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你想输都难的游戏

A Game You Can Always Win

这里是Vsauce频道 我是凯文 今天要玩一个只赢不输的游戏
Vsauce — Kevin here, with a game you can always win.
找一个朋友 你俩轮流报数 数值范围在1到10之间
Grab a friend and take turns counting using numbers from 1 to 10.
谁先把数值加到100 谁就是赢家
The first person to get to 100 wins.
而那个赢家始终会是你
Which can always be you.
为了证明我所言非虚 找个人和我一起友好地玩游戏吧 找谁呢…
To demonstrate, let’s have a friendly game between me and uhhh…
我觉得我只能自娱自乐了
I guess I’ll just play with myself.
嘿 找我呀
Hey me!
见到我很高兴吧
It’s good to see me.
我准备好了吗?
Am I ready to play?
是的
Yes.
是的我准备好了 那么
Yes I am. Okay,
选1到10之间的任何数字加起来 先加到100的人赢
add numbers between 1 and 10 and the person who gets to 100 first wins.
我会记录总数 以便你们跟上
I’ll write the sum in between mes so you can follow along.
我先开始
I’ll start the game.
1 7 4 9 2 10 1
1 7 4 9 2 10 1
你学我随便报数 是吗?
You’re just picking numbers randomly like me, right?
呃 是的
Uhh… yeahhh…
好吧 随便你 3
Okay cool, 3
8 8 3 5 6
8 8 3 5 6
严肃地说 我们两个赢的概率各为50%
Seriously, though. We both have 50/50 odds of getting to 100.

Um.
当然啦
Sure!
好吧
Alright.
4 7 9 2
4 7 9 2
等等 89了?
Wait. 89?
如果我报1的话 总和就是90
If I play 1, that’s 90
然后你报10 你就赢了
and you can play 10 and win
如果我报10 总数就是99 那你报1就又赢了
and… if I play 10 that’s 99 and you can play 1 and win.
哦 好奇怪 我
Oh, weird. I,
一定是走狗屎运了
uh, must’ve gotten lucky.
对 你幸运死了
Yeah, right.
我偏报5
5.
6
6!
加到100了 我赢了
100, I WIN!
我每次都会赢
Every time.
原因就是
Here’s how.
呃 你可以走了 另一个我
Uhh..you can go now, me.
嗯 知道了
Uh, fine.
呃 我不要和你搭档了
Well, I want a rematch.
后会无期 再见面大概是在…镜子里?
I guess I’ll just uhhh…see ya in the mirror?
是的
Yeahhhhh.
好的 咱们现在开始玩游戏
Okay, now let’s play a game
你和我玩 而我会全程为大家讲解我赢的原因
between me and you and I’ll explain along the way how it works.
那么 我知道我自己总是赢的
Ok, the easiest way for me to know I’m
最简单的方式就是
going to win every time is for me to go first and
由我开头 且从1开始
start with the number 1.
无论你接下来要往上加什么数字 5 3 8
No matter what number you add next, 5, 3, 8,
无论什么数字 我就用11减你的数字
whatever it is, I just subtract your number
所得差就是我要报的数字
from 11 to get my next play.
所以我先开始 报上1 如果你报的数是4
So if I start with 1 and if you say 4,
那么它们的总和就是5
then our sum is 5.
我接下来要报的数字就是拿11减去4 等于7
To get my next number, I do 11 minus 4, which equals 7,
所以我接下来要报的数字就是7
so 7 is my next play: 7 plus 5 gives
那么我们得到的新总数就是12
our game a new total of 12.
假如你下一个要报的数字是8
Then you say… 8.
很好
Cool.
8+12=20
8 plus 12 gives our game a new total of 20.
我用11减去你的8 得到3
I do 11 minus your 8, which is 3.
所以我报3 那么总数就等于23
So, I play 3 and our new total is 23.
只要我坚持这个战略
As long as I stick to this strategy
我能保证自己成为那个把总数加到100的人
I’m guaranteed to be the first to 100.
接下来我告诉你原因
This is why it works.
不管你报什么数
Regardless of your number,
我报的数会一直使数值总和
mine will always result in a sum that’s part of an arithmetic
成为公差为11的等差数列1 12 23 34
series separated by elevens: 1, 12, 23, 34,
45 56 67 78 89中的一个数值
45, 56, 67, 78, 89,
然后 下一个数就是100了
and… then finally 100.
由于本轮游戏中你能报的最大数字就是10
Since the highest number you can play in the game is 10 —
所以如果我用11减去你所报的数字
if I separate your moves by eleven…
我就能主宰世界了
I rule the world!
我是说 我能主宰这个简单的游戏世界
Or at least… this simple number game.
不说这个了
Gotta start somewhere.
当你和朋友玩这个游戏时 他们能赢吗?
When you play this with your friend can they ever win?

