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Critical Math and How Your Mind Works


Nakana

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From the BGB, a critical success is 5% and a special success is 20% of whatever your skill is. 

 

It's a great mechanic. It provides two levels or tiers of success and is easy to remember because it is reciprocal. It's balanced. 

 

(Your score/5=20%) and (Your score/20=5%) 

 

It's also a factor pair of 100.

 

However, I've noticed that in my head I do not divide by 5 or 20. Instead what I do, is either double or halve 10%. It just seems quicker to me (most likely because 10% is easier to derive visually because the answer is the score as written, only adjust for the decimal point.)

 

I'm just curious how many of you may follow the same method I do, or if most people simply divide by 5 and 20. 

 

 

Additionally, is there a variant of d100 out there that ignores the special success and just rules critical successes at 10% instead?

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From the BGB, a critical success is 5% and a special success is 20% of whatever your skill is. 

 

It's a great mechanic. It provides two levels or tiers of success and is easy to remember because it is reciprocal. It's balanced. 

 

(Your score/5=20%) and (Your score/20=5%) 

 

It's also a factor pair of 100.

 

However, I've noticed that in my head I do not divide by 5 or 20. Instead what I do, is either double or halve 10%. It just seems quicker to me (most likely because 10% is easier to derive visually because the answer is the score as written, only adjust for the decimal point.)

 

I'm just curious how many of you may follow the same method I do, or if most people simply divide by 5 and 20.

 

It's no longer available to interior inspection, I've been doing it too long... My instinct is that I MULTIPLY sufficiently low numbers to check - I know that a skill of <=100 can ONLY critical on <=5 and special on <=20, and <=60 is <=3 / <=12 for example so if I don't immediately think "that roll is..." I multiply numbers under 5 by twenty  and numbers under 20 by five to see if they fall under the skill concerned...

 

 

Many - the original Stormbringer; Open Quest, RuneQuest 6 and IIRC most if not all of the MRQ derived branch of the family (Legend, Renaissance etc).

 

Cheers,

 

Nick

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It's no longer available to interior inspection, I've been doing it too long... My instinct is that I MULTIPLY sufficiently low numbers to check - I know that a skill of <=100 can ONLY critical on <=5 and special on <=20, and <=60 is <=3 / <=12 for example so if I don't immediately think "that roll is..." I multiply numbers under 5 by twenty  and numbers under 20 by five to see if they fall under the skill concerned...

Ah, multiplying the rolled number by 5 or 20 makes perfect sense, and yet.. without it being pointed out my brain would probably have never thought that way! Excellent!

 

Seems like more than not. =\

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I've used "Knock of the digit and double/halve" in the past and it is quick and dirty.

 

So, with a skill of 65, remove the digit (5), leaves 6, double it for a special (12), halve for a critical (03), the special is not alway exactly right, but it close enough for most purposes.

 

Recently, I have also used "Double roll and and a 0 to the end" or "Halve the roll and add a 0 on the end" to check the skill, which is about as quick.

 

Rolling an 04 means I double and add a 0 to get 80, which is too high for a critical, but halve and add a 0 gives me 20, which is below 65 and means it's a special. Again, not especially accurate, but gives a good ball-park figure.

Simon Phipp - Caldmore Chameleon - Wallowing in my elitism since 1982. Many Systems, One Family. Just a fanboy. 

www.soltakss.com/index.html

Jonstown Compendium author. Find my contributions here

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So, with a skill of 65, remove the digit (5), leaves 6, double it for a special (12), halve for a critical (03), the special is not alway exactly right, but it close enough for most purposes.

Essentially this is the same thing I'm doing, the only difference being that you're rounding the fractions down whereas I'm rounding up.

This is what Nick does by multiplying the rolled number by 5/20, but certainly derived a different way. Again, this makes sense to me once explained, but I'd probably have never come up with this method on my own.

I've just always found the various ways people's brains compute things to achieve the same result fascinating.

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Additionally, is there a variant of d100 out there that ignores the special success and just rules critical successes at 10% instead?

 

I believe Legend does that.

 

I more or less do the math as you do, but I'm leaning toward 10% rounded down for critical, 20% rounded down for special.  For criticals, that means just drop the ones digit - your tens digit is your critical chance - and then double that for special.

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I believe Legend does that.

 

I more or less do the math as you do, but I'm leaning toward 10% rounded down for critical, 20% rounded down for special.  For criticals, that means just drop the ones digit - your tens digit is your critical chance - and then double that for special.

Just keep in mind that you have doubled the chance for a critical. If that is okay for you as the GM that is fine but it could change the feel of your games.

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Just keep in mind that you have doubled the chance for a critical. If that is okay for you as the GM that is fine but it could change the feel of your games.

Ya, I caught that.  :)  I'm usually going for a little more pulpy in my games, so I'm hopeful it will work well (that is, when I finally get my players to agree to try BRP ... ).

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Additionally, is there a variant of d100 out there that ignores the special success and just rules critical successes at 10% instead?

 

Legend and RuneQuest 6 use this mechanic.

