Duck of Earl and Die With All Ones

[RL]

I think the simplest way to deal with this is to get a D100. That being said, Rev. Bob recently emailed me with some ideas about a similar d6+6 die using funky symbols and math -- I've sent an email to Chessex asking them about prices and such. If I decide to go forward with it, I'll post a new thread here to see if anyone's interested.

[Icositetrachoron]

Originally Posted by Rudkin

Personally, I'd be inclined to pack the colour die from Munchkin Quest, or a blank die, or that weird die I have kicking around with shapes instead of numbers....

Sure I couldn't get a level out of it, but guaranteed extra cards with no risk of losing a level is also appealing. After all "Blue" (even "Blue -1" in the case of having a Chicken on your head -- does that even make sense?) would be "any other result"...!

Yeah, I actually had a very similar thought not long after my last post. "On any other result" seems to indicate quite clearly that not only would any number between 2 and 6 (noninclusive) result in one of each card, but so would anything that's not a number. I love the color die idea. "Blue - 1" indeed. :)

Also, even if my inclination is always toward gaining a level over getting two cards, I would still want to have the option of forcing the latter outcome if I am already at the penultimate level, as a GUAL would be useless at that point (unless I wanted to hang on to it in case I lose a level due to a curse or bad stuff).

Originally Posted by Chad Cloman

I think the simplest way to deal with this is to get a D100. That being said, Rev. Bob recently emailed me with some ideas about a similar d6+6 die using funky symbols and math -- I've sent an email to Chessex asking them about prices and such. If I decide to go forward with it, I'll post a new thread here to see if anyone's interested.

Yes! That's perfect. This is even better than the all-different-expressions-that-equal-one die, because in the case that you can't convince the other players that the math works (or even that it counts as a numerical result), you would just get one of each card instead of a level. The only way you could lose is if someone else were to successfully argue that the equation or symbol that came up was actually equivalent to a number less than or equal to 2, which seems pretty unlikely, though I wouldn't put it past an experienced debate team captain with a thorough knowledge of mathematics and a good poker face. If the two of you are the only people in the room who know what the equations mean, and everyone else could be convinced that they mean something else, I could see it happening. But I highly doubt it.

In any case, yeah, I would definitely be interested in such a die! I was just reading through the thread about the infamous dice with all ones, and being a math guy I found the idea very appealing. Sign me up!

[RevBob]

Originally Posted by Icositetrachoron

"Blue - 1" indeed. :)

Blue - 1 = Green, right? ;)

Originally Posted by Icositetrachoron

Yes! That's perfect. [...] If the two of you are the only people in the room who know what the equations mean, and everyone else could be convinced that they mean something else, I could see it happening. But I highly doubt it.

The ideas I've got are relatively basic, with a couple of oddities that allow each face to equate to a positive integer value while neither having duplication nor being boring. I think the trickiest face I came up with is this:

⌊π^2⌋

Pi squared is a bit less than 10 (about 9.86), so the floor of that number is 9.

[Icositetrachoron]

Originally Posted by RevBob

Blue - 1 = Green, right? ;)

Ha! Yes, or cyan. Personally I would choose cyan, but that's because I've been programming computers for years and colors totally work that way for me. In any case it's definitely not violet, as that would be an increase in photonic energy. Unless you're going for wavelength, in which case it's shorter. But I digress.

Originally Posted by RevBob

The ideas I've got are relatively basic, with a couple of oddities that allow each face to equate to a positive integer value while neither having duplication nor being boring. I think the trickiest face I came up with is this:

⌊π^2⌋

Pi squared is a bit less than 10 (about 9.86), so the floor of that number is 9.

I like it. Pi squared would look very nice when written in proper mathematical notation. I would like to hear more of your suggestions. Anything that equates to a 7 or greater will grant a level bonus even with a Chicken on Your Head, and the text of either card does not say anything about requiring integer values, so even decimals will work and they will count as their true values. I think 6.999999999..., written as 6.9 with a bar over the 9, would be a fun one, because it is in fact precisely equal to 7. However, that one is perhaps a bit counterintuitive, and may lose arguments among non-mathematicians in the presence of a Chicken. But it would always win for sure in the more likely case of no Chicken, and it's only one of six possible outcomes for the die, so it's not a big risk. My vote would be to leave it in anyway. Helps keep things interesting, and encourage debate and learning.

[RevBob]

Originally Posted by Icositetrachoron

the text of either card does not say anything about requiring integer values, so even decimals will work and they will count as their true values.

My goal was to make a die that would be useful for this, but also for other purposes - so integer results seemed more desirable. Offhand, I think this is what I came up with:

7: Seven pips, as on Loaded Die.
8: The numeral 8, which can also be read as the infinity symbol.
9: Floor of pi squared.
10: The Roman numeral X, possibly with bars to emphasize the numeric value rather than "times" or "the 24th letter."
11: Absolute value of the square root of 121.
12: 72 divided by three-factorial (72 / 3!), although (4! / 2) works just as well. Both come out to 12...