Yes.
前提是你自己打乱了这个等差数列
If you mess up the series.
从你开始 且从1开始
While going first, playing 1,
然后用11减去对手的数字是最简单的
and subtracting every opponent’s number by 11 is the easiest
保持这个数列的方式
way to stick with the series,
但几轮下来 你可能想转换一下策略
after a few rounds you might want to switch things up
以免对手摸透你的套路
to prevent them from figuring out your strategy.
一开始你可以报一个不是1的数字
You could do that by starting with a number other
然后使用障眼法 渐渐将总数引向
than 1 and choosing wrong numbers until
这个等差数列中的一个数字
later in the game when you land on a number
比如说67或78
in the arithmetic series like 67 or 78.
所以你和朋友玩这个游戏的时候 任选数字就行 当总数达到65时
So if you’re playing with a friend and you pick random numbers until the sum is 65,
你就报2 把总数变成67就可以
then you could play 2 to bring your total
这样你就回到成功之路上了
to 67 and then you’re right on track.
从这里开始 你每次都用11减去对方的数字
From there just subtract your friend’s
得到你要报的数字 这样下去你就能成为第一个
numbers every single time by 11 and you will be the
把总数加到100的人
first to 100.
对那些没有意识到
To players who don’t realize
这个等差数列是最佳策略的游戏玩家来说
that the optimal strategy depends on that series, this game
谁输谁赢就是个运气问题
seems like a game of chance —
但一旦你知道了这个等差数列 你就有了制胜法宝
but once you know the series, you have the secret number knowledge.
但如果你不喜欢这个加到100的游戏
But if adding up to 100 isn’t your cup
那我为你介绍一个类似的火柴棒游戏
of tea you could try a similar game with matchsticks.
这些是可反复使用的谜题火柴
These are Inq’s Durable Match-Like Puzzle Sticks
它们装在新的“好奇盒子”里 现在被拿出来了
that come in the new Curiosity Box that is out right now.
火柴盒里有个小册子 上面有22个智力游戏
It’s packed with a booklet that features 22 different puzzles that you can try to solve
你可以试着用火柴解一下这些迷题
yourself when you get these matchsticks.
但现在我们要用这些火柴为你演示另一个只赢不输的游戏
But for right now we’ll use the matchsticks to visualize another game you can always win.
好的
Alright.
你把11根火柴摊开在桌子上
You have eleven matchsticks spread out on a table.
你和对手轮流移出火柴
You and a friend take turns removing either 1,
一次可移动1根 2根或者3根
2 or 3 matchsticks and the player who picks
谁移动最后一根火柴谁就输了
up the last match loses.
如果由你开头 你就能常胜不败
If you go first, you can always win this game.
总没有人想输吧
Since you don’t want to pick up that last match,
那么咱们就逆向思维揭开谜底
let’s work backwards to uncover the secret.
我们邀请两位参赛者
We’ll play a game
T先生和S先生 因为…我乐意
Mr T. and Skeletor because why not?
好的 咱们就直接跳到游戏末尾来验证一下这个获胜策略
Alright, let’s skip to the end of the game to workout the winning strategy.
如果轮到S先生时T先生留下的火柴棒数量是
If it’s Skeletor’s turn and Mr T. leaves Skeletor
2 3或4根
with 2, 3, or 4 matches,
那么S先生获胜就是板上钉钉的事了
Skeletor can leave T. with the final losing match.
所以T先生要确保自己留给S先生5根火柴棒
So, T. will want to make sure he leaves Skeletor with 5,
这样自己才不会输掉游戏
to guarantee that Mr. T keeps his jewelry.
原因如下
Here’s why.
如果留下两根火柴
If there are 2 matches left,
那S先生拿走一根火柴后 给T先生的就是最后一根火柴了
then Skeletor just takes 1 and leaves Mr. T. with the final losing match.
如果留下3根火柴 S先生拿走两根后T先生又输了
If there are 3 matches left, then Skeletor takes 2, Mr. T. loses.
如果留下4根火柴 S先生拿走3根
And if there are 4, then Skeletor takes 3,
T先生就又输了
then Mr. T loses again.
但如果T先生留下5根火柴
But if T leaves 5, no matter what
那么无论接下来S先生拿走的火柴数量是1 2还是3
Skeletor plays next — 3, 2, or 1 —
T先生可以下出胜负手 完败S先生
T can make a winning move and pity the fool accordingly.
而这个游戏为赢家配备的是公差为4的等差数列
The arithmetic series that will rig the game for T is separated by 4’s…
1 5 9以此类推
1, then 5, and then… 9.
T先生会想要留给S先生9根火柴
Mr T. will want to leave Skeletor
因为要确保剩余的火柴数量
with 9 matches to make sure that ALL his plays match
等于该等差数列中的数值
up with the series.
如果游戏中共有11根火柴 S先生先开始
If Skeletor and T start with 11 matches and T goes first,
那意味着S先生首次要移2根火柴才能赢
that means his initial play will be to remove 2.
因为每个玩家可以移动的火柴数量
Since each player can only remove a maximum
最大为3
of 3 matches per turn, you can dominate the
那意味着要从你这里开始 且你留下的火柴数量等于等差数列里的数值
game every time by going first and making moves that stick to this series.