Simon Phipp - Caldmore Chameleon - Wallowing in my elitism since 1982. Many Systems, One Family. Just a fanboy. 

www.soltakss.com/index.html

Jonstown Compendium author. Find my contributions here

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I came up with a chart for determining a character's degree of success or failure, let me know what you guys think.

 

Die Roll / Success / Failure

01-20 / Marginal Success / Catastrophic Failure

21 - 40 / Moderate Success / Disasterous Failure

41 - 60 / Complete Success / Complete Failure

61 - 80 / Remarkable Success / Moderate Failure

81 - 00 / Extraodinary Success / Marginal Failure

 

So if a character's skill is 45%, and he rolls a 43 (a success), it would be a complete success, but if rolled 47 (a failure) it could be a complete failure. 

 

In combat any roll divisible by "10" is a critical (either a critical hit or a fumble, as the case may be). So a character with a 63% in Sword or whatever would have a 6% chance to score a critical hit (roll of 10, 20, 30, 40, 50 or 60) and a 4% chance to fumble (roll of 70, 80, 90 or 00). 

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@Mjollnir Interesting mechanic. However, in my mind degrees of success are a sliding scale and not always static. 

 

If a character's skill is 87%. That means they are very proficient at that particular skill. At that level, a roll of 85 would certainly be a success (and if using your chart it would constitute an extraordinary success) however it may not necessarily represent a challenge that is proportionate to their proficiency.

 

Worse still, because of the way the system is set up, my mind interprets the lower the number = the better the success (even if it's not a special or critical). So in my example with a skill of 87% and a roll of 85, my mind looks at it as if it barely made it. Whereas a roll of 65 would represent a success that came more easily.

 

Perhaps if the success part of  your chart were reversed it would be easier for my mind to accept?

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Like Mjollnir said, there are visual heuristics you can use which ignore the maths altogether.

Eg. for 20% you can say any 0 or 5 on the units die which is less than your skill is a special success (or you can pick any 2 other numbers if it is more meaningful to you). One advantage of this system is that it allows for special failure, a concept not normally used in BRP because the on-the-fly maths is too tricky. You just apply the same system for numbers greater than your skill. One disadvantage is that if you are used to the calculation method, the visual dice method is confusing. Not quite sure of an easy way to get 05% with this method though.

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@Mjollnir Interesting mechanic. However, in my mind degrees of success are a sliding scale and not always static. 

 

If a character's skill is 87%. That means they are very proficient at that particular skill. At that level, a roll of 85 would certainly be a success (and if using your chart it would constitute an extraordinary success) however it may not necessarily represent a challenge that is proportionate to their proficiency.

 

Worse still, because of the way the system is set up, my mind interprets the lower the number = the better the success (even if it's not a special or critical). So in my example with a skill of 87% and a roll of 85, my mind looks at it as if it barely made it. Whereas a roll of 65 would represent a success that came more easily.

 

Perhaps if the success part of  your chart were reversed it would be easier for my mind to accept?

 

You do have to change the way you think a bit, but I think the chart has a few advantages.

 

  • It scales automatically. A character with a low skill rating (say 17%), can only marginally succeed, but can fail anywhere from catastrophically to marginally. Conversely a character with a skill rating of 83% can achieve any level of success, but only marginal and moderate failure.
  • It works with modifiers, a bonus increases your chance of a higher degree of success and lowers your chances (and severity) of failure. A penalty of course does the opposite.

 

I thought about reversing the chart (lower is always better), but that would mean that whenever an incompetent character succeeds, he does so spectacularly.

 

So think - roll as high as possible within your skill, otherwise just roll as high as possible.

 

 

The "margin of success or failure" is a good system, but has the disadvantage of requiring maths, which science tells us is a drag.

 

Difference (subtract dice roll from modified chance of success)

 

Die Roll / Result

+ 41 and up / Extraordinary Success

+ 21 to + 40 / Complete Success

0 to + 20 / Marginal Success

- 20 to - 1 / Marginal Failure

- 40 to - 21 / Complete Failure

- 41 and below / Catastrophic Failure

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@Questbird I think that may be my problem. I don't like visual dice methods. That also explains why I detest dice pool systems. =\

 

@Mjollnir I definitely see the advantages to your chart, and stand corrected on reversing it. I'll have to give it a try in play to see if I can overcome the challenge of changing the way my mind is used to doing it. 

 

This thread has some good stuff!

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I came up with a chart for determining a character's degree of success or failure, let me know what you guys think.

 

Die Roll / Success / Failure

01-20 / Marginal Success / Catastrophic Failure

21 - 40 / Moderate Success / Disasterous Failure

41 - 60 / Complete Success / Complete Failure

61 - 80 / Remarkable Success / Moderate Failure

81 - 00 / Extraodinary Success / Marginal Failure

 

So if a character's skill is 45%, and he rolls a 43 (a success), it would be a complete success, but if rolled 47 (a failure) it could be a complete failure. 

