1.3娱乐

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  Do football players or coaches need to understand and use statistics? What about track and field competitors or swimmers? Can an understanding of probability make you more likely to win games of chance?
  ::足球运动员或教练是否需要理解和使用统计数据? 赛马和田径竞争者或游泳运动员呢? 了解概率能让你更有可能赢得机会游戏吗?

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  Read on to see how becoming an expert statistician can help you be more successful in ways you might never have imagined.
  ::看看成为一名专家统计学家 如何能帮助你更成功 以你无法想象的方式

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  Probability and Statistics in Entertainment 
  ::娱乐中的概率和统计

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  Competitive sports are extremely popular in countries all over the world. In some countries, players can make huge salaries in competitive sports, and even countries where professional sports are outlawed encourage players to compete for national fame in the Olympics.
  ::竞争体育在世界各国都非常流行。 在一些国家,运动员可以在竞争体育中赚取高额工资,甚至那些专业体育被取缔的国家也鼓励运动员在奥运会中竞争国家名声。

  

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  The obvious part of becoming a successful athlete is the vigorous physical training. Naturally a player will want to develop the instincts and physical prowess appropriate to his or her chosen sport. The less obvious, but no less important, part of becoming a champion athlete is developing and applying an understanding of the statistically important research about the sport.
  ::成为一名成功的运动员的明显部分是积极的体育训练。 运动员自然会想发展适合自己选择的体育的本能和体能。 更不明显但同样重要的是,成为冠军运动员的一部分正在发展和运用对体育统计学上重要的研究的理解。

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  Baseball pitchers need to know the particular types of pitches to throw at each hitter on an opposing team. By reviewing each hitter’s past records of strikes, fouls, base hits, and home runs based on each type of pitch, the pitcher will know who is more susceptible to fast balls, curves, etc., and will be a much more valuable member of his or her team.
  ::棒球投手需要知道投向对立球队中每个击球手的投手的具体投球类型。 通过审查每个击球手以往的打击、犯规、基地点击和基于每种投球的全垒打记录,投球手将知道谁更易受快速球、曲线等的影响,并且将成为他或她球队中一个更有价值的成员。

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  Football players are equally dependent on statistics. A quarterback who has no idea which teammates are most likely to catch a particular throw based on previous performance would not have much chance of leading his or her team to victory. Coaches without a detailed understanding of what training methods are statistically most successful for developing the particular skills a team needs are not liable to lead their teams to victory.
  ::足球运动员同样依赖统计。 一名四分卫如果不知道哪些队友最有可能根据先前的表现而得分某个球员,那他(她)的球队就不会有太多的胜选机会。 没有详细了解哪些培训方法在统计上最有助于培养团队所需的特定技能的教练们不会引导团队取得胜利。

  

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  Another pastime with eager participants all over the world is playing games of chance. Whether involving cards, dice, marbles, or anything else, any game of chance involves some level of probability by definition.
  ::世界各地热切的参与者的另一种消遣正在玩游戏游戏。 不管是涉及牌、骰子、大理石还是其它什么,任何赌博游戏都有某种程度的概率。

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  By becoming an expert on the likelihood of a particular card showing up in a random shuffle, or a specific roll turning up on a fair die , a clever player can significantly improve his or her chances of winning more often. Additionally, by studying and applying the statistical data of his competitors, a skilled player will know when to bet high on a bluff, or even hold an otherwise good play for a better time.
  ::一个聪明的玩家通过成为关于某个卡片出现在随机打乱中的可能性的专家,或者成为在公平死亡时出现某个卷子的专家,可以极大地提高他或她更经常获胜的机会。 此外,通过研究和应用竞争对手的统计数据,一个熟练的玩家将知道什么时候可以高赌一场虚张声势,或者甚至在更好的时间里玩一场其他的好戏。

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  Real-World Application: Football
  ::真实世界应用:足球

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  The Jets, a nationally competitive football team, are planning to play the #1 ranked team in their league in 2 weeks. What kind of statistics might they want to pay particular attention to as they research their future opponents?
  ::喷气机队是一个全国有竞争力的足球队,它计划在两周内在其联盟中扮演排名第一的球队。 当它们研究未来的对手时,它们想特别关注何种统计数据?

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  Very generally, the Jets might want to know whether their opponents are more offensive or more defensive, whether they tend to ‘run the ball’ or pass more often. It would also be beneficial to identify the most dangerous players on the other team so that they can be specifically focused on. All of these things could be relatively easily calculated by a statistician reviewing past games, and would represent a significant advantage to the Jets as they go into the competition.
  ::一般来说,喷气机队可能想知道他们的对手是攻击性更强还是防御性更强,他们是否倾向于“操纵球 ” , 还是更频繁地通过。 确定另一队中最危险的球员,以便他们能够有针对性地集中精力,也是有益的。 所有这些事情都可以比较容易地由统计学家对以往的比赛进行审核,并且对于参加比赛的喷气机队来说将是一个巨大的优势。

