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[sorawotobu]

I have experimentally shown that the mathematical model is not a good fit to human shuffling.

I don't know how you think you've proven the research I linked wrong since you haven't posted any proof, did you just shuffle a deck of cards once and expect us to trust you saying it wasn't well shuffled? Do you think all the research on this subject as well as the experience of card players from the past centuries are wrong and you know better because you shuffled a deck once?

In fact, the mathematical model is the optimal way to shuffle the cards and any human way to shuffle them is worse.

...

What the mathematical model does show is that fewer than seven riffle shuffles can't be enough to randomize the deck, but it doesn't show that seven is enough, it's just a lower bound.

You obviously haven't read any research on this topic. May I suggest actually reading the paper I linked or perhaps this famous paper, which was the first peer reviewed paper on the subject afaik. How you can think that being better at shuffling cards makes you worse at shuffling cards is a mystery to me.

Seven riffles plus a pile shuffle are entirely sufficient though. The patterns are there but it doesn't matter since the pile shuffle makes it practically impossible to detect them.

That doesn't even make any sense. I'm starting to think you're actually trolling.

[Awaclus]

I don't know how you think you've proven the research I linked wrong since you haven't posted any proof, did you just shuffle a deck of cards once and expect us to trust you saying it wasn't well shuffled? Do you think all the research on this subject as well as the experience of card players from the past centuries are wrong and you know better because you shuffled a deck once?

I've played Magic since I was 8 and practiced close-up sleight of hand tricks since high school but yeah, I bet I've only ever riffle shuffled a deck of cards once.

I'm not saying the research on this subject is wrong, I'm saying you are drawing conclusions that don't actually follow from the data.

You obviously haven't read any research on this topic. May I suggest actually reading the paper I linked or perhaps this famous paper, which was the first peer reviewed paper on the subject afaik. How you can think that being better at shuffling cards makes you worse at shuffling cards is a mystery to me.

I have, in fact, read research on this topic, including the paper you linked earlier (I hadn't read the one you just posted though). The better you are at riffle shuffling, the closer you are to the perfect riffle shuffle which is a fully deterministic procedure and not at all random, it is very possible to practice until you get it right every time, and any practice you get in shuffling gets you closer to that and further away from the mathematical model. How this is such a mystery to you is a mystery to me.

That doesn't even make any sense. I'm starting to think you're actually trolling.

It's not a difficult concept. Pile shuffling increases entropy, and entropy makes it more difficult to predict the order in which your cards are.

[sorawotobu]

I've played Magic since I was 8 and practiced close-up sleight of hand tricks since high school but yeah, I bet I've only ever riffle shuffled a deck of cards once.

I'm not saying the research on this subject is wrong, I'm saying you are drawing conclusions that don't actually follow from the data.

You are making claims that contradict the findings of the research, one of which is that their model does in fact accurately represent human shuffling. You claimed to have shown this is not true without telling us how you accomplished that. If you released your work and it turned out to be what you say it is, it will surely be published. there might be fame and money in it for you!

The better you are at riffle shuffling, the closer you are to the perfect riffle shuffle which is a fully deterministic procedure and not at all random, it is very possible to practice until you get it right every time, and any practice you get in shuffling gets you closer to that and further away from the mathematical model.

If you specifically practice the perfect shuffle, you can get it pretty reliably if you try. That doesn't mean you won't be able to stop yourself from shuffling this way unconsciously.

It's not a difficult concept. Pile shuffling increases entropy, and entropy makes it more difficult to predict the order in which your cards are.

So your point of critique against riffle shuffling is that under certain circumstances (which don't arise unless someone is purposely trying to cheat; I'm talking about actual shuffling, not card tricks) it is deterministic. Adding a layer of deterministic rearrangement of the cards ought to fix that!

[LastFootnote]

Don't feed the Awaclus.

[Donald X.]

I always base my shuffling on particles decaying; I mean there's actual randomness. If your deck doesn't have a quantum superposition, it's not really shuffled.

[Awaclus]

You are making claims that contradict the findings of the research, one of which is that their model does in fact accurately represent human shuffling. You claimed to have shown this is not true without telling us how you accomplished that. If you released your work and it turned out to be what you say it is, it will surely be published. there might be fame and money in it for you!

It's not exactly a new idea that experienced shufflers are more skilled (i.e. less random) at shuffling than others. The research you are referring to never says that it applies to skilled shufflers; you are making that part up all on your own. Which is to say that my claims don't contradict the research, they contradict your claims that are not based on the research.

If you specifically practice the perfect shuffle, you can get it pretty reliably if you try. That doesn't mean you won't be able to stop yourself from shuffling this way unconsciously.

