An Even MORE BLASPHEMOUS Polyhedral Dice Concepts for TFT

[Jim Kane]

"Beware all ye who enter unto here..." Here is an old chestnut I published way, way back when. I have resurrected this piece from deep within my filing cabinet for your perusal; as Ty's post caused my to recall this one - so you can blame him for it being on here now. LOL!

3/16/2018: EDIT NOTE: This piece discusses using TWO DIFFERENT Polyhedral dice TOGETHER in combination (i.e. Throwing a D4 AND a D8 together when rolling for a result in TFT, not just one polyhedral)

WHAT HAPPENS WHEN YOU COMBINE POLYHEDRAL DICE OF DIFFERENT VALUES AS A SUBSTITUTE FOR THE "D6s" USED IN THE FANTASY TRIP?

Considering the case of "1d6-1":

We get the following possible outcomes, when we combine together, in one roll, a D2 with a D3: 1+1, 1+2, 1+3, 2+1,2+2, 2+3. Meaning the combination gives us a range of expected outcomes, ranging from 2-5, expressed as Possible Outcomes: 2,3,3,4,4,5; or: D2+D3 = (2) 16.66% (3) 33.33% (4) 33.33% (5) 16.66%; with an average result of 3.5 (being the same as the average of unmodified 1D6).

In game terms, we can think of, or apply, this specific combination as an overall 66% chance of an average result occurring, including a 50% variance between a slightly augmented average outcome (4 vs 3.5), and a slightly diminished average outcome (3 vs 3.5), and a 16.66% chance of a minimum value result (2 vs 3.5), and a 16.66% chance of a maximum value result (5 vs 3.5), including a 50% variance between those two specific cases - and a 33.33% chance of a Min/Max (m/M)result occurring.

Expressed colloquially, one could say the odds are 2:3 (66%) that the event being tested will have an average successful result with an equal chance (50%) of ending up with a slightly greater than expected average result, or resulting in a slightly less then successful result of the average expectation; furthermore, there is a 1:6 (16.66%) chance of a wildly successful outcome, and equally (50%) a 1:6 chance (16.66%) of a wildly less than successful outcome occurring outside of the average expectation.

Next, let us compare the D2+D3 to that of a D5, D6-1, and D4+1:

D2+D3,,,D5,,,D6-1,,,D4+1

AVERAGE: 3.5,,,3,,,2.5,,,3.5
RANGE: 2-5,,,1-5,,,0-5,,,2-5
VARIANCE: +/- 1.5,,,+/- 2,,,+/- 2.5,,,+/- 1.5
TOT OUTS: 4 (6),,,5,,,6,,,4
CENTER %: 66.66%,,,60%,,,50%,,,50%
MIN/MAX%: 33.33%,,,40% ,,,50%,,,50%
HIGH OUT: 16.66%,,,20%,,,16.66%,,,25%
LOW OUT : 16.66%,,,20%,,,33.33%,,,25%


Informed by the table above, in different situations - and at the Referee's discretion - are best simulated by a specific die (with or without modifiers), or certain dice combinations, more than others - even if the result appears the nearly the same to some people.

All things being equal and all results being of equal likelihood - such as when rolling to see where an oasis might be located when exploring un-mapped desert territory, or when placing a single bet on the outcome of a fair spinning-wheel in an honest game of chance - does then the D5 becomes the die to best reflect this?

3/16/2018 Edit Note: "D5" being it's own linear die, versus "D5" being simulate by roll a D2 + D3 together, and NOT as in a single D5 which is linear in nature (Result = 1 thru 5 inclusive) - JK

When rolling for damage you are inflicting upon an enemy, the D6-1 would ideally be your last choice; as after making your successful 'to hit' roll, and then, rolling zero damage with an edged weapon (1-1=0), is not only a let down, but certainly does not reflect reality in the way WE would like; in our favor. When rolling for damage YOU might incur by way of some random impact, such as falling rubble from above, it is quite possible you might incur "no damage" - even though you were hit. In this case, the D6-1 would be the proper die to use for this type of event and the wild randomness of how much rubble hit you, and how hard.

On paper, statistically speaking, the differences between the D2+D3, and the D4+1 seem negligible; however, it becomes a question of WHICH probability curve best reflects, or simulates, the reality of the gaming situation.

