聯盟戰棋金幣:現在花掉的真正代價
您的数据
这里没有任何东西绑定在某一款游戏上:只要那款游戏会为你没花掉的金币付钱,算法就是同一套;真正起作用的那两条规则是输入框,不是写死的数字。
结果
| 如果攒住,这个回合收到的利息 | — |
| 如果花掉,这个回合收到的利息 | — |
| 攒住的话最后有多少金币 | — |
| 现在就花的话最后有多少金币 | — |
| 花掉这笔真正的代价 | — |
| 其中从不被标出来的那部分 | — |
| 代价停止增加还要几个回合 | — |
头两行就是一切的来处。花掉之后你会掉到更低的一级利息,于是从那个回合起,你每一回合都少收一点,而这份缺口会一直累加在你已经付过的价钱之上。
同一笔买卖,在每个金币档位上
| 你当时攒住的金币 | 真正要多少 | 从不标出来的那部分 |
|---|
把这张梯子从下往上读,那条有用的线就跳出来了:一旦你手上的金币已经超过利息所能付的上限,这笔买卖就只值它的标价,别无其他。停在那条线之上的金币,光是停着并不生利,所以把它花掉是真的免费——而在更低的位置花同样的数目,就不是。
这张梯子也不是平滑往下走的,而任何拍脑袋的经验之谈都死在这里。攒得更多,反而可能让同一笔买卖更贵,因为决定损失的是你付完之后落在台阶的哪一侧,而不是你一开始有多少。两个金币数不同的玩家,可能为完全一样的东西付出不同的价钱。
最后一行是安慰。差距会扩大几个回合,然后停住:从那以后你只是固定落后一截,不会再往下掉,也就是说,早买下的那一笔,该造成的损害已经全部造成了。这个页面说不了的是:你买的那样东西,会不会在这段差距变得要紧之前就把这局赢下来——决定的这一半,始终是你的。
花掉十金币,为什么代价不止十金币?
Because the gold you hand over was also earning you interest. Spending drops you onto a lower rung, so from that turn on you collect less every turn, and the shortfall piles up on top of the price you already paid.
With thirty gold, five income a turn, one interest per ten held and a cap of five, spending ten leaves you fourteen behind five turns later. Four of that was never quoted as a price.
有没有什么时候可以放心地直接花掉?
Yes, and the boundary is exact rather than a feeling. Once you are holding more than interest can ever pay for, the gold sitting there earns you nothing by sitting there, so spending it costs its price and nothing else.
In the ladder below that is the point where the last column reaches zero. Above that line the purchase is genuinely free; below it, it never is.
| 你当时攒住的金币 | 真正要多少 | 从不标出来的那部分 |
|---|---|---|
| 10 | 15 | 5 |
| 20 | 17 | 7 |
| 30 | 14 | 4 |
| 50 | 12 | 2 |
| 60 | 10 | 0 |
为什么这个阶梯不是平滑的?
Because interest is paid in whole steps, not in proportion to what you hold. What decides the damage is which side of a step you land on after paying, so holding more can make the very same purchase cost more.
In the table above, twenty gold is the worst place to spend ten, worse than ten and worse than thirty. No rule of thumb produces that, which is the reason the page computes it with your own numbers.
代价会一直涨下去吗?
No. The gap widens for a few turns and then freezes, because once both paths are earning the same interest again they gain the same amount every turn. From there you are behind by a fixed amount and no longer falling further.
What the page cannot judge is whether what you bought wins before that gap matters. It prices the delay exactly and leaves the decision where it belongs.
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