[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:07.75,0:00:09.49,Default,,0000,0000,0000,,Maybe the fates got clumsy.
Dialogue: 0,0:00:09.49,0:00:12.31,Default,,0000,0000,0000,,Maybe Poseidon had one of his angry days.
Dialogue: 0,0:00:12.31,0:00:15.62,Default,,0000,0000,0000,,However it happened, the\Nunderworld is overcrowded,
Dialogue: 0,0:00:15.62,0:00:20.16,Default,,0000,0000,0000,,and Zeus has ordered Hades\Nto let some spirits out.
Dialogue: 0,0:00:20.16,0:00:24.60,Default,,0000,0000,0000,,Hades arranges all the souls of the\Ndead in a line before Cerberus.
Dialogue: 0,0:00:24.60,0:00:28.49,Default,,0000,0000,0000,,When one of his three heads bites \Ndown on the soul in front of it,
Dialogue: 0,0:00:28.49,0:00:31.22,Default,,0000,0000,0000,,they’ll get returned to the \Nland of the living.
Dialogue: 0,0:00:31.22,0:00:36.20,Default,,0000,0000,0000,,Anyone to the left must get out of\Nline and stay in Hades forever.
Dialogue: 0,0:00:36.20,0:00:41.70,Default,,0000,0000,0000,,And everyone else shuffles forward,\Nat which point Cerberus will feed again.
Dialogue: 0,0:00:41.70,0:00:47.28,Default,,0000,0000,0000,,Each of the dog’s heads has an equal\Nchance of being the one to bite each time,
Dialogue: 0,0:00:47.28,0:00:51.28,Default,,0000,0000,0000,,and no two ever bite simultaneously.
Dialogue: 0,0:00:51.28,0:00:55.40,Default,,0000,0000,0000,,Unfortunately, Hades’ minions forgot\Nto tell you what was happening,
Dialogue: 0,0:00:55.40,0:01:00.14,Default,,0000,0000,0000,,and by the time you show up there are\Nonly 99 souls left in line.
Dialogue: 0,0:01:00.14,0:01:04.76,Default,,0000,0000,0000,,Hades looks furious and drawing attention\Nto yourself won’t end well.
Dialogue: 0,0:01:04.76,0:01:09.61,Default,,0000,0000,0000,,But suddenly, time freezes, and Hermes \Nsteps out of the shadows.
Dialogue: 0,0:01:09.61,0:01:12.95,Default,,0000,0000,0000,,He tells you he can instantly put you into\Nthe line,
Dialogue: 0,0:01:12.95,0:01:15.51,Default,,0000,0000,0000,,and no one will realize what happened.
Dialogue: 0,0:01:15.51,0:01:19.51,Default,,0000,0000,0000,,But he’ll only grant his grace to someone\Nclever enough
Dialogue: 0,0:01:19.51,0:01:21.37,Default,,0000,0000,0000,,to take full advantage of it.
Dialogue: 0,0:01:21.37,0:01:24.48,Default,,0000,0000,0000,,Choose the best place in line and \Nhe’ll give you the spot.
Dialogue: 0,0:01:24.48,0:01:27.99,Default,,0000,0000,0000,,Choose wrong, and he’ll leave you to rot.
Dialogue: 0,0:01:27.99,0:01:29.82,Default,,0000,0000,0000,,Which spot should you pick?
Dialogue: 0,0:01:29.82,0:01:31.83,Default,,0000,0000,0000,,Pause the video to figure it out yourself.
Dialogue: 0,0:01:31.83,0:01:32.53,Default,,0000,0000,0000,,Answer in 3
Dialogue: 0,0:01:32.53,0:01:35.06,Default,,0000,0000,0000,,Answer in 2
Dialogue: 0,0:01:35.06,0:01:37.67,Default,,0000,0000,0000,,Answer in 1
Dialogue: 0,0:01:37.67,0:01:41.74,Default,,0000,0000,0000,,It’s possible to calculate the exact\Nprobability of going free
Dialogue: 0,0:01:41.74,0:01:43.88,Default,,0000,0000,0000,,in all 100 spots.
Dialogue: 0,0:01:43.88,0:01:46.60,Default,,0000,0000,0000,,But there’s a much simpler path to\Nthe solution
Dialogue: 0,0:01:46.60,0:01:49.60,Default,,0000,0000,0000,,that requires surprisingly\Nlittle calculation.
Dialogue: 0,0:01:49.60,0:01:52.32,Default,,0000,0000,0000,,Imagine being anywhere in line.
Dialogue: 0,0:01:52.32,0:01:56.41,Default,,0000,0000,0000,,Way up at the front, one of the three\Nheads will pick someone at random,
Dialogue: 0,0:01:56.41,0:01:59.90,Default,,0000,0000,0000,,and you’ll move forward 1, 2, or 3 spaces.
Dialogue: 0,0:01:59.90,0:02:02.23,Default,,0000,0000,0000,,Since each is equally likely,
Dialogue: 0,0:02:02.23,0:02:05.49,Default,,0000,0000,0000,,your chance of survival from wherever\Nyou started
Dialogue: 0,0:02:05.49,0:02:10.52,Default,,0000,0000,0000,,is the average of the chances from\Neach of the three spaces in front of you.