The linear nature (no curve - flat line) of the D4+1 states that: All outcomes are equally possible, with a defined net result occurring; expressed as a positive integer; whereas the parabolic (bell shape) curve of the D2+D3 combination states that: All outcomes are not equally possible, some being more likely than others within an accurate range of variance, and with a net result occurring; expressed as a positive integer.

Consider the example of the Professional Boxer working out on a heavy bag:

If we could scientifically measure the strength of the impact of his blows for a given set - while he is fresh - we would expect to see a very consistent set of scores with very little variance occurring, or at least variance within an expected and believable range. We certainly would not expect him to score: 3,0,0,5,4, as might be the case with the D6-1; or 5,2,2,5,3, which might be the case with the D4+1. However, we would probably expect to see: 5,3,3,5,4, with the D2+D3 combination, tight variance, and Bell Curve applied due to combinations which manifest with the use of two dice.

This was written a looong time ago, and I assume no claim of warranty to it's serviceability in your game LOL!

[tbeard1999]

Oh, I was fully aware that abandoning the bell curve would change the distribution, even if the average damage is the same. I considered that a good thing, since it made attacks more unpredictable. It also helped mitigate the game breaking issues that arise when figures stop a fixed, and high amount of damage. Plus polyhedrals are pretty.

The thing about bell curves is that they are more predictable than a linear distribution. That can be good or bad and in the case of damage, I think it’s more bad than good. As always, this is highly subjective.

[tbeard1999]

As an aside, I’ve considered making damage a fixed amount and making armor variable. For instance, a broadsword does 9 points of damage. 0 armor in TFT would be d4. Leather would be 1d8. chain would be 1d10. Half plate d12. Plate d12+1. Fine plate d12+2.

So, attacker rolls to hit. If he succeeds the target rolls for armor and applies damage. A bit slower compared with the current system.

The problem was (a) it was jarringly unfamiliar to players; and (b) I wasn’t real sure what advantages it might have (if any).

However, I have definitely toyed with the idea of making armor protection ALSO a variable number (I also would use polyhedrals for weapon damage). Using the current polyhedral weapon damage, 1 point of TFT protection stops d4-1 hits. 2 points stop d4 hits. 3 points stop d6 hits. 4 points stop d8. 5 points stop d10. 6 points stop d12. Each additional point of TFT protection adds 1 to the d12 roll.

But again, while it would make combat much more variable (and a little longer), I’m not sure that’s a good thing.

[Jim Kane]

Originally Posted by tbeard1999

Oh, I was fully aware that abandoning the bell curve would change the distribution, even if the average damage is the same. I considered that a good thing, since it made attacks more unpredictable. It also helped mitigate the game breaking issues that arise when figures stop a fixed, and high amount of damage. Plus polyhedrals are pretty.

The thing about bell curves is that they are more predictable than a linear distribution. That can be good or bad and in the case of damage, I think it’s more bad than good. As always, this is highly subjective.

True, true, and true. Did you get that the piece is talking about using pairs of mixed polyhedrals together?

I don't think I stated the core concept strongly enough at the time I wrote that piece - back when my hair was was thick and wavy LOL!

Did that come through Ty, or was it lost? Pairs of mixed polyhedrals.

[Jim Kane]

Originally Posted by tbeard1999

As an aside, I’ve considered making damage a fixed amount and making armor variable.

NOW THAT is a unique idea! I want to give that one some serious consideration,.. increases the significance of WHO you swing that sword at; but without any extra die rolls. I will definitely get back to you on that concept Ty.

[tbeard1999]

Originally Posted by Jim Kane

True, true, and true. Did you get that the piece is talking about using pairs of mixed polyhedrals together?

I don't think I stated the core concept strongly enough at the time I wrote that piece - back when my hair was was thick and wavy LOL!

Did that come through Ty, or was it lost? Pairs of mixed polyhedrals.

I don’t care for mixing different sized dice. It adds a bit more complexity to calculating probabilty and I’m usually trying to simplify things, not make them more complex. Plus, I’m currently sour on a bell curve for damage, combined with fixed armor protection. It’s too easy to break such a system, when you add magic, warrior/veteran and heavy armor/shields.

