你压到牌底的那张牌,什么时候会回来
您的数据
让这件事可以数、而不是靠猜的,是你压到牌底的牌,是按你压下去的顺序排在那里的。这里没有任何东西绑定在某一款游戏上:任何一副从顶上抽、从底下加的牌组,都是一条队伍,而不是一次洗牌。
结果
| 整副牌转一圈要几个回合 | — |
| 现在压到牌底的牌,第几个回合回来 | — |
| 有多少个回合的牌会在同一个回合回来 | — |
| 牌组每回合少几张 | — |
| 牌组再也凑不出一次完整抽牌的回合 | — |
一个回合一个回合看,各自什么时候回来
| 回合 | 牌组的张数 | 要等几个回合 | 第几个回合回来 |
|---|
把最后一列从上往下读,有用的东西就出现了:它在重复。连着好几个回合,都把自己的牌送回同一个回合——因为它们排队的时候队伍在变短,后压下去的牌追上了先压下去的牌。
也就是说,把一张牌多留一个回合,往往完全不会改变你下次见到它的时间。选择“压什么下去”是真正的选择;而在那个窗口里选择“什么时候压”,多半不是。
这里一点概率都不需要,而这正是它值得去数的原因。一旦底下的顺序已知,问题就不再是“这张牌出现的可能性有多大”,而是“它在第几个回合出现”——后者是可以据以安排的,而不是只能指望的。
这为什么算得出来?
Because what goes underneath goes underneath in order. That makes the deck a queue rather than a shuffle, and a queue has positions you can count instead of odds you have to guess at.
A card you put under now sits below everything already there, so it comes up once those have been drawn: the deck size divided by what you draw each turn, rounded up.
我在第几回合把它放到底部有影响吗?
Far less than it feels, once the deck is shrinking. The queue in front of the card gets shorter while the card waits, so a card put under later catches up with one put under earlier and they arrive together.
With forty cards, drawing four and putting one under each turn, everything put under on turns two, three, four and five comes back on turn twelve.
| 把它放到底部的回合 | 牌组的张数 | 要等几个回合 | 第几个回合回来 |
|---|---|---|---|
| 1 | 40 | 10 | 11 |
| 2 | 37 | 10 | 12 |
| 3 | 34 | 9 | 12 |
| 4 | 31 | 8 | 12 |
| 5 | 28 | 7 | 12 |
这从什么时候起就不成立了?
When the deck stops shrinking. If you put under exactly as many as you draw, the queue never gets shorter and each card waits the same number of turns as the one before it.
Then the arrivals spread out one per turn instead of bunching, and choosing the turn really does choose the arrival.
本页不知道什么?
Anything that reorders the deck: a shuffle, a search, a card that moves others from the bottom, or drawing an extra card outside the normal turn.
It also treats every turn as identical, so a turn where you draw more or put more under has to be read as a different line rather than fitted into this one.
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