💬 Proven correct
@LivInTheLookingGlass The shuffle I'm most familiar with involves taking cards from the middle of the deck and placing them on the top or bottom of the deck, and there aren't any cards in the middle of a two card deck.
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Martin Randall made M$2!
You can roll a D1 -- no one questions that you can roll a marble. The fact that the outcome is a foregone conclusion is not relevant.
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@Duncan A marble isn't a one-sided die, because the sides of a die have to be flat.
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@MartinRandall Is that a real requirement or did you make it up on the fly just now? I would think that the sides just need to have equal probability of being landed on. https://en.wikipedia.org/wiki/Dice#Spherical_dice
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@MichaelWheatley !!!! what a boring definition!
You can certainly buy dice without flat sides: https://www.atomicempire.com/Item/266717
And all kinds of fun dice with sides that can't be landed on at all:
https://www.pippd.com/products/the-dice-lab-unique-individual-d3-die-1-piece-or-assortment-choose-your-color
There's not a large market for unfair dice (officially) but loaded dice are still dice.
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On a more serious note, the idea that any part of a 'dice' concepts is that it be a platonic solid is bunkum. The point of a die is to distribute probabilities in a known fashion (and there are plenty of ways of doing this without having equal probabilities, e.g., average dice). What makes something a die is that it does this and rolls, rather than spins. A marble rolls and distributes probabilities in a known fashion, so ergo, it is a die.
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(You can also spin a marble to distribute probabilities in a known manner, so marbles are also spinners. Yay marbles!)
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@Duncan @MichaelWheatley I agree that the concept is fuzzy around the edges, like all concepts. Still, a marble isn't a die.
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@MartinRandall Very fuzzy. I'd say that a marble is totally a die, as long as you write the number 1 on it, but a countdown die is only sort of a die -- a counter that could be used as a die, if you didn't have a proper D20 at hand. Neither of these would meet the standard of common usage.
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No. For people who answer yes, can you shuffle a list of 0 items?
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@BionicD0LPH1N if you're a programmer, does
`fun shuffle(X)` accept the empty array?
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You have to define this before you shuffle, otherwise the shuffle is invalid and you have to restart the process. However, any definition is okay as long as all involved parties agree.
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No. You can perform the shuffle operation on a list of any (finite) size, but if it is not possible to change the order, it doesn't make sense to call it shuffled
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@LivInTheLookingGlass maybe you can shuffle it, but it cannot be 'shuffled'?
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@LivInTheLookingGlass The shuffle I'm most familiar with involves taking cards from the middle of the deck and placing them on the top or bottom of the deck, and there aren't any cards in the middle of a two card deck.
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Another way of saying it: cutting a deck is not the same as shuffling it.
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@MartinRandall If you cut by taking half the deck and placing it under the remaining half, then some would say that a cut is the atomic unit of shuffle.
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@Duncan no, if you keep cutting then you never change the looped order. 123 with a cut can't become 213.
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@MartinRandall Hm... good point. Not an issue is the 'list of one' case, but I now agree that you can't count cutting and shuffling as the same thing on different levels.
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@MartinRandall Right, but you could count "taking a card from the deck and placing it in the deck at an arbitrary position" to be the atomic unit, in which case you could see this two card shuffling as doing that
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I think this is a serious filter effect, I think most random people in the street would actually answer no
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Followup: Does the answer to this question change if we are talking about physical objects? IE - Can you shuffle a single card in your hand?
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@SneakySly I would say you can. To me, shuffling is about making the epistemic status in superposition with every configuration (ie. if I have three cards, then my prior should be equally divided between 123, 132, 213, 231, 312, 321)
If I only have a single card in hand, then it's in superposition with every other configurations - of which there are none
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@JoyVoid So can I hold a card in my hand, and claim to have just shuffled my hand a million times?
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@SneakySly I want to say no, it is shuffled, but you haven't shuffled it a million time. The reason why is that the sense I was using "shuffle" (putting it in superposition with every other states) is different to the mechanical action of taking cards and putting them together in an interlaced fashion
In my shuffle-as-superposition acceptation, it doesn't make to shuffle a million times, it's equivalent to doing it once. In the shuffle-as-mechanical-action acceptation, though, it completely makes sense, you can see several well-defined moments, perhaps you also use different methods (bridge shuffle, pile shuffle, etc)
I agree that you can't really shuffle-as-mechanical-action a deck containing a single card. I'm not sure I can meaningfully shuffle a deck of two cards several times either
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@JoyVoid Oh, I wouldn't say that shuffling makes every state equally possible. The final distribution can still be influenced by the starting distribution, that would be a difference between shuffling and randomizing.
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Oh I'm not saying it makes every state equally possible. What I am saying is that it makes - if I shuffled thoroughly enough - my epistemic uncertainty maximally confused, that I cannot know any useful fact on my deck, as opposed to the deontic probability of the configuration of this deck
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> I'm not sure I can meaningfully shuffle a deck of two cards several times either
@JoyVoid I think you can, just put them next to eachother and shove them together.
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:D
It still doesn't feel like "shuffling", probably because it's hard to lose track of which is which
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@JoyVoid what if the shuffling process is like this:
1. take 2 cards
2. add 50 blank cards
3. shuffle the deck
4. remove the blank cards
I think with 2 cards, this would be shuffling. With only one card not so much.
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