If I were going to insist on a bell curve, I’d use 2d6 as the base system. For daggers, I’d roll 2d6-4 for daggers (glumly accepting the possibility of 0 damage)*, 2d6-3 for rapiers, 2d6-2 for cutlasses, up to 2+1 for ST13 one handed hand weapons. 2 handed bastard sword would be 2d+2. 2 handed sword would be 3 dice. Battle axe 3+1. Greatsword 3+2.

*With a bell curve, the mathematical average roll is also the most likely roll.

But when the subtractions exceed the number of dice, the real world average amount of damage is different than the mathematical average amount of damage. That’s because the mathematical average includes negative numbers, while in the real world, zero is the minimum damage. I.e., 2d-4 would have a damage range of -2 to 8 so the mathematical average - and the most likely damage roll - is 3. But since 0 is the real world minimum damage, the real world average damage would be slightly more than 3. Yet 3 would still be the most likely damage roll.

This would also happen if you decided to provide that every weapon does a minimum of 1 point of damage. Using this rule:

With a 2d-5 roll, the average damage would be 2.55, while the most probable damage is 2.

With a 2d-4 roll, the average damage would be 3.28, while the most probable damage number is 3.

With a 2d-3 roll, the average damage is 4.11, while the most probable damage is 4.

With a 2d-2 roll, the average damage is 5.03,while the most probable damage is 5.

These differences are negligible until you subtract 5 or more from the 2d. So my proposed 2d6 based damage system could be amended to provide that all weapons will do at least 1 point of damage. With Sha-Ken, the normal average damage is 1 2/3 points of damage. I’d make them d3 weapons and be done with it.

[Jim Kane]

Originally Posted by tbeard1999

I don’t care for mixing different sized dice.

Agreed. I am no way promoting this method AT ALL. This was an old piece I had written years ago. In play-test, EVEN with the charts in front of you, it is B-O-R-I-N-G & S-L-O-W; I posted here as one of my "Food for Thought" pieces ONLY.

Originally Posted by tbeard1999

It adds a bit more complexity to calculating probabilty and I’m usually trying to simplify things, not make them more complex.

100% AGREED.

Originally Posted by tbeard1999

Plus, I’m currently sour on a bell curve for damage, combined with fixed armor protection. It’s too easy to break such a system, when you add magic, warrior/veteran and heavy armor/shields.

I would like to hear more about your thought on the problem, solution, and implications you are thinking about. Tell me more.

Originally Posted by tbeard1999

If I were going to insist on a bell curve, I’d use 2d6 as the base system.

Reason being?

Originally Posted by tbeard1999

For daggers, I’d roll 2d6-4 for daggers (glumly accepting the possibility of 0 damage)*, 2d6-3 for rapiers, 2d6-2 for cutlasses, up to 2+1 for ST13 one handed hand weapons. 2 handed bastard sword would be 2d+2. 2 handed sword would be 3 dice. Battle axe 3+1. Greatsword 3+2.

One thing I can say was totally correct about MtM/GURPS: SJ absolutely got it right that weapons are generally "force multipliers"; I just could not get around the massive damage those rules - with the cutting and impaling bonus added in did to unarmoured figures - but that was a whole other piece I posted here about why MtM simply did not work for my types of "scantily clad" Barbarians LOL!

I have to tell you straight, I always cringe as a response when I see a prescribed damage assigned to a weapon where no associated generator is BEHIND that weapon (i.e figure exerting ST) - that's just me. I need time work over your damage estimates, as they are specific, and not just purely conceptual. Will get back to you on this after I have had time evaluated it.

Originally Posted by tbeard1999

*With a bell curve, the mathematical average roll is also the most likely roll.

True 1d6 = 3.5, 2d6=7, 3d6=10.5...

Originally Posted by tbeard1999

But when the subtractions exceed the number of dice, the real world average amount of damage is different than the mathematical average amount of damage.

I am only familiar with: "Arithmetic Mean", "Median", and "Mode" as types of Statistical Averages. What is the definition you are ascribing to the term "real world average"?

