NP Comic for Tuesday, November 22, 2022

[Darth Fluffy 302]

NP Comic for Tuesday, November 22, 2022

Put that D20 in the chair of shame!

... And so, the skilled martial artist, who incidentally can fly, falls down the stairs (in character).

[Pharaoh RutinTutin 1,586]

No matter what you do, there is at least a five percent chance something will go terribly wrong.

The life lesson I took from this was simple.  Do nothing.

[Darth Fluffy 302]

DO a breathing check every five minutes. If you roll a one, you've passed out. If you roll another one while you are passed out, you have failed to breathe and die. Roll up another character.

[mlooney 3,417]

Most TTRPG that I play (granted that just D&D 5e and Traveller)  say that unless there is a good reason (i.e important side effects of failing, difficult situation, in combat) don't roll for every possible "check".  Example given in Traveller, for example, is driving a ground car to the store.  A GM that makes you roll for every possible event has issues.

[ijuin 572]

1 hour ago, Darth Fluffy said:

DO a breathing check every five minutes. If you roll a one, you've passed out. If you roll another one while you are passed out, you have failed to breathe and die. Roll up another character.

Statistically, a character should pass out an average of at least once every two hours, and should have an average lifespan of only two days using those numbers.

[mlooney 3,417]

 

1 hour ago, ijuin said:

Statistically, a character should pass out an average of at least once every two hours, and should have an average lifespan of only two days using those numbers.

In the worst game every written ,"F.A.T.A.L",¹ a possible sided effect of failing a spell casting roll was casting the "FATAL spell" which ended all life on the game world.  Average life span of the world would be measured in hours assuming a fairly large number of casters.

¹ Trust me, it's the worse game ever written for both content and play mechanics. 

[Darth Fluffy 302]

1 hour ago, ijuin said:

Statistically, a character should pass out an average of at least once every two hours, and should have an average lifespan of only two days using those numbers.

That was the point.

[Darth Fluffy 302]

8 minutes ago, mlooney said:

 

In the worst game every written ,"F.A.T.A.L",¹ a possible sided effect of failing a spell casting roll was casting the "FATAL spell" which ended all life on the game world.  Average life span of the world would be measured in hours assuming a fairly large number of casters.

¹ Trust me, it's the worse game ever written for both content and play mechanics. 

Isn't that the basis for Fudge dice? I kind of like those.

[mlooney 3,417]

23 minutes ago, Darth Fluffy said:

Isn't that the basis for Fudge dice? I kind of like those.

Oh, no.  Those come from Fudge and/or Fate, both good game engines.  F.A.T.A.L uses d100 or larger.  As I recall some tables are d10000.

[Darth Fluffy 302]

1 hour ago, mlooney said:

Oh, no.  Those come from Fudge and/or Fate, both good game engines.  F.A.T.A.L uses d100 or larger.  As I recall some tables are d10000.

Somewhere, buried for years, I have a set of D10s in x10 increments, starting as small fractions, and going to big numbers. Still the mental image of a very large die with an unimaginable configuration of faces to cover that range requiring an earth mover to roll, and hoping it stops before it plows through the walls is too good to ignore. Fabricated by Lou Zocchi, no doubt.

[mlooney 3,417]

 

1 hour ago, Darth Fluffy said:

Fabricated by Lou Zocchi, no doubt.

Ah, yes, the ultimate Zocchihedron 

https://en.wikipedia.org/wiki/Zocchihedron

[Darth Fluffy 302]

1 hour ago, mlooney said:

 

Ah, yes, the ultimate Zocchihedron 

https://en.wikipedia.org/wiki/Zocchihedron

It is impossible to absolutely fairly distribute 100 detents over a sphere such that each is equally likely to occur. In the Zocchihedron, the number of detents is large enough that the error might be considered acceptable, although, see your article for 'fine tuning the design'. It is still impractical, a pair of D(0-9) and D(00-90) is far more manageable and easier to deal with.

The most brilliant thing about the Zocchihedron is that it incorporates loose fill as an internal brake. Much needed. He spent too much time optimizing a fabricated shape for the particles, sand would have served OK.

