Coin Game \ Magic Trick \ Maths: The Penney Ante Part 1 (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

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• Maths
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• probability
• penney
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[ANGRYHILLBILLY2]

OMG U CAME TO MY SCHOOL!

[singingbanana]

@ANGRYHILLBILLY2 I do that sometimes.

[hyperm0d]

In the case of the first player picking HHH, you list your probability of being right by picking THH to be 7/8, yet you state that if the first player picks TTT, you only have a 2/3 chance when you pick HTT. Please explain as this makes no sense to me whatsoever. At about 2:46 is where you are holding this particular table.

[singingbanana]

@hyperm0d Turn on your annotations. The last four are in the wrong order. My mistake.

[bj7up]

2\1HHHHHTHTHHTTTHHTHTTTHTTT

HHH 1/22/52/51/85/123/101/2

HHT1/2 2/32/31/45/81/27/10

HTH3/51/3 1/21/21/23/87/12

HTT3/51/31/2 1/21/23/47/8

THH7/83/41/21/2 1/21/33/5

THT7/123/81/21/21/2 1/33/5

TTH7/101/25/81/42/32/3 1/2

TTT1/23/105/121/82/52/51/2

Just found the answer, thanks very much!

[singingbanana]

That's it, that's the full table. And for each choice by Player 1 you just need to go down the column and pick the smallest probability to find the worst choice for Player 2. Good question!

[drzfrofro]

man you are brilliant!!! i enjoy watching your videos on mathematics!!! especially this one, it helped me understand a concept in probability..

[FanaticDamen]

Seriously... this guy... probably the most under estimated youtuber ever... I enjoy watching his videos more than anyone elses

[PivotSweden]

He reminds me of Johnny Rotten somehow...

[kinglynx]

can you help me find the game on derren browns channel four website? the link he gave didnt work?

[ninjanerd98]

The 'way to remember' doesn't work... Help!

[chaoscloudz]

this guy's so cool that youtube advertisments do not appear on his videos :D

[Berntisso]

The prediction that appears first? Doesn't that mean that player one wins every time? Please explain a bit clearer, I didn't understand anything of the concept of the game.

[Reapinangel91]

This was featured on scam school awhile back, a very nice mathematical trick.