[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.41,0:00:10.56,Default,,0000,0000,0000,,You and a fellow castaway\Nare stranded on a desert island
Dialogue: 0,0:00:10.56,0:00:13.61,Default,,0000,0000,0000,,playing dice for the last banana.
Dialogue: 0,0:00:13.61,0:00:15.60,Default,,0000,0000,0000,,You've agreed on these rules:
Dialogue: 0,0:00:15.60,0:00:17.15,Default,,0000,0000,0000,,You'll roll two dice,
Dialogue: 0,0:00:17.15,0:00:21.07,Default,,0000,0000,0000,,and if the biggest number \Nis one, two, three or four,
Dialogue: 0,0:00:21.07,0:00:23.35,Default,,0000,0000,0000,,player one wins.
Dialogue: 0,0:00:23.35,0:00:28.33,Default,,0000,0000,0000,,If the biggest number is five or six, \Nplayer two wins.
Dialogue: 0,0:00:28.33,0:00:30.15,Default,,0000,0000,0000,,Let's try twice more.
Dialogue: 0,0:00:30.15,0:00:33.25,Default,,0000,0000,0000,,Here, player one wins,
Dialogue: 0,0:00:33.25,0:00:35.97,Default,,0000,0000,0000,,and here it's player two.
Dialogue: 0,0:00:35.97,0:00:37.74,Default,,0000,0000,0000,,So who do you want to be?
Dialogue: 0,0:00:37.74,0:00:42.21,Default,,0000,0000,0000,,At first glance, it may seem \Nlike player one has the advantage
Dialogue: 0,0:00:42.21,0:00:46.22,Default,,0000,0000,0000,,since she'll win if any one \Nof four numbers is the highest,
Dialogue: 0,0:00:46.22,0:00:47.24,Default,,0000,0000,0000,,but actually,
Dialogue: 0,0:00:47.24,0:00:53.62,Default,,0000,0000,0000,,player two has an approximately\N56% chance of winning each match.
Dialogue: 0,0:00:53.62,0:00:57.53,Default,,0000,0000,0000,,One way to see that is to list all\Nthe possible combinations you could get
Dialogue: 0,0:00:57.53,0:00:59.53,Default,,0000,0000,0000,,by rolling two dice,
Dialogue: 0,0:00:59.53,0:01:02.67,Default,,0000,0000,0000,,and then count up \Nthe ones that each player wins.
Dialogue: 0,0:01:02.67,0:01:05.31,Default,,0000,0000,0000,,These are the possibilities\Nfor the yellow die.
Dialogue: 0,0:01:05.31,0:01:07.78,Default,,0000,0000,0000,,These are the possibilities \Nfor the blue die.
Dialogue: 0,0:01:07.78,0:01:13.21,Default,,0000,0000,0000,,Each cell in the chart shows a possible\Ncombination when you roll both dice.
Dialogue: 0,0:01:13.21,0:01:15.27,Default,,0000,0000,0000,,If you roll a four and then a five,
Dialogue: 0,0:01:15.27,0:01:17.44,Default,,0000,0000,0000,,we'll mark a player two \Nvictory in this cell.
Dialogue: 0,0:01:17.44,0:01:22.50,Default,,0000,0000,0000,,A three and a one gives \Nplayer one a victory here.
Dialogue: 0,0:01:22.50,0:01:24.82,Default,,0000,0000,0000,,There are 36 possible combinations,
Dialogue: 0,0:01:24.82,0:01:28.09,Default,,0000,0000,0000,,each with exactly the same \Nchance of happening.
Dialogue: 0,0:01:28.09,0:01:31.24,Default,,0000,0000,0000,,Mathematicians call these\Nequiprobable events.
Dialogue: 0,0:01:31.24,0:01:34.80,Default,,0000,0000,0000,,Now we can see why \Nthe first glance was wrong.
Dialogue: 0,0:01:34.80,0:01:37.47,Default,,0000,0000,0000,,Even though player one \Nhas four winning numbers,
Dialogue: 0,0:01:37.47,0:01:39.56,Default,,0000,0000,0000,,and player two only has two,
Dialogue: 0,0:01:39.56,0:01:43.70,Default,,0000,0000,0000,,the chance of each number \Nbeing the greatest is not the same.
Dialogue: 0,0:01:43.70,0:01:48.68,Default,,0000,0000,0000,,There is only a one in 36 chance\Nthat one will be the highest number.
Dialogue: 0,0:01:48.68,0:01:52.86,Default,,0000,0000,0000,,But there's an 11 in 36 chance \Nthat six will be the highest.
Dialogue: 0,0:01:52.86,0:01:55.59,Default,,0000,0000,0000,,So if any of these \Ncombinations are rolled,
Dialogue: 0,0:01:55.59,0:01:57.47,Default,,0000,0000,0000,,player one will win.
