This post is part of 🐶 Bleptember, a month-long celebration of our dog's inability to keep her tongue inside her mouth.
“Is is walkies time yet? How about now? Now? What about now?” Her blep partially-engaged, our doggo buzzes with excited anticipation as I put on my shoes.
A quick and easy cache-and-dash in-between errands. I’ve got gardening gloves; I’ve got supplies to make brunch… and I’ve got ten minutes spare, so I came to find this cache.
Container might enjoy some camo tape or something if it’s not to be mistaken for litter! TFTC.
Dungeons & Dragons players spend a lot of time rolling 20-sided polyhedral dice, known as D20s.
In general, they’re looking to roll as high as possible to successfully stab a wyvern, jump a chasm, pick a lock, charm a Duke1,
or whatever.
Roll with advantage
Sometimes, a player gets to roll with advantage. In this case, the player rolls two dice, and takes the higher roll. This really boosts their chances of not-getting a
low roll. Do you know by how much?
I dreamed about this very question last night. And then, still in my dream, I came up with the answer2.
I woke up thinking about it3
and checked my working.
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Table illustrating the different permutations of two D20 rolls and the “advantage” result (i.e. the higher of the two).
The chance of getting a “natural 1” result on a D20 is 1 in 20… but when you roll with advantage, that goes down to 1 in 400: a huge improvement! The chance of rolling a 10 or 11 (2 in
20 chance of one or the other) remains the same. And the chance of a “crit” – 20 – goes up from 1 in 20 when rolling a single D20 to 39 in 400 – almost 10% – when rolling with
advantage.
You can see that in the table above: the headers along the top and left are the natural rolls, the intersections are the resulting values – the higher of the two.
The nice thing about the table above (which again: was how I visualised the question in my dream!) is it really helps to visualise why these numbers are what they are. The
general formula for calculating the chance of a given number when rolling D20 with advantage is ( n2 – (n-1)2 ) / 400. That is, the square of the number
you’re looking for, minus the square of the number one less than that, over 400 (the total number of permutations)4.
Why roll two dice when one massive one will do?
Knowing the probability matrix, it’s theoretically possible to construct a “D20 with Advantage” die5. Such a tool would
have 400 sides (one 1, three 2s, five 3s… and thirty-nine 20s). Rolling-with-advantage would be a single roll.
This is probably a totally academic exercise. The only conceivable reason I can think of would be if you were implementing a computer system on which generating random numbers
was computationally-expensive, but memory was cheap: under this circumstance, you could pre-generate a 400-item array of possible results and randomly select from it.
But if anybody’s got a 3D printer capable of making a large tetrahectogon (yes, that’s what you call a 400-sided polygon – you learned something today!), I’d love to see an “Advantage
D20” in the flesh. Or if you’d just like to implement a 3D model for Dice Box that’d be fine too!
Footnotes
1 Or throw a fireball, recall an anecdote, navigate a rainforest, survive a poisoning,
sneak past a troll, swim through a magical swamp, hold on to a speeding aurochs, disarm a tripwire, fire a crossbow, mix a potion, appeal to one among a pantheon of gods, beat the
inn’s landlord at an arm-wrestling match, seduce a duergar guard, persuade a talking squirrel to spy on some bandits, hold open a heavy door, determine the nature of a curse, follow a
trail of blood, find a long-lost tome, win a drinking competition, pickpocket a sleeping ogre, bury a magic sword so deep that nobody will ever find it, pilot a spacefaring rowboat,
interpret a forgotten language, notice an imminent ambush, telepathically commune with a distant friend, accurately copy-out an ancient manuscript, perform a religious ritual, find
the secret button under the wizard’s desk, survive the blistering cold, entertain a gang of street urchins, push through a force field, resist mind control, and then compose a ballad
celebrating your adventure.
2 I don’t know what it says about me as a human being that sometimes I dream in
mathematics, but it perhaps shouldn’t be surprising given I’m nerdy enough to have previously recorded instances of dreaming in (a) Perl, and (b) Nethack (terminal mode).
3 When I woke up I also found that I had One Jump from Disney’s Aladdin stuck in my head, but I’m not sure
that’s relevant to the discussion of probability; however, it might still be a reasonable indicator of my mental state in general.
4 An alternative formula which is easier to read but harder to explain would be ( 2(n
– 1) + 1 ) / 400.
5 Or a “D20 with Disadvantage”: the table’s basically the inverse of the advantage one –
i.e. 1 in 400 chance of a 20 through to 39 in 400 chance of a 1.
Maintaining a blog can be a lot of work. A single article can take weeks of research, drafting and editing, collecting and producing included materials, etc. It’s not unusual to
seek some form of compensation for it, and those rewards require initiative. With a good monetization strategy, it can become a fairly
lucrative venture.
So let’s talk about monetizing a blog, starting with the most obvious and perhaps easiest avenue: display advertising.
A content creator with an established audience can leverage that audience and sell ad space on their blog. Here’s an example:
…
I’m not sure I have words for how awesome this blog post is. If you’ve ever wanted to monetise your blog and are considering an ad-driven model, this should absolutely be the first (and
perhaps last) thing you read on the subject.