Originally Posted by tbeard1999

That’s because the mathematical average includes negative numbers, while in the real world, zero is the minimum damage. I.e., 2d-4 would have a damage range of -2 to 8 so the mathematical average - and the most likely damage roll - is 3. But since 0 is the real world minimum damage, the real world average damage would be slightly more than 3. Yet 3 would still be the most likely damage roll.

As above; I need your definition of "real-world-average" to answer accurately.

Originally Posted by tbeard1999

This would also happen if you decided to provide that every weapon does a minimum of 1 point of damage. Using this rule:

With a 2d-5 roll, the average damage would be 2.55, while the most probable damage is 2.

Can I assume you mean 2d6-5 here? I calculate 2d6 to average as 7; whereas: {[(3.5+3.5)=7]-5}=2. Where are you picking up the 0.55 from? Are you getting that from a theory chart with is taking the formula out over 10,000 rolls or something like that? Clarify please.

Originally Posted by tbeard1999

With a 2d-4 roll, the average damage would be 3.28, while the most probable damage number is 3.

As above.

Originally Posted by tbeard1999

With a 2d-3 roll, the average damage is 4.11, while the most probable damage is 4.

As above.

Originally Posted by tbeard1999

With a 2d-2 roll, the average damage is 5.03,while the most probable damage is 5.

As above.

Originally Posted by tbeard1999

These differences are negligible until you subtract 5 or more from the 2d. So my proposed 2d6 based damage system could be amended to provide that all weapons will do at least 1 point of damage. With Sha-Ken, the normal average damage is 1 2/3 points of damage. I’d make them d3 weapons and be done with it.

May I assume you are meaning at least 1 point of damage BEFORE armor/shields/ect. are factored in? Yes or No?

Great post by the way! Very MEATY, much to consider here. Let's stay with it.

PS - Do you know why in TFT Shuriken are called "Sha-Ken"? I have a theory on that one! LOL!
.

[tbeard1999]

Originally Posted by Jim Kane

I have to tell you straight, I always cringe as a response when I see a prescribed damage assigned to a weapon where no associated generator is BEHIND that weapon (i.e figure exerting ST) - that's just me. I need time work over your damage estimates, as they are specific, and not just purely conceptual. Will get back to you on this after I have had time evaluated it.

Of course GURPS has that mechanic - base damage is a function of ST and weapons act as modifiers. For instance, this is ST and average base swing damage:

8      1.5
9      2.5
10     3.5
11     4.5
12     5.5
13     6
14     7
15     8
16     9

The various GURPS 1 handed broadswords require ST 10 and add +1 to swing damage. So a GURPS ST 12 character with a broadsword will average 6.5 points. A ST 10 character will average 4.5 points. Not very different from TFT (7 and 5 respectively), if you choose the ST appropriate weapon. (Yes, I know GURPS treats damage types differently, but that's another discussion).

The 2 handed bastard sword does +2 damage and requires ST 10. A ST13 figure would do 8 points of damage on average - the same as TFT. The Greatsword requires ST 12 and does +3 damage. A ST16 figure would average 12 points of damage (vs. 11.5 in TFT).

You could very easily adapt this system to TFT. However, you'd wind up with very generic weapons, since TFT lacks nuances like Reach and different damage types:

• 1 handed small sword/dagger, +0 dmg, ST 6+"
• 1 handed sword, +1 dmg, ST10+"
• bastard sword, +1 dmg one-handed; +2 dmg two handed, ST10+ (or ST 13+ if you wanted to replicate TFT)"
• 2 handed big ass sword, +3 dmg, ST12+ (or ST 16+ if you want to replicate TFT"

***

BUT... in TFT damage does increase with ST, if you change weapons, at least through ST 16. Here's an outline of ST and average damage in TFT, assuming you choose the appropriate weapon for your ST:

One handed hand weapons

8 or less - 2.5
9 - 3.5
10 - 5 (4.5 with hammer)
11 - 6
12 - 7
13 -8

2 handed hand weapons:

13 - 8.5*
14 - 9.5
15 - 10.5
16 - 11.5

*The bastard sword does only 1/2 point more damage on average when used 2 handed, which is not enough to justify using it two handed. Maybe this is intentional? Maybe bastard swords were not particularly good 2 handed weapons? An easy tweak would be to have it do 2+1, but make it useable 2 handed at ST 12 or even ST 11.