[Icositetrachoron]

Those are all great, and a nice spread of symbols and math concepts.

I still like my 6.999... idea (it is an integer, so it satisfies your additional restrictions), but I absolutely agree that we should pay homage to the seven pipped face on the Loaded Die card, a visual gag which I have always loved. Perhaps we should consider using the concept for another (higher-valued) face? This would negate any possible arguments about whether the result truly is >= 7, and so would be fully Chickenproof. How about 9.9(bar) for 10? This one has the advantage of looking particularly nice with the twin nines, and we could then use XI (with bars) for 11, which unlike X is quite clearly a Roman numeral and not simply a letter. Remember, the result must be unequivocally numeric, or it runs the risk of falling under the "any other result" umbrella.

For 12, I would tend to favor 4! / 2 over 72 / 3! for the former's simplicity, but the latter does have the advantage of still being 7+ if the factorial symbol is misinterpreted as excitement (it would then be 24). Another possibility is to use XII instead (a stately Roman numeral for the highest-valued face seems fitting), and then use the cube root of 1331 for 11 (a nice palindrome and an odd root so the result is unequivocally positive; no absolute value bars necessary).

I love the fact that the numeral 8 could also be interpreted as infinity; we will have to be sure that whatever font we use has both the top and bottom halves of the digit identical in size and shape (or just use the infinity symbol itself). This brings me to one thought I've been kicking around my head for a couple days: what would a roll of 1/0 grant you? The limit goes to both + and - infinity, so would you both gain AND lose a level, thus yielding no net effect? Or would it count as "undefined", thus granting you a face-up Treasure and a face-down Door? I'm not suggesting we attempt such mathematical foolishness for our die, I'm just curious what you think. :)

[RevBob]

Originally Posted by Icositetrachoron

How about 9.9(bar) for 10? This one has the advantage of looking particularly nice with the twin nines, and we could then use XI (with bars) for 11, which unlike X is quite clearly a Roman numeral and not simply a letter.

Trouble is, XI has no cues to distinguish it from IX. There's always 012 (octal for 10), but that's a mite obscure; 1010 (binary) or 0x0A would be better for that approach.

Originally Posted by Icositetrachoron

Another possibility is to use XII instead (a stately Roman numeral for the highest-valued face seems fitting), and then use the cube root of 1331 for 11 (a nice palindrome and an odd root so the result is unequivocally positive; no absolute value bars necessary).

I like the cube-root idea here, and XII is unambiguous where IX/XI is not. (5! / 12) would preserve the factorial concept for 10, but it feels weak to me. (60 / 3!) might be better, or (0x3C / 3!) to bring in the hexadecimal concept as well. Maybe 3C-sub-16 to use more math-standard "base 16" notation instead of the Perl/C version?

Originally Posted by Icositetrachoron

This brings me to one thought I've been kicking around my head for a couple days: what would a roll of 1/0 grant you?

I would count it as undefined; that's the conventional treatment.

[Icositetrachoron]

Originally Posted by RevBob

There's always 012 (octal for 10), but that's a mite obscure; 110 (binary) or 0x0A would be better for that approach.

I like the cube-root idea here, and XII is unambiguous. (5! / 12) would preserve the factorial concept for 10, but it feels weak to me. (60 / 3!) might be better, or (0x3C / 3!) to bring in the hexadecimal concept as well. Maybe 3C-sub-16 to use more math-standard "base 16" notation instead of the Perl/C version?

Yes, 5! / 12 should probably be avoided as it's another factorial fraction that would reduce to a small number if the symbol is misinterpreted. I like the hex idea, but I fear that it may be difficult to explain to (and convince) other players. But if we can get away with it it's great, particularly with the addition of the factorial as well. (Btw, for the record, 10 in binary is 1010, not 110; that's 6, and not so good if you've got a Chicken on Your Head. Oops.)

I still really, really like 9.9(bar). Did you have a particular objection to that?

Originally Posted by RevBob

I would count it as undefined; that's the conventional treatment.

Yeah, that's what I figured, but it would be very munchkinly for your opponents to argue that it counts as +/- infinity and thus grants you nothing. ;)

By the way, it occurs to me that your ⌊π^2⌋ suggestion for 9 has the additional advantage of being a Simpsons reference. Mmmm...floor pie...

[Icositetrachoron]

So what's up, guys? Are we doing these dice or what? I for one can't wait to get my hands on mine.

[RevBob]

Originally Posted by Icositetrachoron

So what's up, guys? Are we doing these dice or what? I for one can't wait to get my hands on mine.

There are discussions. Patience...

To avoid any possible confusion due to my job: nobody's talking about this being an SJGames product. Chessex makes custom-engraved dice in small quantities at a reasonable price; I believe that's who Chad went through last time. The project's his baby; I'm just a math geek with ideas.