Dialogue: 0,0:01:57.47,0:01:59.67,Default,,0000,0000,0000,,And if any of these \Ncombinations are rolled,
Dialogue: 0,0:01:59.67,0:02:01.40,Default,,0000,0000,0000,,player two will win.
Dialogue: 0,0:02:01.40,0:02:03.72,Default,,0000,0000,0000,,Out of the 36 possible combinations,
Dialogue: 0,0:02:03.72,0:02:09.82,Default,,0000,0000,0000,,16 give the victory to player one,\Nand 20 give player two the win.
Dialogue: 0,0:02:09.82,0:02:12.16,Default,,0000,0000,0000,,You could think about it this way, too.
Dialogue: 0,0:02:12.16,0:02:14.36,Default,,0000,0000,0000,,The only way player one can win
Dialogue: 0,0:02:14.36,0:02:18.64,Default,,0000,0000,0000,,is if both dice show \Na one, two, three or four.
Dialogue: 0,0:02:18.64,0:02:21.60,Default,,0000,0000,0000,,A five or six would mean \Na win for player two.
Dialogue: 0,0:02:21.60,0:02:26.70,Default,,0000,0000,0000,,The chance of one die showing one, two,\Nthree or four is four out of six.
Dialogue: 0,0:02:26.70,0:02:30.56,Default,,0000,0000,0000,,The result of each die roll \Nis independent from the other.
Dialogue: 0,0:02:30.56,0:02:33.87,Default,,0000,0000,0000,,And you can calculate the joint \Nprobability of independent events
Dialogue: 0,0:02:33.87,0:02:36.39,Default,,0000,0000,0000,,by multiplying their probabilities.
Dialogue: 0,0:02:36.39,0:02:40.82,Default,,0000,0000,0000,,So the chance of getting a one, two, \Nthree or four on both dice
Dialogue: 0,0:02:40.82,0:02:46.28,Default,,0000,0000,0000,,is 4/6 times 4/6, or 16/36.
Dialogue: 0,0:02:46.28,0:02:48.47,Default,,0000,0000,0000,,Because someone has to win,
Dialogue: 0,0:02:48.47,0:02:54.50,Default,,0000,0000,0000,,the chance of player two winning\Nis 36/36 minus 16/36,
Dialogue: 0,0:02:54.50,0:02:57.30,Default,,0000,0000,0000,,or 20/36.
Dialogue: 0,0:02:57.30,0:03:01.41,Default,,0000,0000,0000,,Those are the exact same probabilities\Nwe got by making our table.
Dialogue: 0,0:03:01.41,0:03:04.04,Default,,0000,0000,0000,,But this doesn't mean \Nthat player two will win,
Dialogue: 0,0:03:04.04,0:03:09.41,Default,,0000,0000,0000,,or even that if you played 36 games\Nas player two, you'd win 20 of them.
Dialogue: 0,0:03:09.41,0:03:12.62,Default,,0000,0000,0000,,That's why events like dice rolling \Nare called random.
Dialogue: 0,0:03:12.62,0:03:15.90,Default,,0000,0000,0000,,Even though you can calculate \Nthe theoretical probability
Dialogue: 0,0:03:15.90,0:03:17.42,Default,,0000,0000,0000,,of each outcome,
Dialogue: 0,0:03:17.42,0:03:22.07,Default,,0000,0000,0000,,you might not get the expected results\Nif you examine just a few events.
Dialogue: 0,0:03:22.07,0:03:26.42,Default,,0000,0000,0000,,But if you repeat those random events\Nmany, many, many times,
Dialogue: 0,0:03:26.42,0:03:30.36,Default,,0000,0000,0000,,the frequency of a specific outcome,\Nlike a player two win,
Dialogue: 0,0:03:30.36,0:03:33.42,Default,,0000,0000,0000,,will approach its theoretical probability,
Dialogue: 0,0:03:33.42,0:03:36.37,Default,,0000,0000,0000,,that value we got by writing down \Nall the possibilities
Dialogue: 0,0:03:36.37,0:03:39.04,Default,,0000,0000,0000,,and counting up the ones for each outcome.
Dialogue: 0,0:03:39.04,0:03:42.99,Default,,0000,0000,0000,,So, if you sat on that desert island\Nplaying dice forever,
Dialogue: 0,0:03:42.99,0:03:46.91,Default,,0000,0000,0000,,player two would eventually \Nwin 56% of the games,
Dialogue: 0,0:03:46.91,0:03:49.100,Default,,0000,0000,0000,,and player one would win 44%.
Dialogue: 0,0:03:49.100,0:03:53.56,Default,,0000,0000,0000,,But by then, of course, the banana\Nwould be long gone.