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  Real-World Application: Xio 
  ::真实世界应用程序: Xio

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  Xio is playing a card-based game of chance with two other people. The game is played in rounds. In each round each player is dealt one card from the deck, and each player bets that his or her cards have the highest point value in that round.
  ::Xio 正在和另外两个人一起玩牌牌牌牌游戏。 游戏以回合方式进行。 在每一回合中, 每个玩家都会从甲板上拿到一张牌, 每个玩家都打赌他或她的牌在该回合中具有最高点值 。

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  If the deck starts with 4 each of the cards numbered 1-10, and Xio knows that there have been two 9's, and three 10's out of the 15 cards already played, how confident should he be that the 9 he was just dealt will represent a positive outcome the next round?
  ::如果甲板开始时每张牌牌号为1-10, Xio知道15张牌中有两张是9张, 三张是10张, 那么他应该有多有信心,

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  There are 24 unknown cards remaining in the deck: 40(original deck) – 15(dealt previously) – 1(Xio’s card), and only a 10 will beat Xio’s 9. If there is only a single 10 remaining out of the 24 unknown cards, Xio can be pretty confident that his 9 will at least tie in this round.
  ::甲板上还有24张未知牌:40张牌(原牌) — — 15张(前期) — — 1张Xio牌) — — 1张Xio牌,只有10张能击败Xio的9张。 如果24张未知牌中只剩下10张,Xio可以非常自信地相信他的9张牌至少会在这轮中打平。

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  The actual chance is  $\begin{align*}\frac{1}{24}\end{align*}$  or approximately 4% for the first player, and  $\begin{align*}\frac{1}{23}\end{align*}$  or also approximately 4% for the second:
  ::第一个球员的实际机会是124个或大约4%,第二个球员的实际机会是123个或大约4%:

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  $\begin{align*}4 \% + 4 \% = 8 \%\end{align*}$  chance that Xio will lose this round, pretty good odds
  ::四千四千四百八百八百八的希望是Xio输掉这轮比赛 机会相当大

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  Real-World Application: Dice 
  ::真实世界应用:骰子

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  Jane is playing a game of chance with dice. The object is to roll two dice as many times in a row as possible  without  rolling a 7. If Jane has already rolled 5 times without getting a 7, how likely is it that she will roll a 7 on the next toss?
  ::Jane用骰子玩一个赌博游戏。 对象是连续滚两骰子, 不滚7 。 如果Jane已经滚了5次, 却拿不到7 。 如果Jane 已经滚了5次, 却得不到7 , 那么她会不会在下一局滚7 呢 ?

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  The first, and perhaps somewhat  counter-intuitive , point to note is that dice do not have any memory! That means that Jane’s chances of rolling a non-seven on her next roll are exactly the same as they were on her first roll, so we need to get an idea of how likely a roll of seven is on any given toss.
  ::首先,也许有些反直觉,但要指出的是骰子没有任何记忆!这意味着简在她的下一个卷上推出一个非七人的机会与第一个卷上的机会完全相同,所以我们需要了解一个概念,即任何特定卷子上都可能出现一个七人卷。

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  Seven is a common key number when discussing two “fair” (each number has the same chance of appearing) six-sided dice. This is because there are more ways to roll a seven than any other . The chart below shows the number of ways to roll each possible value of 2-12:
  ::讨论两个“公平”(每个数字都有相同机会出现)六面骰子时,七是常见的关键数字。这是因为滚动一个七比任何其他方法都多。下图显示滚动每个可能值2-12的方法数:

  Roll:

  2	$\begin{align*}1+1\end{align*}$
  3	$\begin{align*}1+2\end{align*}$	$\begin{align*}2+1\end{align*}$
  4	$\begin{align*}1+3\end{align*}$	$\begin{align*}3+1\end{align*}$	$\begin{align*}2+2\end{align*}$
  5	$\begin{align*}1+4\end{align*}$	$\begin{align*}4+1\end{align*}$	$\begin{align*}2+3\end{align*}$	$\begin{align*}3+2\end{align*}$
  6	$\begin{align*}1+5\end{align*}$	$\begin{align*}5+1\end{align*}$	$\begin{align*}2+4\end{align*}$	$\begin{align*}4+2\end{align*}$	$\begin{align*}3+3\end{align*}$
  7	$\begin{align*}1+6\end{align*}$	$\begin{align*}6+1\end{align*}$	$\begin{align*}2+5\end{align*}$	$\begin{align*}5+2\end{align*}$	$\begin{align*}3+4\end{align*}$	$\begin{align*}4+3\end{align*}$
  8	$\begin{align*}2+6\end{align*}$	$\begin{align*}6+2\end{align*}$	$\begin{align*}3+5\end{align*}$	$\begin{align*}5+3\end{align*}$	$\begin{align*}4+4\end{align*}$
  9	$\begin{align*}3+6\end{align*}$	$\begin{align*}6+3\end{align*}$	$\begin{align*}5+4\end{align*}$	$\begin{align*}4+5\end{align*}$
  10	$\begin{align*}4+6\end{align*}$	$\begin{align*}6+4\end{align*}$	$\begin{align*}5+5\end{align*}$
  11	$\begin{align*}5+6\end{align*}$	$\begin{align*}6+5\end{align*}$
  12	$\begin{align*}6+6\end{align*}$