You don't have to specifically practice the perfect shuffle. Any time you spend riffle shuffling contributes towards your future shuffles being less random, because the randomness comes from the fact that you're supposed to suck at it.

So your point of critique against riffle shuffling is that under certain circumstances (which don't arise unless someone is purposely trying to cheat; I'm talking about actual shuffling, not card tricks) it is deterministic. Adding a layer of deterministic rearrangement of the cards ought to fix that!

My point is not really a critique against riffle shuffling. Riffle shuffling is fine if you do it more than 10 times. I'm specifically taking an issue with your incorrect stance that exactly 7 times is enough. What's more is that you also can't apply the 52-card deck math to 60-card decks as directly as you might think based on the fact that the difference between 52 and 60 doesn't seem that big, because the difference between 52! and 60! is actually pretty big.

The problem with riffle shuffling, though, is that it can damage unsleeved cards more than a lot of people are willing to damage their TCG or board game cards, and that's why they'll stick to something like the overhand shuffle, which is actually super crap at randomization. But if you start with a deck that is in no particular order but you know some parts of that order, pile shuffle it and overhand shuffle it for a while, that's basically enough to achieve all the purposes you need the randomization for.

[Loempiaverkoper]

The problem with riffle shuffling, though, is that it can damage unsleeved cards more than a lot of people are willing to damage their TCG or board game cards, and that's why they'll stick to something like the overhand shuffle, which is actually super crap at randomization. But if you start with a deck that is in no particular order but you know some parts of that order, pile shuffle it and overhand shuffle it for a while, that's basically enough to achieve all the purposes you need the randomization for.

Well I agree with this.
If this is actually what you were getting at, why go through all those weird lines of argumentation against the math, with mentions of private experiments and appeals to your own authority?

[Cave-o-sapien]

The more interesting thing to me with respect to Dominion shuffling is that you are very rarely shuffling your entire deck. Usually your deck gets compartmentalized into sub-decks, some of them quite small, which can result in certain sets of cards showing up in the same hands with greater probability than if you were shuffling the entire deck. Smarter players than me no doubt take advantage of this.

(I suppose it's also worth pointing out that shuffling small sub-decks makes it easier to cheat IRL).

The problem with riffle shuffling, though, is that it can damage unsleeved cards more than a lot of people are willing to damage their TCG or board game cards, and that's why they'll stick to something like the overhand shuffle, which is actually super crap at randomization. But if you start with a deck that is in no particular order but you know some parts of that order, pile shuffle it and overhand shuffle it for a while, that's basically enough to achieve all the purposes you need the randomization for.

Do you mean mash shuffling or overhand shuffling? In theory, mash shuffling, if well-executed, is equivalent to a riffle shuffle. When playing paper Dominion I mash shuffle my sleeved cards (as do most other players I've played with).

If you mean strictly overhand shuffles, then I disagree that a combination of pile shuffling and overhand shuffling would achieve sufficient randomness.

[sorawotobu]

Don't feed the Awaclus.

I'll try stick to that advice from now on, just one last thing because I can't help it:

What's more is that you also can't apply the 52-card deck math to 60-card decks as directly as you might think based on the fact that the difference between 52 and 60 doesn't seem that big, because the difference between 52! and 60! is actually pretty big.

I don't know why you think the difference between 52! and 60! plays a role if you are, as you claim to be, familiar with the research on this problem. From the first paragraph of the paper by Bayer & Diaconis:

3/2 log2(n)+θ shuffles are necessary and sufficient to mix up n cards.

Logarithmic growth <linear < polynomial < exponential < factorial growth, in case you weren't aware.

[Awaclus]

Well I agree with this.
If this is actually what you were getting at, why go through all those weird lines of argumentation against the math, with mentions of private experiments and appeals to your own authority?

This is what I was originally getting at. The riffle shuffle discussion was largely unrelated but I had to have it because sorawotobu's claim about 7 times being sufficient was wrong.

Do you mean mash shuffling or overhand shuffling? In theory, mash shuffling, if well-executed, is equivalent to a riffle shuffle. When playing paper Dominion I mash shuffle my sleeved cards (as do most other players I've played with).

If you mean strictly overhand shuffles, then I disagree that a combination of pile shuffling and overhand shuffling would achieve sufficient randomness.

I mean overhand shuffles. I'm not saying it achieves much randomness at all, I'm saying it doesn't matter that it's not very random since the shuffle is both fair and unpredictable, which are the qualities that you really want from a random shuffle anyway.

I don't know why you think the difference between 52! and 60! plays a role if you are, as you claim to be, familiar with the research on this problem.

Because I'm not a mathematician. Point taken though.