A recent discourse in this forum on shuffling made me compose this list of points.
"Shuffling" means to take a deck of cards from one order to another in such a way that all cards' positions are unknown.
It is not humanly possible to perfectly shuffle a deck through physical manipulation.
What that means, is that some residual bias from the original order will remain in the final order. Assuming it is gone, or even that it can be made unnoticeable, is the first mistake laypersons make when they try to describe shuffling.
"Bias" does not have to mean "observable pattern." That is the second mistake laypersons make.
"Bias" means many things, depending on what you look at. If you look at two specific cards, it means the probability that the ordered difference in their positions is not equal, for all possible values.
If you look at two pairs, it means that when one difference is lower than average, the other tends to be lower and/or higher than average. This is called correlation.
When you look at a group, such as lands, it means that complex measures of how the group is distributed are not what is expected. The two most interesting are the density in certain subsets of the deck, and the distances between lands. While different, these two measures of land-bias are related. And there are others, that relate to correlation. Most do not appear visible when you look at a deck, and do not affect game play.
By far, the most significant land-bias a deck could have is to place a large number of them together. Every possible measure of land-bias is at its worst. All of the density is in one portion. The distances are minimum in that portion, and maximum elsewhere. The discrepences from expected values are completely correlated.
By comparison, placing them evenly throughout the deck is a very small land-bias, since most (but definitely not all) measures of bias are what is expected. The average density is what is expected. The average distances are what is expected. The bias that does exist is in correlation, but that actually is not as large as in the stacked deck.
"Sufficient shuffling" can not mean all bias is removed, since that is impossible. It means that residual bias does not significantly affect the play of the deck. Assuming it is gone was the first mistake I mentioned above. And residual bias in the realm of correlation is probably quite high, numerically speaking, for most people's shuffles.
In general, the closer a deck starts to being unbiased with respect to a group of cards, such as land, the less bias there will be in the final deck.
Residual land-bias does not have to be the same kind of bias as the original bias. This is the third mistake.
A shuffle that starts with the land all stacked at one end will have the most residual bias. A shuffle that starts with the most significant land-bias measures set to the expected values will have the least.
The statement "If you shuffle sufficiently, you totally remove any effect of weaving" is incorrect. It represents the best starting position, short of an already randomized deck. It will have the least residual land-bias.
The statement "If you think weaving has any effect on the final order, you are counting on an advantage from it and so you are cheating" is incorrect. If you are shuffling honestly, you are counting on not being placed at a disadvantage due to the residual land-bias from stacking.
But I do not recommend weaving. It's not because it isn't a good idea. It's because of the people who think the two weeks they spent on probability theory in High School, and probably misunderstand most of, is sufficient for them to lecture others on the fine details of doctorate-level information theory. Those people will be prejudiced toward any activity they suspect you could to use to cheat, either intentionally or unintentionally. They will look for evidence that you are cheating, valid or invalid, and you will get the maximum penalty if they think they found it.
And to be fair to them, it is possible to cheat that way, both intentionally or unintentionally. But the fallacy in their prejudice is that anybody skilled enough to do it intentionally does not need to weave to do it, and anybody who ends up doing it unintentionally is already not randomizing sufficiently with respect to other kinds of cards. Probably to their disadvantage.
Your shuffling method does not completely randomize your deck, but it doesn't need to. Close is indeed good enough in hand grenades, horseshoes, and shuffling. But if your technique is suspect, you will do better (meaning "get closer to random," not "always get favorable land distribution in general") if you spread any one group of cards out approximately evenly as the first act of shuffling.
What I'd do is take all of the cards that were in use (play, grave, rfg) the game before, and mix them once with whatever you call "one shuffle." This spreads out the various kinds of cards you used, relative to one another, more or less evenly. Then do one shuffle between the cards from play, and the ones in the library. Then proceed with your normal shuffle. This should not be seen as an attempt to cheat, and will accomplish all the same things.
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And to be fair to them, it is possible to cheat that way, both intentionally or unintentionally. But the fallacy in their prejudice is that anybody skilled enough to do it intentionally does not need to weave to do it, and anybody who ends up doing it unintentionally is already not randomizing sufficiently with respect to other kinds of cards. Probably to their disadvantage.
Your shuffling method does not completely randomize your deck, but it doesn't need to. Close is indeed good enough in hand grenades, horseshoes, and shuffling. But if your technique is suspect, you will do better (meaning "get closer to random," not "always get favorable land distribution in general") if you spread any one group of cards out approximately evenly as the first act of shuffling.
What I'd do is take all of the cards that were in use (play, grave, rfg) the game before, and mix them once with whatever you call "one shuffle." This spreads out the various kinds of cards you used, relative to one another, more or less evenly. Then do one shuffle between the cards from play, and the ones in the library. Then proceed with your normal shuffle. This should not be seen as an attempt to cheat, and will accomplish all the same things.