这就是为什么 用20根火柴游戏也是有效的
… which is why the game works with 20 matches, too.
为了确保用20根火柴你也能获胜
To guarantee a win with 20 matches on the table,
那你首次移动的火柴数量应该是3
your first play should be to remove
给对方留下17根火柴
3 to land you at 17.
所以如果T先生拿走3根火柴 剩下17根
So let’s say T. starts and removes 3 to get to 17.
那么无论S先生要移动几根火柴
No matter what Skeletor does,
T先生只要保证留下13根火柴就肯定能胜利
T just needs to get to 13 to stay on course to win.
那么假如S先生移走2根火柴 留下15根火柴呢
So, if Skeletor removes 2 to get
此时T先生只需移走2根火柴使剩下的火柴数量为13
to 15, then Mr. T. just needs to remove 2 to get to 13.
然后下一步T需要使余下的火柴数量为9
Now T. needs to get down to 9.
所以如果S先生拿走3根 留下10根
So, if Skeletor removes 3 to get to 10,
那T先生就要移走1根 这样才能留下9根
then Mr T. just has to remove 1 match to get to 9.
然后T先生的下一个目标就是5
The next milestone is 5,
如果S先生移走一根剩下8根 那T先生就要移走3根才能剩下5根
so if Skeletor removes 1 to get to 8, then Mr. T can remove 3 to get to 5.
现在基本上游戏就结束了
And now it’s officially over.
无论S先生移走的火柴数量为1 2还是3都没关系
Skeleton can’t do anything — 1, 2, 3, itdoesn’t matter.
T先生肯定能赢就对了
Mr T. is leaving Skeletor with the finallosing match.
咱们看看S先生能不能握住小火柴
Let’s see if it’ll fit in his hand.
用这只手握吧
What about this one?
干得好
Good enough.
以上的报数游戏和火柴游戏都被叫做“取物游戏”
Both the counting game and this matchstick one are referred to as “Nim-like,”
因为它们在概念上都类似于一种古代游戏
because they’re conceptually similar to a game
这种古代游戏发展成目前数学家称作的“取物游戏”
from ancient times that evolved into what mathematicians now call Nim.
玩家从一堆或一摞物体中移出部分物体
Players take turns removing objects from heaps or stacks,
最后一个物体落入谁手谁就输了
and the player to remove the last object loses
但是取物游戏可以更复杂
… but it gets a lot more complex
比坚持依靠等差数列要难得多
than sticking to a basic arithmetic series.
但我们喜欢复杂
We like complex.
有史以来 人们就一直发明一些锻炼大脑的游戏
Humans have been inventing brain-teasing games to pass the time, sharpen their minds, and
一方面打发时间 一方面使大脑越用越灵光
extend collective knowledge for as long as recorded history shows.
我们所知的古老游戏之一是塞尼特棋
One of the oldest games we know about is Senet,
所用材料是木条 这个游戏是古埃及人发明的
with board pieces from Ancient Egypt dating
有5000多年的历史了
back over 5,000 years.
就在同时期
About the same time humans were
我们现在所用的书面语系统也渐具雏形
inventing the precursors to our modern written language systems,
人们发展数字游戏以消磨时光
we were developing number games to
并让我们对这个可以估量的世界
occupy ourselves and tease out a better understanding
有了更好的理解
of the quantifiable world.
制造人为的挑战 并为此开动脑筋
Creating artificial challenges — and then out-thinking them —
是我们锻炼思维的一种方式
is a way we exercise our minds.
通过发现已知现实世界的隐藏部分——
By discovering the hidden patterns that govern reality,
不管是以火柴游戏的形式
whether we’re just practicing with
还是以解开当今时代科学难题的形式
a matchstick game or unwinding the great scientific challenges of our times,
这种活动弥补了我们的不足 使我们更加完整
we’re engaging in an integral part of what makes us — us.
尽管我目前还处于要请S先生来解释数学问题的阶段
Even those of us who use Skeletor to explain math games.
一如既往地 感谢观看
And as always – thanks for watching.
嘿 这是新推出的好奇盒子
Hey, the brand new Curiosity Box
里面有火柴游戏 还有很多精心挑选
which includes the matchstick game and a bunch of other awesome hand-picked,
并设计的科学玩具供你把玩
designed and developed sciencetoys is available right now.
迈克尔 杰克和我在此向你推荐这个好奇盒子
Michael, Jake and I created this subscription
它如Vsauce频道一样奇妙 可以直接派送到你家门前
box to bring physical Vsauce to your doorstep.
所以请点击下方链接
So, check out the link below,
前往CuriosityBox.com 立即入手属于你的盒子吧
it’s CuriosityBox.com, to secure yours right now.
我还要再待一会儿
I’m going to stay here and, uh,
试着解一些智力游戏
try and figure out some of these puzzles.
移动一根火柴搭建正方形
Move one match to make a square.

Uhh.

Um.
我做到了
SQUARE.
我们是好奇三兄弟啊
Three curious bro.

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视频概述

看似无理可循的两个游戏,却大有玄机,一起来看看在玩这两个游戏时如何只赢不输吧。

听录译者

收集自网络

翻译译者

ABC

审核员

审核员CX

视频来源

https://www.youtube.com/watch?v=dUXW3Kh_kxo

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