## 13,983,816 and the Lottery – Numberphile

JAMES CLEWETT: Today’s video is
going to be all about the National Lottery. And if you’re a number freak
like me, then the National Lottery is great because it’s
that two times a week when all the people at home get
to share in my enthusiasm for numbers. So what I want to do today is
talk a little bit about some of the probabilities involved
in the National lottery. So before we start, I think we
should choose some numbers for our lottery. So our first number is going
to be the number 14. That’s my birthday. Then I think we’ll have
the number 19. That was a nice, good year
for me, 19 years old. We’ll have a few in the 30s– 31, and 33, and 34. OK, and then one more, 45. So I’ve chosen the number 14
for my birthday, the number 19, and then, a few in the 30s,
number 31, 33, and 34, and number 45. So now, what are the odds of
us picking those same six balls out of our homemade
there are six balls in here which are winners for us. And there are 49 balls
just like the national lottery game. OK, so I’m going to look away. And I’m going to select. And it’s number 19,
a 6 out of 49. OK, so we put that
one to one side. But now they’re only 48 balls
left in the basket. And we’ve got five winners
left in the box. OK, let me give that
a good stir around. And it’s the number 45. Put that one to one side, and
again, now, we’ve got one less ball in the box. So we’re down to 47 balls and
just four winners now. Give them a good stir. It’s the number 31. And that one, again, goes to
one side with our other winning balls. Just 46 balls left in here
now, and only 3 winners. There it is. The number 14. OK, again, put that
one on one side. Give ourselves a little stir. Now there’s only 45 balls left
and just two winners. There it is. The number 33. OK, so we’ve got one winning
ball left in the bucket. So give it a stir. There it is. The number 34. OK, so my chances of picking out
the number 34, were just 1 from 44 balls. And there we have it. What were the odds of me
winning the lottery and retiring to become a part-time
physicist? Well, let’s have a look at it. The chance of getting the first
number was 6 in 49. Then it’s a completely
independent event, so we can just multiply that by the chance
of getting the second number, which is 5 in 48. So I can just just
multiply that. Then we multiply that
by the chance of winning the third number– the top line we can
do in our head– is simply 720. The bottom line– I’m going to cheat– I’m going to use a calculator. 49 times by 48 times by
47 times by 46 times by 45 times by 44. And that’s the number 10
billion and change. So we’re going to write down
our 10 billion here. So that gives us our final
answer in math speak, if you like, of 7.151 times
10 to the minus 8. That number doesn’t really mean
anything to most of us. And so I’m going to write
this as 1 over 13983816. So the odds of winning the
lottery are one part in 13,983,816. Or in real money, about one
part in 14 million. I play the lottery
at Christmas. Actually, I find it’s been
really good fun. So I tend to spend
about a fiver a year on lottery numbers. And for that one week that
I’ve bought a ticket, I daydream about all the really
cool things that I’m going to do if I win the lottery. So how much is that worth? I don’t know. I really enjoy it. I really enjoy just
the process of owning a lottery ticket. But I know– I’m reasonably numerically
grounded– I know that my chances
of winning are very, very close to zero. I think my chances of being
struck by lightning are something like seven times
higher than my chances of winning the lottery. So I’m kind of hoping
that doesn’t happen. So we’ve won the lottery. We’ve matched six balls. That’s absolutely fantastic. But it doesn’t really explain
why every time I’ve bought a lottery ticket, I’ve not matched
any balls at all. So what’s the probability of
buying a lottery ticket and matching no balls? So let’s go back to the numbers
that we selected. So we had 14– OK, so this were our
magic numbers. So what are the odds of
selecting a first number which doesn’t match? Well, there are 43 balls
in there, out of 49 which don’t match. So I’m going to select one. It’s number 38. OK, so that doesn’t match. I don’t want that one. Give it a stir. Now remember, here we go. That’s the number 35. And, again, it doesn’t match. Give them a stir. It’s the number 25. Again, no use to me. 41 out of 47. OK, so the next one. Number 23. Getting a little annoyed
with this. That’s no good to me either. So the chance of pulling
out a nonwinner there were 40 out of 46. OK. Do another one. I’ve got the number 41. No use. OK. So the chances, again– 39 out of 45. And our last ball– BRADY HARAN: Hang on, what do
you think it’s going to be? JAMES CLEWETT: Well,
I don’t think it’s going to be a winner. That’s for sure. Uh, give it a stir. I hope it’s not a winner. Number 43. OK, so we’ve got no
balls at all. Rubbish. Right. The chances of a nonmatch– 38 out of 44. If we calculate this number
through– again I’m going to turn to my calculator. OK? So our probability of picking
no matches whatsoever is 4 billion divided by 10
billion, which is– sorry– 43%, 43.59649%. Somebody is spending a pound
a week playing the lottery. And for that pound a week,
they’re getting hope and excitement and a Saturday
night buzz. I think that’s great
value to be honest. So that’s fine. But if I hear of somebody who’s
spending 10, 20 quid a week buying lottery