You can, however, create a D120. Take a D30, and replace every rhombus with a shallow rhomboidal pyramid. D120.

You could take a golf ball and number each dent. It would be roughly as fair as a Zocchihedron. The range varies, golf balls are not all the same. Per Wiki, 330 is typical on a British golf ball, and 336 on an American golf ball, but possibly as high as 500.

The really bad Zocchi designs are the D5 and the D7. I don't believe his claim that the ends are equally likely to the other sides, it seems like it would vary with the rolling surface and with dice wear, and he made no effort to distribute the numbers to minimize effect of the error on the average roll nor the variance. Anyway, a D5 is not difficult to make from a D10 or D20. I've seen double pyramid D14s that could be D7s, if you should need such a die. But mostly it's pointless.

[Don Edwards 548]

6 hours ago, mlooney said:

In the worst game every written ,"F.A.T.A.L",¹
...
¹ Trust me, it's the worse game ever written for both content and play mechanics. 

In fact I strongly recommend NOT looking it up. Just imagine something as horrible as you can, and add 15%.

[ijuin 572]

5 hours ago, Darth Fluffy said:

Somewhere, buried for years, I have a set of D10s in x10 increments, starting as small fractions, and going to big numbers. Still the mental image of a very large die with an unimaginable configuration of faces to cover that range requiring an earth mover to roll, and hoping it stops before it plows through the walls is too good to ignore. Fabricated by Lou Zocchi, no doubt.

Here’s a D65536

[Darth Fluffy 302]

3 hours ago, ijuin said:

Here’s a D65536

At least it's not a D666 ...

[Darth Fluffy 302]

3 hours ago, ijuin said:

Here’s a D65536

Oops, should have mentioned, it is easy to implement a D65536 with either 16 D2s (coins), 8 D4s,  4D8s and 2 D4s, or 5 D8s and a D2.

10 D2s or 5 D4s will go to a bit over 1000   (1024)

20 D2s or 10 D4s will go to a bit over 10^6   (1,048,576)

30 D2s, 15 D4s, or 10 D8s will go to a bit over 10^9   (1,073,741,824)

The numbering is analogous to using two D10 for a D100, one of them is in powers of 10; in this case you need successively higher powers of two.

... and you won't need heavy machinery to toss them.

[ijuin 572]

You could also use D16 dice, which are uncommon, but available.

[Darth Fluffy 302]

26 minutes ago, ijuin said:

You could also use D16 dice, which are uncommon, but available.

I have seen them; I assumed that a normal dice collection would not have a lot of them.

4 D16s to go to 65536

There are many alternatives. Any two procedures which produce indistinguishable mathematical results are 'isomorphic'. There are two basic ways of generating discrete random values, selecting randomly without replacement, like drawing a random card and holding it, or selecting randomly with replacement, drawing a card and recording it, then putting it back in the deck, so that the next draw could be the same card. Dice are isomorphic to 'with replacement'. So is a roulette wheel. Or actually replacing a card back into a deck. Bags with random value tiles are fairly common in some games. With replacement, these are isomorphic to dice. Lottery machines are without replacement, isomorphic to how cards work, but if you had the machine and replaced the balls after each draw, it would be like a dice. I have a 'Bingo Game Set' that I got at Dollar Tree, it has a bingo cage ball selector, and 60 numbered balls (oddly, not the x-y letter-number you'd expect). In normal Bingo use, you would not replace. I bought it because for a dollar (at the time) I have what is effectively any die size up to 60. They are easy to replace between rolls; there is a side feed into the cage.

You could go electronic, this may be the best bet. If you rely purely on software, the results are not random, they are based on a deterministic pseudorandom sequence that has varying degrees of random statistical behavior. These have been studies since the early days of electronic computers, and modern algorithms can be quite good. But there is a better way. It is not difficult to introduce actual random values. The time of day can be used as a seed value to generate a pseudorandom value that is actually random. Sometimes device movements, such as 'move your mouse' are measured as a seed. There are attributes of your phone that can work. It is also doable to create a thermal or radioactive random value generator. (The radioactive one I've seen described was safe to use, much like your smoke detector. You wouldn't want to eat it.) Input the range, and let it generate.

