Do you like variance?

qdmcg · #1 11-01-2006, 07:33 PM

How much do you pay to play this game?

Game:

At each stage of the game, a fair coin (H/T) is tossed. The coin is tossed until it comes up heads. The game is over once the coin lands on heads.

Round 1
H: You win $1 (game is over)
T: $0, proceed to round 2

Round 2
H: You win $2 (game is over)
T: $0, proceed to round 3

Round 3
H: You win $4 (game is over)
T: $0, proceed to round 4

Round 4
H: You win $8 (game is over)
T: $0, proceed to round 5

..and so on.

#2 11-01-2006, 07:35 PM

i hate it

Monty Cantsin · #3 11-01-2006, 07:44 PM

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..and so on.

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Define.

/mc

Sk00l4m3nts · #4 11-01-2006, 07:46 PM

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..and so on.

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You can't lose 5 coinflips or more in a row, duh. This game aint gonna last very long.

citanul · #5 11-01-2006, 07:49 PM

plz go to SMP forum, k thx?

RikaKazak · #6 11-01-2006, 07:51 PM

gay post

and variance is gay

I wish I just got my hourly rate deposited into my account each day after playing

alphatmw · #7 11-01-2006, 08:02 PM

your EV is (0.5)*1 + (0.25)*2 + (0.125)*4 + .... or 0.5 + 0.5 + 0.5 .... or infinity so in theory you should pay any amount for it. in practice, i don't think i'd pay more than $5-10 per play.

mak15 · #8 11-01-2006, 08:04 PM

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your EV is (0.5)*1 + (0.25)*2 + (0.125)*4 + .... or 0.5 + 0.5 + 0.5 .... or infinity so in theory you should pay any amount for it. in practice, i don't think i'd pay more than $5-10 per play.

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um pretty sure your ev is not infinit, but i suck at math now a days.

nubs · #9 11-01-2006, 08:07 PM

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your EV is (0.5)*1 + (0.25)*2 + (0.125)*4 + .... or 0.5 + 0.5 + 0.5 .... or infinity so in theory you should pay any amount for it. in practice, i don't think i'd pay more than $5-10 per play.

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um pretty sure your ev is not infinit, but i suck at math now a days.

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It is infinite. I would pay about $6 for this because of the huge variance.

MrBlah · #10 11-01-2006, 08:08 PM

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your EV is (0.5)*1 + (0.25)*2 + (0.125)*4 + .... or 0.5 + 0.5 + 0.5 .... or infinity so in theory you should pay any amount for it. in practice, i don't think i'd pay more than $5-10 per play.

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um pretty sure your ev is not infinit, but i suck at math now a days.

[/ QUOTE ] Yes it is. It's called the St. Petersburg paradoxon and this guy came up with it to show that you can't base all your decisions solely on EV but also have to take variance and utility into account.