Dialogue: 0,0:02:10.52,0:02:14.75,Default,,0000,0000,0000,,And this is where you can\Nfind a huge shortcut.
Dialogue: 0,0:02:14.75,0:02:20.80,Default,,0000,0000,0000,,Averages must be on or between the \Nextremes of what you’re averaging––
Dialogue: 0,0:02:20.80,0:02:25.50,Default,,0000,0000,0000,,they can never be higher than the\Nhighest value or lower than the lowest.
Dialogue: 0,0:02:25.50,0:02:29.35,Default,,0000,0000,0000,,So whatever your chances of survival\Nare where you start,
Dialogue: 0,0:02:29.35,0:02:33.85,Default,,0000,0000,0000,,one of the three places in front \Nof you is at least as good,
Dialogue: 0,0:02:33.85,0:02:34.99,Default,,0000,0000,0000,,and probably better.
Dialogue: 0,0:02:34.99,0:02:38.25,Default,,0000,0000,0000,,This observation is incredibly powerful.
Dialogue: 0,0:02:38.25,0:02:41.13,Default,,0000,0000,0000,,It means that wherever you are in line,
Dialogue: 0,0:02:41.13,0:02:45.99,Default,,0000,0000,0000,,it’d be wise to trade your place for one\Nof the three spots in front of you.
Dialogue: 0,0:02:45.99,0:02:50.18,Default,,0000,0000,0000,,Let’s ignore which for now and think of\Nthem as a trio––
Dialogue: 0,0:02:50.18,0:02:54.96,Default,,0000,0000,0000,,this trio’s maximum value is better than\Nthis trio’s, and so on.
Dialogue: 0,0:02:54.96,0:02:57.36,Default,,0000,0000,0000,,Keep going and you’ll reach the front...
Dialogue: 0,0:02:57.36,0:03:01.94,Default,,0000,0000,0000,,These three spots must contain the\Nextreme values––
Dialogue: 0,0:03:01.94,0:03:04.22,Default,,0000,0000,0000,,the best and worst probabilities––
Dialogue: 0,0:03:04.22,0:03:05.47,Default,,0000,0000,0000,,for the entire line.
Dialogue: 0,0:03:05.47,0:03:09.93,Default,,0000,0000,0000,,In other words,\Nthey’re all we need to consider.
Dialogue: 0,0:03:09.93,0:03:11.25,Default,,0000,0000,0000,,Place 1 is bad.
Dialogue: 0,0:03:11.25,0:03:14.72,Default,,0000,0000,0000,,Head one would save you, and the other\Ntwo doom you forever.
Dialogue: 0,0:03:14.72,0:03:17.51,Default,,0000,0000,0000,,That’s just a 1 in 3 chance to escape.
Dialogue: 0,0:03:17.51,0:03:21.06,Default,,0000,0000,0000,,Place 2 is better: head two is great,
Dialogue: 0,0:03:21.06,0:03:26.57,Default,,0000,0000,0000,,head 3 is bad, and head 1 is ok\Nin that it gives you another chance.
Dialogue: 0,0:03:26.57,0:03:31.32,Default,,0000,0000,0000,,But place 3 is best, because head \N3 saves you
Dialogue: 0,0:03:31.32,0:03:35.68,Default,,0000,0000,0000,,while heads 1 and 2 both\Ngive you extra chances.
Dialogue: 0,0:03:35.68,0:03:39.33,Default,,0000,0000,0000,,If you did want to consider the exact \Nprobabilities,
Dialogue: 0,0:03:39.33,0:03:45.57,Default,,0000,0000,0000,,the odds of surviving in place 3 are 16\Nout of 27, or close to 60%.
Dialogue: 0,0:03:45.57,0:03:51.62,Default,,0000,0000,0000,,The spots later in line tend to be very \Nclose to having a 50% chance of survival.
Dialogue: 0,0:03:51.62,0:03:52.94,Default,,0000,0000,0000,,Why 50%?
Dialogue: 0,0:03:52.94,0:03:57.20,Default,,0000,0000,0000,,Because every time Cerberus sends\None soul up to be reborn,
Dialogue: 0,0:03:57.20,0:04:01.57,Default,,0000,0000,0000,,he leaves 0, 1, or 2 souls\Nin the underworld.
Dialogue: 0,0:04:01.57,0:04:07.04,Default,,0000,0000,0000,,That averages out to one person\Nstaying for each one who gets freed.
Dialogue: 0,0:04:07.04,0:04:11.10,Default,,0000,0000,0000,,But you can beat those odds handily\Nwith what you now know.
Dialogue: 0,0:04:11.10,0:04:14.06,Default,,0000,0000,0000,,Hermes has places to be, and so do you.
Dialogue: 0,0:04:14.06,0:04:18.06,Default,,0000,0000,0000,,He rewards your insight by sneaking \Nyou into the third spot.
Dialogue: 0,0:04:18.06,0:04:22.40,Default,,0000,0000,0000,,And from there it’ll be just a short\Nwait to learn your ultimate fate.