If you’re not convinced that Tyler is an appropriate authority to speak on this subject, I highly suggest you visit their other site that’s got a wealth of useful tips, PutAToothpickInTheChargingPortDoctorsHateThatShit.christmas. Yes, really.
This post is part of 🐶 Bleptember, a month-long celebration of our dog's inability to keep her tongue inside her mouth.
Such poise! Such grace! While out for a run around with her doggy pals this Eleventh of Bleptember, our dog takes every opportunity to show off her elegance and style and definitely
not just look like a derpy little wazzock.
I like pickled onions. And I imagine that the flavourings used in pickled onion crisps are basically the onion flavouring from cheese & onion and the vinegar flavouring from salt &
vinegar, both of which are varieties I like.
Perhaps inspired by my resharing of Thomas‘s thoughts about the biggest problem in
AI (tl;dr: he thinks it’s nomenclature; I agree that’s a problem but I don’t know if it’s the biggest issue), Ruth posted some thoughts to LinkedIn that I think are quite well-put:
I was going to write about something else but since LinkedIn suggested I should get AI to do it for me, here’s where I currently stand on GenAI.
As a person working in computing, I view it as a tool that is being treated as a silver bullet and is probably self-limiting in its current form. By design, it produces average
code. Most companies prior to having access to cheap average code would have said they wanted good code. Since the average code produced by the tools is being fed back into those
tools, mathematically this can’t lead anywhere good in terms of quality.
However, as a manager in tech I’m really alarmed by it. If we have tools to write code that is ok but needs a lot of double checking, we might be tempted to stop hiring
people at that level. There already aren’t enough jobs for entry level programmers to feed the talent pipeline, and this is likely to make it worse. I’m not sure where the next
generation of great programmers are supposed to come from if we move to an ecosystem where the junior roles are replaced by Copilot.
I think there’s a lot of potential for targeted tools to speed up productivity. I just don’t think GenAI is where they should come from.
This is an excellent explanation of no fewer than four of the big problems with “AI” as we’re seeing it marketed today:
It produces mediocre output, (more on that below!)
It’s a snake that eats its own tail,
It’s treated as a silver bullet, and
By pricing out certain types of low-tier knowledge work, it damages the pipeline for training higher-tiers of those knowledge workers (e.g. if we outsource all first-level tech
support to chatbots, where will the next generation of third-level tech support come from, if they can’t work their way up the ranks, learning as they go?)
Let’s stop and take a deeper look at the “mediocre output” claim. Ruth’s right, but if you don’t already understand why generative AI does this, it’s worth a
little bit of consideration about the reason for it… and the consequences of it:
Mathematically-speaking, that’s exactly what you would expect for something that is literally statistically averaging content, but that still comes as a surprise to people.
Bear in mind, of course, that there are plenty of topics in which the average person is less-knowledgable than the average of the content that was made available to the model.
For example, I know next to noting about fertiliser application in large-scale agriculture. ChatGPT has doubtless ingested a lot of literature about it, and if I ask it what
fertiliser I should use for a field of black beans in silty soil in the UK, it delivers me a confident-sounding answer:
When LLMs produce exceptional output (I use the term exceptional in the sense of unusual and not-average, not to mean “good”), it appears more-creative and interesting but is even
more-likely to be riddled with fanciful hallucinations.
There’s a fine line in getting the creativity dial set just right, and even when you do there’s no guarantee of accuracy, but the way in which many chatbots are told to talk makes them
sound authoritative on basically every subject. When you know it’s lying, that’s easy. But people don’t always use LLMs for subjects they’re knowledgeable about!
In my example above, a more-useful robot would have stated that it didn’t know the answer to the question rather than, y’know, lying. But the nature
of the statistical models used by LLMs means that they can’t know what they don’t know: they don’t have a “known unknowns” space.
Regarding the “damages the training pipeline”: I’m undecided on whether or not I agree with Ruth. She might be on to something there, but I’m not sure. Needs more
thought before I commit to an opinion on that one.
Oh, and an addendum to this – as a human, I find the proliferation of AI tools in spaces that are all about creating connections with other humans deeply concerning. I saw a lot of
job applications through Otta at my previous role, and they were all kind of the same – I had no sense of the person behind the averaged out CV I was looking at. We already have a
huge problem with people presenting inauthentic versions of themselves on social media which makes it harder to have genuine interactions, smoothing off the rough edges of real people
to get something glossy and processed is only going to make this worse.
AI posts on social media are the chicken nuggets of human interaction and I’d rather have something real every time.
Emphasis mine… because that’s a fantastic metaphor. Content generated where a generative AI is trying to “look human” are so-often bland, flat, and unexciting: a mass-produced
most-basic form of social sustenance. So yeah: chicken nuggets.
This post is part of 🐶 Bleptember, a month-long celebration of our dog's inability to keep her tongue inside her mouth.
How is it the Tenth of Bleptember already? This young lady has so-far put off her morning nap and is instead intently watching me to see what I do next with my workday. Maybe it’ll
involve dog treats! (Spoiler: it probably won’t. But you never know…)