## 100 thoughts on “13,983,816 and the Lottery – Numberphile”

1. G 5 says:

Lottery ticket winners are upon luck and fate I do belive so nothing else

2. Rashawn Moore says:

It was me

I've only gotten 3/6 numbers right when choosing my own numbers a couple times now and I've only been playing a few months.

4. Simon Hamburg says:

If the Jackpot is higher than ~14.000.000 € than you should go and Fill out 14 million lottery Ticket with every possible combination.. 100% Chance of winning!

5. Chand Khan says:

USA LOTTO NICE

6. kingmike40 says:

The person who buys a ticket has a little bit better chance of winning than a person who doesn't buy a ticket. I know people who spend 300/month on tickets.

7. Yavuzsan San says:

Play this
8 11 20 34 45 48
and win

8. Sean Nolan says:

I'm going to try and predict the lottery numbers for the USA. Tell me what lottery and how many numbers there is, I am from Europe.

9. Lodonna LoDonna says:

Michigan lotto 47 was 1 6 9 11 26 38

10. Martin Milligan says:

Check out Mark Haughton on YouTube

11. Goul Delucks says:

Their is no formula for lottery, its just a fate or luck to wind thats it, just be positive always.

12. Josue DelMonde says:

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13. Prime Captain says:

Cheers for this, been searching for "gail howards" for a while now, and I think this has helped. Ever heard of – Weyoralyn Winning Willingly – (Have a quick look on google cant remember the place now ) ? Ive heard some unbelievable things about it and my mate got great success with it.

14. Wally's War ZONE says:

How much is A Quid??? Check out Wallys War zone, I blow tons \$\$\$\$\$
😆

15. time less says:

How to win lottery, 6/45

16. Eyewill Sie says:

Didn't know that Baron Corbin is now an Educator

17. holborn says:

There's no prediction at all.Just luck no more.

18. Quoc Khanh Nguyen says:

Wrong, first 1/50 because we choice 1 number in 50 number, 1/50*1/49*1/48*1/47*1/46*1/45

19. manbdr thapa says:

thailenD LOTTERY S NUMBER ALSO ?

20. noel pineda says:

there's a trick in this video . lot's of cut on the video

21. Catgirl says:

Yes if you have the camera looking at your hand when you pick the numbers and make believe you are looking away.

22. Goul Delucks says:

Lottery has no formula, its just a faith if you win or lost,

23. Delroy Williams says:

Cash pot win

24. Novella James says:

Kl

25. Myrna Lachica says:

If you wanna get rich. I belive that we need to work hard

26. rekha pundge says:

I pay last 10 yr back the Indian lottery supar lotto but I looser every time … why I do to win 2 or 3 cr win by supar lotto Manday to Sunday the difference numbaŕ 6 mubar 5 number

27. Desmond Dwyer says:

It's is just enjoyable two day of daydreaming for a fiver,, 😉

28. Daniel Habte says:

Lottery is tax on the poor!