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  We can see by counting on the chart that there are thirty-six possible combinations of two six-sided dice. There are six different combinations that result in a 7, thus, the chances of rolling a 7 would be:
  ::我们依靠图表就能看出,两张六面骰子可能有36个可能的组合。 有6个不同的组合导致7个组合,因此,滚动7个组合的几率是:

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  $$\begin{align*}\frac{6}{36}=\frac{1}{6} \ or \ 17 \% \ chance \ of \ rolling \ a \ 7\end{align*}$$
  ::636=16 或17% 滚7的机会

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  It is clear that at the beginning of each roll, Jane’s chances of not getting the infamous 7 are really quite good. In later lessons we will discuss the overall probability of rolling a 7 six times in a row, which is quite different than the probability of rolling a 7 on a sixth toss.
  ::很明显,在每卷开始时,Jane得不到臭名昭著的7号的几率确实相当不错。 在后来的教训中,我们将讨论连续7次滚动7次的几率,这与6次滚动7次的几率大不相同。

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  Earlier  Problem Revisited
  ::重审先前的问题

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  Do football players or coaches need to understand and use statistics? What about track and field competitors or swimmers? Can an understanding of probability make you more likely to win games of chance?
  ::足球运动员或教练是否需要理解和使用统计数据? 赛马和田径竞争者或游泳运动员呢? 了解概率能让你更有可能赢得机会游戏吗?

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  We can certainly see, based on the examples above, that statistics and probability calculations are integral to sports of all kinds, and that understanding the probabilities involved with any given outcome can help you make smart decisions in games of chance.
  ::根据上述例子,我们当然可以看到,统计和概率计算是各种体育运动的组成部分,了解任何特定结果的概率有助于你在偶然游戏中作出明智的决定。

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  Examples 
  ::实例

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  Example 1
  ::例1

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  Suppose you have a single six-sided die, what is the probability of rolling any number for a game of chance?
  ::假设你有一个单一的六方死亡, 滚动任何数字的概率是多少?

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  The sample space would be each of the possible numbers: 1, 2, 3, 4, 5, and 6. Since you can only roll one of them, and all are equally likely, the probability of any particular number is  $\begin{align*}\tfrac{1}{6}\end{align*}$ .
  ::样本空间将是每个可能的数字:1、2、3、4、5和6。 因为你只能卷一个,而且所有都同样可能,因此任何特定数字的概率为16。

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  Example 2
  ::例2

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  Suppose you are playing a game where you flip two coins and try to guess how they will land. Would it be better to guess that both land with the same side up or that they would land with different sides showing?
  ::假设你正在玩一个游戏,在那里你翻两个硬币,并试图猜测他们如何登陆。 最好还是猜一猜两边都在同一一边的土地,或者他们会以不同方向降落?

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  If you flip two coins, the sample space is: {(H, T), (H, H), (T, T), (T, H)}. Since there are four possibilities, and two show the same side, while two show different sides, the probabilities are equal: 50%
  ::如果您翻了两个硬硬币, 样本空间是 {( H, T), ( H), ( H), ( T, T), ( T), ( T), ( T, H) 。 因为有四种可能性, 两种可能显示同一面, 而两种则显示不同的两面, 概率是相等的: 50%

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  Example 3
  ::例3

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  If you draw a card at random from a single deck, what is the sample space of possible outcomes ?
  ::如果您从一个甲板随机抽取一张牌,那么可能的结果的样本空间是什么?

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  The sample space is the entire deck. Ace, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King of each of the four suits (The probability of pulling any single particular card is  $\begin{align*}\frac{1}{52}\end{align*}$ ).
  ::A, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, 四个西装的国王,四张西装中的每张(拉任何一张特定卡的概率是152张)。

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  Review 
  ::回顾

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  1. Identify four kinds of entertainment or sports that benefit from statistics.
     1.  
     2.  
     3.  
     4.  
     
     ::确定从统计数据中受益的四种娱乐或体育形式。
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  2. How could it be worthwhile for a pitcher to study the type(s) of pitch that a specific hitter is most likely to score a run on?
     ::投手怎么会值得研究投手最可能得分的投手投出投出的类型?
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  3. How could a strategy gamer benefit from studying the play style statistics of an opposing team?
     ::战略游戏者如何能从研究对立团队的游戏风格统计中受益?
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  4. How do players of online multiplayer games like World of Warcraft or Second Life use statistics?
     ::网络多玩家游戏的玩家如何使用统计?
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  5. Is there a benefit to learning statistics before playing games of chance? Give an example.
     ::在玩赌博之前学习统计数据是否有好处?举一个例子。

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。