 1% chance after 2?

Desired Threshold of Failure (%chance to have rolled a failure)               
                              0.75          0.5     0.25        0.1       0.01     0.001
Chance    0.05|          1         1      1             1         2       3

Offline Zionpopsickle

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I put percentages in decimal form and had it round to integer results.

If you have a 5% chance to succeed a save (thus need a 20 to succeed) then the number of effects you are likely to be able to take before you have a 75% (.75) to fail one is 1. 

It is very over-simplified and I may have screwed a few cells up but it is just to provide a very general guideline.

Offline lans

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The part where I am having trouble is with the last columns, with 3 rolls required for passing a .001 chance to roll a failure. It seems like that would be the chance to have not rolled a success.
 

Offline dipolartech

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Zion can you write out in sentence form how you are reading this graph?

for example: At a chance of success of 95% (19 of the 20 possible outcomes on a D20 is a success) I will roll 6 times before the statistics math says i have a 75% of failing.

Now I don't think i'm reading your graph right so i don't think my example is right but it would be helpful to me at least if you wrote it out like that. The reason I don't think I'm reading your graph right is because the number of rolls should not be getting bigger to fail less at the same success chance right? I must be looking at this backwards.

Offline Zionpopsickle

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I put percentages in decimal form and had it round to integer results.

If you have a 5% chance to succeed a save (thus need a 20 to succeed) then the number of effects you are likely to be able to take before you have a 75% (.75) to fail one is 1. 

It is very over-simplified and I may have screwed a few cells up but it is just to provide a very general guideline.
IGNORE ME!

Sorry, I had a brainfart so totally ignore this post.

The graph should be read by taking the chance of success and what you consider an acceptable threshold for failure (IE I need to make x% of these kinds of rolls) and then finding the number that corresponds.

For example, if I think that making 50% of my saves is acceptable and I have a 80% chance of making the save then I can expect it to take 4 effects before I will dip below that failure threshold.

To see the chance of failure subtract the threshold from one and that is the chance of you failing a roll over the number of effects with said chance for success. 

Sorry, I am not very good at explaining probability in layman terms since I usually deal with it in a mathematical sense.

The biggest things to draw from it is that the approach towards unity is asymptotic; that no matter how many rolls you make you will never actually hit a 100% chance of failure, and that minor variations (aka a cloak +2) have a large effect over numerous rolls.

To give a funny little example, if we have a 95% (anything but a one) chance of a save, plus a reroll we have a 99.75% chance to succeed.  If we take 90% as our acceptable threshold we get 42 effects.  If we want a 50% threshold we get 277 effects.  For the 1% chance we get the hilariously high 1840 effects, more than you would likely see in a game (nearly 100 effects per level).

Offline dipolartech

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Ok i think we're almost to laymen's terms, but lets see if I have this right,

99.75% chance of success, means that if my total number of rolls is 42, i have a 90% of failing?
99.75% chance of success, means that if my total number of rolls is 1840, i have a 1% chance of failing?


You see now where I'm not getting it? And wouldn't that mean for the second larger set that I could see something like 18 fails? course I probably shouldn't mention that because I hate getting statisticians started on distribution fields....

I think my problem isn't your math (which I can't look at to screw up cause its just the chart right now) its your nomenclature. I'm getting confused about the chances of failure. The only thing I totally get is "the approach towards unity is asymptotic;" which is of course weird cause there's nothing laymen's about "unity is asymptotic".

Offline Endarire

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When can we expect to see this thread reposted?

Offline Zionpopsickle

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Ok i think we're almost to laymen's terms, but lets see if I have this right,

99.75% chance of success, means that if my total number of rolls is 42, i have a 90% of failing?
99.75% chance of success, means that if my total number of rolls is 1840, i have a 1% chance of failing?


You see now where I'm not getting it? And wouldn't that mean for the second larger set that I could see something like 18 fails? course I probably shouldn't mention that because I hate getting statisticians started on distribution fields....

I think my problem isn't your math (which I can't look at to screw up cause its just the chart right now) its your nomenclature. I'm getting confused about the chances of failure. The only thing I totally get is "the approach towards unity is asymptotic;" which is of course weird cause there's nothing laymen's about "unity is asymptotic".

Not quite.  If you roll 42 times you have a 90% chance of making them all.  Roll 1840 times you only have a 1% chance.

