Talk:Binary lot

Hi user:Phil wink. Nice. I've not read all yet.

So far, I have a few minor things I'd suggest changing:

• A style guide thing: Integers below 10 are spelled out when appearing in plain text. Larger numbers "expressible in one or two words" can be spelled out. I think this rule should be applied with some discretion; e.g., I wouldn't like to see sth like "x is between nine and 101".
• There are two things about the diagram of outcomes of casting one to eight coins that I'd suggest changing:
• # Seems you've made it as a screen shot, which is OK, but there's an unwanted mouse-over label at one data point.
• # The data are points, not curves, so I'd show the points as bullets. The lines are useful as a visual aid, so I'd include them, but make them thin.

Nø (talk) 10:18, 13 April 2025 (UTC)

: Thanks for reviewing. For spelled numbers, I decline. There may be a place for such rule in, say, novels, where consistency of texture is desirable. But in a fundamentally technical work in which the numbers exist to be compared with other numbers, added to them, etc., the rule is counterproductive. If other editors feel the need to degrade the clarity of this article by spelling out numbers, sobeit; but I won't. On the chart: oops. Good catch. Thanks. You're right about the data, but in my view adding points would make the graphics distractingly prickly, without really adding to the clarity; I think Tufte would be on my side. However, it struck me that white points -- essentially perforations in the lines -- might be acceptable to both of us. Re-uploaded. What do you think? Phil wink (talk) 21:28, 13 April 2025 (UTC)

::Numbers: MOS:NUMERAL allows for (among other exceptions), quote:

:::... "numbers as numbers" are rarely spelled out in ... mathematical contexts (the first three primes are 2, 3, and 5 not the first three primes are two, three, and five; but zero-sum game and roots of unity).

::(I'm not sure what they mean by "numbers as numbers", with the quotation marks in the original!) I tend to agree with you on this, but I think it is likely other editors will not.

::The diagram: I've been trying a number of things myself (in Excel); I have not found a solution that I really like, but I'd consider

::#making the lines much thinner

::#making them smooth rather than stright (one is not more "correct" than the other - only no lines is "correct", but they are needed to guide the eye)

::#I think you've used white circular markers to make the gaps; I'd add a thin line (a circle, that is) around each marker; same width as the curves

::#but it's annoying that e.g. the point with coordinates (2, 37.5%) should have two colours at the same time (so one could make all the circles black)

::#Arguably, a curve for one die could be added to the diagram.

::#I think it makes the graph easier to read (though it needs a few more words for explanation) if you only show data for (1,) 2, 3, 5 and 8 dice. (This could go with thin smooth curves and solid circular markers of the same colour.)

::Nø (talk) 17:16, 14 April 2025 (UTC)

:::Here's a suggested alternative.

:::File:Casting undistinguished binary lots.png

:::user:Phil wink, if you more or less like it, you could

:::* use it

:::* ask me to make modifications you'd prefer and upload again

:::* ask me to share (e-amil?) the underlying Excel file so you can make modifications

:::Also, the following diagrams in the article could and should in my opinion be modified in a similar vein - I could do those too ... ? Nø (talk) 11:25, 20 April 2025 (UTC)

I think many readers (of those few who ever read this article) would like an answer to this question: What are the typical probabilities when casting staves or cowries? But we cannot answer that without a reliable source, which I don't have. While cowries may be quite reproducible, I think small modifications to the geometry of the staves can make significant difference for the probabilitites.

(A COMPLETELY different subject, and probably OR, is this: How can one with one type of randomizer simulate another type, or produce any desired probablity distribution?

1. With any binary lot (with known or unknown, but constant, probabilities), like cowries, staves or thumbtacks, one can simulate a fair coin by throwing twice (or by casting two distinguished lots with identical probabilities), logging the outcome A-then-B as head and B-then-A as tail, but starting over with outcomes A-then-A and B-then-B.
2. With a fair coin, one can generate any discrete probability distribution (technically: with a finite number of possibilities) with a finite number of coin tosses (on average), through writing the cumulated probability distribution in binary notation. Let head=0, tail=1, and write the outcome of successive tosses as 0.xyz...(2), where x is the first toss, y 2nd, etc., and where (2) means read this as a binary number (which will be between 0 and 1, both included). E.g., to get odds 1:2, i.e. P(success)=1/3 and P(fail)=2/3, first write 1/3 = 0.01010101...(2). If the first toss is a tail, so we have the outcome 0.1(2)=0.5, we're above 1/3 and finish with a fail. If the first toss is a head we have 0.0(2)=0, but as continued tossing could yield 0.011111...(2)=0.5, we don't know yet if we are above or below 1/3, so we throw again. If we get 0.00(2) (the second throw is also head), we are below (as even 0.0011111...(2) = 0.25 is below) and finish with a success, but with 0.01(2) we don't know yet, so we throw again, etc.
3. There are many other cases, such as getting any distribution with a normal die or with any binary lot.

These procedures may perhaps be optimized to get the result in fewer throws on average (e.g., in case 1., AABB may be interpreted as head and BBAA as tail).

) Nø (talk) 12:08, 20 April 2025 (UTC)