Coin Game \ Magic Trick \ Maths: The Penney Ante Part 2 (Re: Derren Brown: How to Win the Lottery)

Penney Ante is a coin game devised in 1969 by a mathematician called Walter Penney. In it, two players predict three coin tosses. The prediction that appears first in a run of coin tosses wins. This should be a fair game. However, if Player 2 makes his prediction after Player 1, he can use mathematics and probability to increase his chances of winning.

On Wednesday 9th of September 2009 (09-09-09) UK magician Derren Brown predicted the national lottery numbers on live TV. The following Friday he explained how he did it. This included a demonstration of the Penney Ante.

For further reading see http://www.combinatorics.org/Volume_13/PDF/v13i1r35.pdf

Category:

Education

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• probability
• penney
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[mccahill124]

Its annoying. In school I'm sitting the lowest level possible for maths (foundation) yet I can follow all your videos fairly well, genuinley it's my teacher who is terrible and cant teach me anything :( life goes on

[singingbanana]

@mccahill124 I hope you'll keep watching then. Just taking an interest shows you in a good light!

[tippytoemonkey]

I'm so proud of myself! This is the first of your videos I've watched that I completely followed on the first watch! :D This seems like a good occasion to say thank you for posting them all, they're really interesting :D

[singingbanana]

@tippytoemonkey Thank you.

[jaykay1053]

If only you had been my math teacher! Thank you so very much for posting these lessons online. You are providing a wonderful service to anyone who would like to finally learn how to work out probabilities! Thank you for your generosity, singingbanana.

[zyzzyzus]

Probability is difficult for some people to fully understand but you explain things clearly.

I am studying for a degree in Mathematics and probability is my favourite part of Maths. After watching your videos you helped me fully understand this game so thank you.

I wish when I worked things out on paper they were that neat.

[MrTanookiMario]

Gah. Probability is definitely my weak point when it comes to math. There's just something about it that eludes me.

[BaumannBiehl]

i would love to understand you but i cant speak english (especially english maths) very well :) but the thing with the black/white balls was nice! (i understand it)

[zebb1111]

@mccahill124 keep surfing youtube for math presentations. there are many outstanding teachers here for all levels.

[antares5245]

Hey nice vid. I found a slightly different way to solve this problem...I made an 8x8 stochastic transition matrix where each cell is the probability of going to the next.

DId it all in software and got the exact same answer as you did at 7:39, so your work is totally correct :)

God I hope you didn't have to do all of that by hand...but if you did it's amazing you did it perfectly.

[kinglynx]

i lost u in this part lol

[Horinius]

I'm *happy* to have watched this video :) and thanks for the explanation. It's a lot funnier than the dull proba. course I had ages ago. But lucky that I didn't have this problem during test or exam ^_^'

Proba. is a tricky thing. You might need to give more explanation to others how you get from

P(player 2 wins)

= P(P2W|HH)P(HH) + P(P2W|not HH)P(not HH)

(according to an earlier explanation you gave) to that longer expression.

[darklyXlit]

I don't really get it, but, I like you're voice, so I'm continueing watching anyway XD

[bartjuu5]

I understand what you were saying but your were going a little bit fast

But its still a very good vid

[supersayin201]

my head hurts :(