你的回合会交给对手多少

您的数据

这一切背后只有一条规则:只要计数器还在你这一侧,你就可以继续出牌;它越过去的那一刻,回合就交出去了。它越过去多少,就是对手开始自己回合时手上的量。

这里没有任何东西绑定在某一款游戏上:任何有共享计数器、并在它倾斜的那一刻就把回合交出去的游戏,算法都是同一套。

结果

按你的顺序塞得下几次
按你的顺序,对手拿多少开始
先出便宜的,塞得下几次
先出便宜的,对手拿多少开始
你最少可能交出去多少
只交出那个最少量时,塞得下几次

你的回合,一手一手看

第几手要付多少计数器落到哪里之后轮到谁

把最后一列从上往下读,这条规则就不吓人了:并没有谁在一回合一回合地从你手里拿走什么,你只是在选择要越过零多少,而越过去多少,就是你交出去多少。定下这个数的是回合里的最后一手,不是你花掉的总额。

所以在这么简单的一件事上,顺序才会这么要紧。同样的三四手,换个排法,交出去的可能是一点,也可能是六点;而没能出掉的那些牌,无论如何都还留在你手上。

让人不舒服的地方在最后四行,因为你想要的两件事,通常对应着不同的顺序。先出便宜的总能从一个回合里榨出最多的出牌次数,而它交出去的往往比必要的更多。多出一手是有价钱的,这个页面把这个价钱标了出来;至于值不值,取决于那一手做了什么——那正是算术永远看不到的另一半。

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对手开局手上有多少,是由什么决定的?

Only the last play of your turn. You keep playing while the counter is on your side, and the moment it crosses, the turn passes and whatever it crossed by is what they get.

The total you spent does not appear anywhere in that. Four cheap plays that land you one past zero hand over one; a single expensive play that lands you six past zero hands over six.

我出牌的顺序真的有影响吗?

It changes both of the things you care about, and usually not in the same direction. Cheapest first always fits the most plays into a turn, and it very often gives away more than you needed to.

With seven on the counter and plays costing one, two, three and four, cheapest first gets all four down and hands over three. Giving up one play brings the handover down to one.

废除花费放得下的操作数交给对手的量
71, 2, 3, 443
71, 2, 3, 431
43, 3, 133
43, 3, 122
那么先出最便宜的是正确的习惯吗?

It is the right habit for squeezing plays out of a turn, and that was checked rather than assumed: across twenty thousand random hands it never lost to any other order on the number of plays.

It is not the right habit for keeping the handover small, and it lost on that in about four hands out of ten. Which of the two you want is the part of the decision the arithmetic cannot make for you.

本页做了哪些假设?

That every play on your list is legal when its turn comes, that costs are fixed, and that nothing gives the counter back to you part way through the turn.

Anything that moves the counter the other way, or that changes what a play costs once the turn has started, sits outside it.