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Lumifer comments on Open Thread - Aug 24 - Aug 30 - Less Wrong Discussion

7 Post author: Elo 24 August 2015 08:14AM

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Comment author: tetronian2 24 August 2015 03:26:59PM *  3 points [-]

Suppose someone offers you the chance to play the following game:

You are given an initial stake of $1. A fair coin is flipped. If the result is TAILS, you keep the current stake. If the result is HEADS, the stake doubles and the coin is flipped again, repeating the process.

How much money should you be willing to pay to play this game?

Comment author: Lumifer 24 August 2015 03:42:54PM *  -2 points [-]

As formulated, zero -- under the rules you posted you never win anything. Is there an unstated assumption that you can stop the game at any time and exit with your stake?

Comment author: tetronian2 24 August 2015 03:52:39PM *  2 points [-]

I guess I didn't formulate the rules clearly enough--if the coin lands on tails, you exit with the stake. For example, if you play and the sequence is HEADS -> HEADS -> TAILS, you exit with $4. The game only ends when tails is flipped.

Comment author: Lumifer 24 August 2015 04:13:18PM *  0 points [-]

Also notice that as formulated ("You are given an initial stake of $1") you don't have any of your own money at risk, so... And if the game only ends when TAILS is flipped, there is no way to lose, is there?

If the first $1 comes from you, you are basically asking about the "double till you win" strategy. You might be interested in reading about the St.Petersburg paradox.

Comment author: jkaufman 24 August 2015 06:11:02PM 3 points [-]

Reading the wikipedia article on the St Petersburg paradox, that's exactly the game tetronian2 has described.

A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, 8 dollars if a head appears on the first two tosses and a tail on the third, 16 dollars if a head appears on the first three tosses and a tail on the fourth, and so on. In short, the player wins 2k dollars, where k equals number of tosses (k must be a whole number and greater than zero). What would be a fair price to pay the casino for entering the game?

Comment author: tetronian2 24 August 2015 08:23:34PM 1 point [-]

Yep. I don't think I was ever aware of the name; someone threw this puzzle at me in a job interview a while ago, so I figured I'd post it here for fun.

Comment author: DanielLC 25 August 2015 04:04:41AM 1 point [-]

The money that's "at stake" is the amount you spend to play the game. Once the game begins, you get 2^(n) dollars, where n is the number of successive heads you flip.

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