 

 

[Don Edwards 548]

7 hours ago, ijuin said:

Here’s a D65536

Round dice are actually pretty easy to roll. What's hard is getting them to stop, and then deciding which number is on top.

[mlooney 3,417]

13 hours ago, Don Edwards said:

In fact I strongly recommend NOT looking it up. Just imagine something as horrible as you can, and add 15%.

Only 15%?  I'd add at least 50%, maybe even double.

[mlooney 3,417]

10 hours ago, Darth Fluffy said:

Oops, should have mentioned, it is easy to implement a D65536 with either 16 D2s (coins), 8 D4s,  4D8s and 2 D4s, or 5 D8s and a D2.

10 D2s or 5 D4s will go to a bit over 1000   (1024)

20 D2s or 10 D4s will go to a bit over 10^6   (1,048,576)

30 D2s, 15 D4s, or 10 D8s will go to a bit over 10^9   (1,073,741,824)

The numbering is analogous to using two D10 for a D100, one of them is in powers of 10; in this case you need successively higher powers of two.

... and you won't need heavy machinery to toss them.

This does lead to the question as to why you need d65536.  That's a big table.

[Darth Fluffy 302]

5 hours ago, Don Edwards said:

Round dice are actually pretty easy to roll. What's hard is getting them to stop, and then deciding which number is on top.

This is why the loose fill brake in the Zocchihedron is such a good idea. A D20 could benefit, but then balancing it would be much more difficult. With only 20 faces, it needs the benefit of being a well constructed, well balance polyhedron.

D6s seem to have the best roll characteristics. They roll well enough, and they stop in a reasonable amount of rotations. D4s do not quite roll well; but a D2 coin flip works OK.

I tend to like systems like D20 that rely on a small subset of dice; the plethora of sizes does not bring much to the table and can be simulated by other means.

That said, if you want to make dice to reach from one to some integer, you should know that in a sense, any upper number kind be reached, kind of. You want a D7? You can make a seven sided prism or lozenge; make the ends small so they do not factor in. (This is isomorphic to a roulette wheel - a circular one dimensional selection.) If your number is even, or if you repeat each number twice, you can use two pyramids joined at the base, like common D10s. THe practical limit is that the facets get small when the upper limit gets big. When it looks too much like a cylinder, stopping rolling is an issue.

Then we have the five convex Platonic solids, and extensions based on these. The five are D4, D6, D8, D12, D20. You can't have a face with less than three edges, and not more than five; six tiles a flat plane, so isn't a dice, more won't fit together at all in 3-D.

These can be arranged in 'duals' where the verticies and surfaces are swapped, and the edges then cross. The D6 and D8 are duals, The D12 and D20 are duals, and the D4 is a weird self-dual. You will notice if you factor these, there are 2s, 3s, and a 5. If you replace each edge with a rhombus, such that the acute verticies meet and the obtuse verticies meet, you can generate a semi-regular polyhedron that has the verticies of both duals, and the number of faces of either (which are the same number). D6 and D8 yield a rhombic D12; these are sometimes encountered as dice. D12 and D20 yield D30, which you can buy in a well stocked game shop. D4 and D4 yield a cube, a D6. Notice that the same factors are still present.

You can split the rhombs in 2 or in four, bumping the faces out a little, and still have totally fair dice. So a D6 could yield a D24, I have seen these in stores, a D12 could yield a D48, and a D30 could yield a D60 or a D120 (eliminating redundant results). That's it. There are no more. Anything else involves some compromise of absolute equality of the faces.

You can make a pretty good D14 mixing a cube and an octaheron. You can make a related D18. You can make a related D26. You can distribute the biases to minimize their effect, but they won't be truly unbiased.

Doing something similar with a dodecahedron and an icosahedron, you should be able to do D32, D42, D50, and D62.

 

[Darth Fluffy 302]

8 minutes ago, mlooney said:

This does lead to the question as to why you need d65536.  That's a big table.

Another advantage of computerizing, automatic look up.