 

In combat any roll divisible by "10" is a critical (either a critical hit or a fumble, as the case may be). So a character with a 63% in Sword or whatever would have a 6% chance to score a critical hit (roll of 10, 20, 30, 40, 50 or 60) and a 4% chance to fumble (roll of 70, 80, 90 or 00). 

 

So, if I roll an 01 then that's a Catastrophic Failure/Marginal Success and if I roll 100, That's an Extraordinary Success/Marginal Failure?

 

That's completely against all the D100 systems that I use (RQ/BRP/Legend).

 

Two opponents, A and B, with skills of 60% and 65%, the first rolls 10, the second 70, what would be the result under your table?

Simon Phipp - Caldmore Chameleon - Wallowing in my elitism since 1982. Many Systems, One Family. Just a fanboy. 

www.soltakss.com/index.html

Jonstown Compendium author. Find my contributions here

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Sorry you don't like visual dice methods Nakana, but this has got me thinking.

Here's a visual dice method which produces statistically and conceptually similar results to straight BRP.

 

Roll d100

1 or 2 on the units die is a special. If the result is equal to or under your skill, special success; over and it's a special failure (optional)

If you roll an odd 'tens' result, eg 10, 30, 50 etc. which is equal to or under your skill, it's a critical success*

 

In other words, a 0, 1 or 2 on the units die indicates a more powerful result. Roll low still applies!

 

This system still allows for normal fumbles (99 and 00 are not specials), and rewards very low rolls (01 and 02 are specials unless you have no skill).

 

In Soltakss' example above:

Two opponents, A and B, with skills of 60% and 65%, the first rolls 10, the second 70, what would be the result under your table?

This system: A has a critical success, B rolls a failure*

Vanilla BRP: A has a special success, B rolls a failure

 

*OPTIONALLY, if you roll an odd 'tens' result over your skill it's a critical failure (though there aren't rules for this in BRP). If you use this rule you shouldn't use the normal fumble rules. Note that such critical failures are more likely than fumbles.

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Roll d100

1 or 2 on the units die is a special. If the result is equal to or under your skill, special success; over and it's a special failure (optional)

If you roll an odd 'tens' result, eg 10, 30, 50 etc. which is equal to or under your skill, it's a critical success*

 

In other words, a 0, 1 or 2 on the units die indicates a more powerful result. Roll low still applies!

 

*OPTIONALLY, if you roll an odd 'tens' result over your skill it's a critical failure (though there aren't rules for this in BRP). If you use this rule you shouldn't use the normal fumble rules. Note that such critical failures are more likely than fumbles.

 

In fact the optional critical failure system described is exactly how BRP fumbles are supposed to work (BGB p. 173): 5% of the chance to fail. I didn't realise because my base system is Elric! which uses the 99 or 00 fumble rule.

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...not sure about this, its all new to me, I will have to check the BGB tonight. Roll under, the lower the better, has been a big principle of BRP I would think. Otherwise we're playing Rolemaster :-)

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" Sure it's fun, but it is also well known that a D20 roll and an AC is no match against a hefty swing of a D100% and a D20 Hit Location Table!"

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BGB uses a series of ordered numerical ranges to indicate a level of success.

Questbird's example of a visual dice method uses a series of ranges based on visual dice cues.

Both produce similar percentages of results. 

 

The only mathematical discrepancy is that by using Questbird's example, one gains a 3% increase to roll a special success. (Which is not a big deal in my opinion.)

 

Graph_zps1dbe8efb.jpg

 

I think this is probably the best way I could explain why I don't like visual dice mechanics. 

 

edit: The graph is based on a skill of 60%

edit: I also meant to mention that somewhere in an old BRP system I read that if you roll the same number as your skill it meant something (Can't remember if it was good or bad.) I didn't like that either lol. 

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BGB uses a series of ordered numerical ranges to indicate a level of success.

Questbird's example of a visual dice method uses a series of ranges based on visual dice cues.

Both produce similar percentages of results. 

 

The only mathematical discrepancy is that by using Questbird's example, one gains a 3% increase to roll a special success. (Which is not a big deal in my opinion.)

Nice graph :)

 

Well that is true but, technically it's the traditional method which reduces the chance of a special by 3%, because the critical range and special range are lumped together, and critical takes precedence. So in my dice method (to use a non-visual explanation) there is a 12% chance of special (= 20% of 60). That is, 12 numbers in 100: 01, 02, 11, 12, 21, 22, 31, 32, 41, 42, 51 52.

In the vanilla method, as Nakana points out, there are only 9 numbers in 100 which are special: 04, 05, 06, 07, 08, 09, 10, 11, 12. That's not 20% of 60, it's 15% of 60.

 

Each method has the same number of criticals: 3. Those 3 are subtracted from the special success range in the BGB method, and additional in the visual method.

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Well, that all depends on the flavor of BRP. RQ3 combined the effects of Specials and Criticals when you rolled a crit. So a Broadsword would get an Impale, max damage, and ignore armor. I seem to remember a small section in the BGB which mentioned this, but I don't have the book with me at the moment. 

 

Other versions of BRP did handle things like this differently. 

 

SDLeary

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