I prefer TFT's approach, which allows for some descriptive variation in weapons and does increase damage with ST (at least through ST 16). Also, I think that many hand weapons DO require a certain amount of physical strength to handle effectively, particularly in an extended melee.

As noted, I modified the rules a bit and allow figures to use weapons that they lack the ST for. Damage is -1 if the figure is 1 point of ST short or -2 if the figure is 2 points short. At -3 ST, damage is -3 and DX is reduced by 2. (I reviewed my notes and realized my previous posts were inaccurate).

Similarly, figures get a +1 damage bonus if they have 1-2 points more ST than required. They get a +2 damage bonus if they have 3+ more points of ST than required.

But at the end of the day, a ST 16 guy will benefit more from using a 1 handed bastard sword (2d+3 in my system) than a cutlass (2d in my system). And a ST 10 guy will be better off using a cutlass (2d-2) than a 1h bastard sword (2d-2; DX -2).

Both of these are desirable in my opinion.

Incidentally, you can use the chart on page 21 AM and create a GURPS-like system. Take the unarmed combat damage from the chart, then add the listed damage for each weapon type:

Dagger 1d-1
Rapier 1d
Cutlass 1d+1
Shortsword 1d+1
Broadsword 1d+2
1h Bastard Sword 1d+3
2h Bastard Sword 2d-1
2h Sword 2d
Battleaxe 2d
Greatsword 2d+1

Convert adjustments of +3 into +1 die and adjustments of +7 into +2 dice.
Convert adjustments of -3 into -1 die and adjustments of -7 into -2 dice.

So, a ST 16 figure does 1d bare handed. With a Greatsword, he does 3d+1. With a Broadsword, he does 2d+2.

A ST 10 figure does 1d-3 bare handed. With a Cutlass (1d+1), he does 2d-2. With a dagger, he does 2d-4 which converts to 1d-1. If you let him use a Greatsword - I wouldn't - he'd do 3d-2.

You'd need to decide if you will require minimum ST for weapons (I would).

True 1d6 = 3.5, 2d6=7, 3d6=10.5...I am only familiar with: "Arithmetic Mean", "Median", and "Mode" as types of Statistical Averages. What is the definition you are ascribing to the term "real world average"?As above; I need your definition of "real-world-average" to answer accurately.

Average = mean.

I have no idea if there's a term of art to describe "actual average". However, an example might suffice. A weapon that does 1d-3 damage will mathematically average 0.5 points of damage. You add up all possible modified rolls and divide by 6. The sum of -2, -1, 0, 1, 2, and 3 is 3. Divide by 6 and you get 0.5 - the mean.

But in the Real World, you can't do -2 points of damage or -1 point of damage. These are treated as zero damage. So the possible damage rolls are actually 0, 0, 0, 1, 2, and 3. As a result, a 1d-3 weapon would average 1 point of damage, not 0.5.

With bell curves, there's another odd result. With a normal die roll, the average roll is also the most probable roll. So, a 2d6, Broadsword, will average 7 points of damage and 7 is the most likely damage it will inflict. This holds true so long as the negative modifiers don't exceed the number of dice being rolled. So a 2d-2 cutlass will average 5 points of damage and 5 will be the most likely damage it will inflict.

With a 2d-5 weapon (for instance), the most likely damage rolled will be 2.
And mathematically, the average damage rolled will be 2. BUT, the actual average damage will be 2.277 points of damage. The reason is that the mathematical average includes the possibility of rolling -3, -2 and -1 damage. In reality, those are converted to zero. This raises the average. Here are the mathematical averages and actual averages for other rolls:

2d-3  4   4.02
2d-4  3   3.19
2d-5  2   2.28
2d-6  1   1.55
2d-7  0   0.96

THIS is why I don't like negative modifiers that exceed the number of dice rolled - the probabilities get harder to calculate. And, the actual damage reduction per step starts getting significantly less than 1. IOW, applying a -3 modification to a 2d-3 weapon will reduce actual average damage by 2.47 points (4.02 minus 1.55), not by 3 points.

