扩展阅读

MTR 3.9 Card Shuffling. 万智牌规则明确指出, 卡组需要充分随机化, 分堆洗只能用于数卡组数量. https://blogs.magicjudges.org/rules/mtr3-9/

Decks must be randomized at the start of every game and whenever an instruction requires it. Randomization is defined as bringing the deck to a state where no player can have any information regarding the order or position of cards in any portion of the deck.

The phrase “order or position” is key. A deck that is “mana-weaved” is not random; even though the player may have no information about the location of a specific card, they have information about the cards’ order (that is, land-spell-spell, land-spell-spell). Also key is that a player shouldn’t know any information on where a card is, not even which half of the deck it is in.

Pile shuffling alone is not sufficiently random and may not be performed other than once each at the beginning of a game to count the cards in the deck.

Pile shuffling is completely non-random, since individual cards can be tracked and since cards are shuffled into a deterministic order. A single pile shuffle can help players count their decks and loosen sticky cards, but more than that a pile shuffle does not contribute to randomization and will qualify as Slow Play. Once the game has begun the need to count the deck during randomization is largely gone. As such, a single pile shuffle at the start of the game is permitted, but is not allowed at any other time. Please remember when applying the IPG that habits are hard to break, and a single caution may be appropriate the first time.

洗牌视频范例

贝吉特比赛视频, 拉到换 side 部分观看, 7 次插洗 + 1 次分堆. https://www.bilibili.com/video/av11256479?from=search&seid=6623988737135052825
MTG GP Prague 2017, 拉到换 side 部分观看, 双方都有 riffle shuffle, 略有不同, 洗牌次数也特别多. https://www.bilibili.com/video/av9535928?p=18

不涉及数学地谈洗牌

Shuffling: The Truth and Maths (Primer). https://www.mtgsalvation.com/forums/magic-fundamentals/magic-general/334934-shuffling-the-truth-and-maths-primer
最好和最坏的洗牌方式, Diaconis 本人出镜解释. https://www.bilibili.com/video/av2339183
郭城: 谈谈洗牌. https://mp.weixin.qq.com/s/H25kkfFRde0stbUEFzwivg

关于洗牌的论文

Trailing the Dovetail Shuffle to its Lair by Diaconis. 关于洗牌最著名的文章, 正文如文章名一般有趣. https://statweb.stanford.edu/~cgates/PERSI/papers/bayer92.pdf
The cutoff phenomenon in finite Markov chains. Diaconis 尝试在一定程度上解释 cut-off 现象出现的原因. https://www.pnas.org/content/pnas/93/4/1659.full.pdf
How many times should you shuffle a deck of cards. 我觉得最易读的论文. https://www.dartmouth.edu/~chance/teaching_aids/Mann.pdf

关于本文

起因是吐槽一篇日本文章不可靠, 见 https://weibo.com/ttarticle/p/show?id=2309404477060755095579

后来顺便就写了这篇. 这篇是 3 月 7 日的修改版, 因为还没有收到反馈, 仅仅是修正了少许 typo, 增删少量内容. 3 月 5 日原版见 https://mp.weixin.qq.com/s/wQLWX7x9NFpVCK3Dk9u7Xw

虽然标题带有 ''数学'' 二字, 但通篇几乎不涉及稍微复杂一点的计算和证明, 只讲想法.

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有温度的玩家社区

洗牌的真相

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