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# Probability: equal sequences

Best Answer Rob_G, 14 April 2014 - 08:31 PM

Spoiler for I would say
Go to the full post

5 replies to this topic

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Posted 14 April 2014 - 02:58 AM

Try out (or imagine) the following simple game with a friend:

You each toss a fair coin as many times as necessary to get a required sequence.
Your required sequence is H T H
Your friend's required sequence is H T T.
Do this several times and each time write down the number of tosses you needed

The winner is the player whose average number of tosses is the lowest. For example:

Game 1:
You toss: H T T H T H
Friend tosses: H T H H H T H H T T

Game 2:
You toss: T T H T T H H T H
Friend tosses: T T H H T H T T

Game 3:
You toss:   T T H H T H
Friend tosses:   H H T H T T

You both 'score' 6.

At this point your average is 7 and your friend's average is 8.

The conundrum: Assuming you played the game many times, which of the following outcomes would you expect?

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### #2 bonanova

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Posted 14 April 2014 - 05:58 AM

Spoiler for Looks like

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Vidi vici veni.

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Posted 14 April 2014 - 02:49 PM

agreed

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### #4 Rob_G

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Posted 14 April 2014 - 08:31 PM   Best Answer

Spoiler for I would say

Edited by Rob_G, 14 April 2014 - 08:31 PM.

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### #5 bonanova

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Posted 15 April 2014 - 07:10 AM

Spoiler for I would say

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Vidi vici veni.

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Posted 15 April 2014 - 12:15 PM

Hmmm. I did not consider a single coin
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