***

The effect of stating that all weapons do a minimum of 1 point of damage (before reductions for armor, shields, etc.) can be assessed with this approacj as well. Repeating my previous post somewhat and assuming this rule is in effect:

A 2d-2 weapon will mathematically average 5 points of damage; the actual average is 5.03. The difference is that 1 time in 36, you'll roll a 2. The -2 modifier would normally reduce that to 0 points of damage. But my rule would increase it to 1 point of damage. Hence, a very slight increase in the real world average. This is an insignificant difference, so the rule doesn't cause any trouble.

Here are the actual average damage before implementing the rule and after implementing it:

2d-2   5.00   5.03
2d-3   4.02   4.11
2d-4   3.19   3.28 
2d-5   2.28   2.55
2d-6   1.55   1.97
2d-7   0.96   1.55

Conclusion - adapting a rule that weapons will always do 1 point of damage (before armor, shields, etc.) will have minimal impact on 2 die weapons until you get to 2d-6 or so. Even then, the effect is to increase average damage by only about 0.5 damage points.\

However, a weapon doing 2d-6 may well be a boring weapon - 42% of the time, it will only do 1 point of damage.

With 1 die weapons, here are the numbers:

1d-1   2.50   2.67
1d-2   1.67   2.00
1d-3   1.00   1.50
1d-4   0.50   1.17

Conclusion - adapting a rule that weapons will always do 1 point of damage (before armor, shields, etc.) will significantly increase average damage with negative modifiers starting at -3. I don't consider this a big deal, so I'd adapt the rule.

This will increase the average damage of a one ST magic fist and fireball. But for 2+ ST magic fist and fireball, it's almost irrelevant, because the negative modifier be applied to the entire roll - A 3 point magic fist rolls 3d and subtracts 6. It does NOT three dice and subtract 2 from each die.

PS - Do you know why in TFT Shuriken are called "Sha-Ken"? I have a theory on that one! LOL!
.

No idea. We called them "throwing stars" until the early 1980s...

BOTTOM LINE - Letting all weapons do a minimum of 1 point of damage will not materially change the average amount of damage done, so add this rule if doing zero points of damage irritates you.

[tbeard1999]

Continuing the insanity, here are the real averages for 3 die weapons currently and assuming a minimum damage of 1 (rounded to 1 decimal place):

3d-3    7.5   7.5
3d-4    6.5   6.5
3d-5    5.5   5.6
3d-6    4.6   4.7
3d-7    3.7   3.8
3d-8    2.8   3.1
3d-9    2.1   2.5
3d-10   1.5  2.0
3d-11   1.0  1.6
3d-12   0.6  1.3

Conclusion: Adapting a "minimum damage of 1 point" rule doesn't distort average damage much until you get to 3d-10.

[JLV]

Originally Posted by tbeard1999

As an aside, I’ve considered making damage a fixed amount and making armor variable. For instance, a broadsword does 9 points of damage. 0 armor in TFT would be d4. Leather would be 1d8. chain would be 1d10. Half plate d12. Plate d12+1. Fine plate d12+2.

So, attacker rolls to hit. If he succeeds the target rolls for armor and applies damage. A bit slower compared with the current system.

The problem was (a) it was jarringly unfamiliar to players; and (b) I wasn’t real sure what advantages it might have (if any).

However, I have definitely toyed with the idea of making armor protection ALSO a variable number (I also would use polyhedrals for weapon damage). Using the current polyhedral weapon damage, 1 point of TFT protection stops d4-1 hits. 2 points stop d4 hits. 3 points stop d6 hits. 4 points stop d8. 5 points stop d10. 6 points stop d12. Each additional point of TFT protection adds 1 to the d12 roll.

But again, while it would make combat much more variable (and a little longer), I’m not sure that’s a good thing.

Actually, that system was used in a British RPG, Dragon Warriors, which was published contemporaneously with TFT in the early '80's. Dragon Warriors has a LOT of interesting ideas in it (and was republished a few years ago and is available from DTRPG). Systemically it wouldn't be hard to convert DW to TFT or vice versa -- they're close enough to make it do-able. I've often thought it would have resulted in a very interesting game if the designers of TFT and DW would have gotten together and collaborated on their designs -- so many great ideas that didn't overlap exactly but were easily applicable from one design to the other.