Offline dipolartech

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Ok so definitely a language issue with your labeling of that axis.  Desired Threshold of Failure (%chance to have rolled a failure) implies that I should be able to say:
If Chance of Success = .95, and my total rolls for the set is 135, then I have a .1% of failure for that set......
but you just said that i would have a 1% chance of success..... so thats where I'm getting confused.

Offline Endarire

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The definitive guide to Iterative Probability and IP Proofing. Discussion
« Reply #12 on: July 12, 2012, 10:59:09 PM »
When will this be posted?  It's been about 4 months!  Inquiring minds want to know!

Offline veekie

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Basket Burner has permanently left the boards after his last altercation, and removed his handbook in the process of demanding the locking and deleting of any discussion on it. I believe its open for anyone to make an alternative IP-proofing handbook now.
« Last Edit: July 14, 2012, 07:46:36 AM by veekie »
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Offline Scythal

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I think the 1st post isn't spelled like it should. Let's try calling this "When should i use power attack/expertise"?

And now, let's do some easy understandable maths:

You're a warrior lv 20 with 10 strength, and only power attack (not even weapon foc, or 13 STR, but who cares). => Your BAB is 20.

1st case: your opponent as 10 AC
2nd case: he has 20
last case: he has 40

For these cases, you only do one attack, so let's see:

1st case: since you have a full BAB, you can easily take a power attack  (PA for short) of 12 and you'll only miss on a 1 (5%), if you take 16, you miss with 5 or less (so 25% chance to fail) and on a full 20 PA, you fail on 9 or less (so 45% chance).

2nd case: with no PA or a PA of 1, you'll have the same 5% chance of failing.

3rd case: with no PA or a full 20 PA, you will still only have 5% of ..... succeeding your attack.

The same thing can be applied with expertise:

If your AC is 20 and your opponent has a +15 on his attack:
With no expertise, you take the risk of being hit 80% of the time.
With 5 expertise, you reduce that chance to 55%.
And finaly, if the monster try to use a PA of 10, it becomes a 5% hit only situation.


So what the OP wanted to say is your multi attacking monster with 5 attacks and 80% to hit for each and in need on 3 of them to kill his opponents one by one before being killed will statisticly go down after killing 4 of them. But, it's pure statistic and we all know that you more frequently fail a save on 5 or less(more so if it's a save or die) than hitting on a 13+ with your 2H weapon and a PA of 10.

Offline Empirate

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Re: Iterative probability and multi layer defenses.
« Reply #15 on: August 09, 2012, 06:07:14 PM »
Nice to see this started up again. IP proofing is indeed a very important part of CO. Just one thing to note, and a section you might want to include: If you can replace one kind of defense for another, that might do worlds of good. Not only does it reduce resource expenditure (from MAD to items to feats etc.). It can also have surprising additional effects.

A simple example is an effect that replaces one requisite ability score with another, for example replacing Dex with Con for AC mod. This can be goof for obvious reasons, and is fairly simple to apply.

A more complex and more far-reaching method is replacing one mechanic of defense with another one. The Diamond Mind save replacers are a good example of this: instead of rolling a save, you're making a skill check. Not only are skill checks fairly easy to boost - more importantly, skill checks don't fail on a natural 1, unlike saving throws. Get that Concentration check up high enough, and 1/round you're basically immune to an effect allowing a save!

Offline lans

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Would putting the odds of a character with AC x and HP Y surviving an attack/full attack from various creatures at various levels be appropriate? Let's say for example grimlock or light warhorse at level 1 vs a wizard with 4 hp and 10 ac or a fighter with 12hp and 16 ac type of things

Offline veekie

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You'd suffer a rather large scope explosion. The range of possible numbers is already tremendous even with the monster side alone and unoptimized.
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Offline Unbeliever

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You'd suffer a rather large scope explosion. The range of possible numbers is already tremendous even with the monster side alone and unoptimized.
You could use averages, I suppose.  Trailblazer and others compiled some. 

Although I don't think that's particularly helpful for IP proofing.  Some benchmarking might be good -- a sufficiently high AC/hit points is actually a pretty good defense at various points in the game, and it'd be good to know what qualified as "sufficiently high."  The same could be said for saves. 

Offline lans

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You'd suffer a rather large scope explosion. The range of possible numbers is already tremendous even with the monster side alone and unoptimized.
I figured I would just use the grimlock and light horse, they seem to have the best standared action attack/full attack of stock cr 1 monsters