29. Macsidia says:

RIP 49 Ball National Lottery…

30. michael c says:

how numbers work the fall in groups

31. Ricardo Ortiz says:

This was great, thanks, been searching for "six winning lottery numbers" for a while now, and I think this has helped. Have you ever come across – Zenulian Lottify Bonkers – (search on google ) ? Ive heard some amazing things about it and my buddy got excellent results with it.

32. suong sung says:

so beautiful so dangerous.xxxxxxxxxxxxxxxxx

33. januar januar says:

34. Michael Walker says:

Can someone send me 1\$ I'll really appreciate it cashapp \$blanco146

35. William Harrison says:

picking those numbers that way give you incredibly low odds even for the national lottery

36. damage1_1 says:

He looked at the ball. Spun them round then says… Oh look.. Its a winner!!!

37. Christian Clark Uy says:

I want to win Lottery!!
Jackpot – 7 Times in my lifetime!!

38. Gabriel Mascarenhas says:

Hello…My name Gabriel/Indian….I want help or sorry to say your fees…I want to predict one number for the day out of 10 numbers. eg..0..1..2..3..4..5..6..7..8..9…the lottery name is Kalyan matka…pls. sent me message n what is best to talk to u…pls. reply. Thank u

39. tarik aikido says:

Could u predict the marocan lottery for 23 march this year it's the same from 1 to 49 i hope you answer me sir thnxs

40. Sonofgod Jesuschrist says:

PLEASE PRAY THAT ALL MY NUMBERS MATCH FOREVER THANK YOU AMEN.

41. Maria Fernanda Escalona Ramirez says:

So you got more chance playing in the casino

42. Takjua Takjua says:

Are you fine

43. maxwell Tyoka says:

Dude,are for real or you tryna be funny.

44. Hienie Nguyen says:

interesting this is great i enjoyed watching this. i may use this and see if i can win lol

45. Omar Rubaa says:

Then, why didn t you win the last lotto????!

46. My NewPhone says:

The chances for the winner are 100%. The chances for the loser are 0%. The chance of winning or loseung is 50%. You either a winner or a loser for the jackpot. This is rubbish

47. Celio Cardoso says:

Ok I am going to make Your life's easy. The lottorie does not work the way you all belive.
Every combination of number's that the computer recieve, the computer program eliminate (is a simple task for computer to do).
No under people often say " the numbers I forgot to put in come up) of course they did the computer did Not recieved it.
Now You know Why existe roll over special every Christman's.

48. Warren Buffett says:

they should make a lottery where you win if you dont match the numbers!!!

49. Tyson says:

'Soooooo you're telling me there's a chance?'

50. Aguidemo Batista says:

thanks, but like they say you cant win if you dont play.

its just joke dont take serious

52. Justin King says:

Contact me if you are interested in pick 3 or 5. I have studyed it for a long time and have invented a great method.

53. Cris Iverson says:

Huh??

54. RIK Kechroud says:

I don't believe on lottery. The winning numbers are prepared in advance with computer, specially lottery Canada OLG

55. Norellys Álvarez says:

Cheers for this, been searching for "the inverted lottery system" for a while now, and I think this has helped. Have you heard people talk about – Zenulian Lottify Bonkers – (do a google search ) ? Ive heard some incredible things about it and my cousin got cool results with it.

56. SHALIN MAY AUJERO says:

If that's true maybe that guy is the most richest right?

57. Mark Lennon says:

his calculations was based on a combination of numbers where it should be a permutation the difference being in a combination the order matters in a permutation it does not so unless lotto is played that the order you have has to match the order they are drawn so his answer should be divided by 6x5x4x3x2x1=720 which changes the odds of a combination of 6 numbers to a permutation

58. PÁSSARO NEGRO says:

Ótima análise . Calculo simples porém ..poderoso ..rs. ( Great analysis, simple calculation though, powerful !!)

59. Vergify says:

Did you ever won one?

60. diane ward says:

WHAT?

61. Lucid X says:

When you buy every possible combo and 'win' a little compared to the huge loss

62. Roger Diogo says:

If casino Dealers are forbidden to play on the casino, is ONLY fair for mathmaticians to BE forbidden to play the lottery.

