probability

Coin Flipping Problem

Elo from LessWrong suggested this problem:

I write a sequence of n heads or tails on paper.

I then start flipping a sequence of n coins. If next coin does not match my sequence, I restart a new sequence of n coins.

What is the rule for the relationship between how many coins I need to flip to get the sequence I have pre-committed to and the length of the sequence of?

Discussion there:

http://lesswrong.com/r/discussion/lw/pg3/open_thread_september_25_october_1_2017/dxlt

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algorithms

Sleeping Beauty Problem Variant

Say, it’s you who is the Sleeping Beauty, awaken and told by the dungeon master:

Here is a fair coin. I will toss it and if it lands head up, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.

If the coin lands tails up, however, you’ll get this fair coin to play with as long as you wish. After then, you will be asked for a number. If that number is equal to the number of times you have been awakened like this, you will be freed.

If your number isn’t right, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.

What is your strategy to be freed? If not this time, but eventually?

You know that this dungeon master is telling you the truth. So this may be your first time or the second or the Nth time.

What is your best strategy to escape?

Talk about it here:

http://lesswrong.com/r/discussion/lw/pd5/open_thread_august_28_september_3_2017/dwkw

 

 

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