63. Lord Skeptic says:

This needs an update.
The odds now are 1/45057474.
59!÷(59-6)!÷6!=45057474.

64. may del says:

Hi .nice this lottery i want to try also..hope i can win

65. Draconic says:

Thanks, now I can convince my friend Josef to spend less than 1/8 of his paycheck on lotto.

66. ITSUKA wong says:

1/13,983,816
1/13,983,816
1/13,983,816
1/13,983,816
1/13,983,816
1/13,983,816
1/13,983,816
1/13,983,816 1/13,983,816
The one and the only one time I will buy a lottery is when the prize has been snowball to 13983816X+tax.
IF I HAVE THAT PRINCIPAL

67. Rollshel Baker says:

looks like 36 not .. 34👀

68. I don't give a Fork says:

Guaranteed way!!!!!….Simply buy as many Ripple XRPs as you can afford…..It will be like winning the lottery in slow motion!!

69. Cynthia Garret says:

I have chosen my numbers
Just waiting on its arrival

70. Wilhelm Johannes says:

I want to become one of the winner one day register my dream.

71. Myky Mejia says:

traducirlo al español para entenderlo. por favor. gracias

72. Million LUCKY says:

Why u don't win if u know?

73. AKHILESWARI VS says:

lswmac98*90fali/a/c no 1909101020677,ifsc code CNRB001909BI/

74. Ron Smith says:

They always say ur more likely to be hit by lightning than hit the lottery, so can someone please tell me of all the people who've hit the jackpot in every lottery how many of them has been hit by lightning?

75. maureencora1 says:

5'7" 42*28*44

76. Forecasting Lottery says:

reverse engineering

77. Life of a schizophrenic says:

I am going to win the loterry

78. Sevinch Orujova says:

I am attracted to him 😅

79. Jon skelin says:

What the point of this video if he himself is not a lottory jackpot winner?

80. Struture of Ambition says:

I Truly Have a Gifted With Predicting

81. Milton Dicxon says:

82. ReverendRichie says:

This is the reason I play ONLY one set of numbers per drawing. Makes no sense to play more, it does not change the odds of winning by much but to win, one has to be entered.

83. Gislaine Pinto says:

Quer namorar comigo?

84. Athena Millay says:

Winning the Lottery is not just a out the odds. It's about "Law Of Attraction!"

85. Athena Millay says:

Do you really believe that you deserve to win the Lottery? It's the "Law Of Attraction" that is the real message here.

86. Traci O says:

The last ball drawn was not the number 34 as was said, but the number 36!

87. engkostas says:

Basically the number of chances that you write is not correct using the numbers you write … Not those on the calculator that are more exact. So with the numbers you show on the bord the chances are 1 in 13.984.058

88. Tan Tan says:

why is the camera shaking and moving non stop , torture watching this video , bad cameraman .

89. Emile Zaha says:

Useless video

90. plablop4310 plablo says:

Luck -10 haha

91. Dribin' Dropping says:

So next time when I got hit by a lightning I have six times more to go before winning a lottery

92. esnath constance moyo says:

You owe me big time

93. Michael Johnson says:

Winner of a video, I've been looking for "lona lottery software" for a while now, and I think this has helped. Have you ever come across – Zenulian Lottify Bonkers – (do a google search ) ? Ive heard some decent things about it and my m8 got cool results with it.

94. Alberto Serna says:

I had a friend who was a policeman, he said scratchoffs have a system…..he was always winning.

95. Mrqwerty2109 says:

"You said one out of 14 million yeah? Tell me this is it."

"If I tell you what happens, it won't happen"

96. M VGSV says:

Brits…..

97. H Jones says:

Your chances of winning are like everyone else’s: nil.

98. Johnny Bravo says:

Nice edited video. Record the ball picking first then edit so it looks like you picked the numbers before hand

99. Clau Gledhill says:

But somebody has to win ,if you play you are in with a chance be in it to win it.

100. L.A Antonio says:

Fake fake fake fake fake fake…