Stroggoz New Zealand. Oct 30 2019 11:27. Posts 4494

I am trying to learn game theory atm and came across this cool problem in my textbook:

You play a game where a fair coin is flipped until it comes up tails the first time. At that point the player wins $2^n, where n is the number of times the coin was flipped. How much should one be willing to pay for each game to still be +EV

Is there some trick here? This seems simply ev = payoff*probability = (2^n)*(1/2^n) = 1

Researchers used brain scans to show that when straight men looked at pictures of women in bikinis, areas of the brain that normally light up in anticipation of using tools, like spanners and screwdrivers, were activated.

Nitewin United States. Oct 30 2019 22:34. Posts 1163

Raul Oly ...?

EV = 1 yes

Stroggoz New Zealand. Oct 31 2019 02:53. Posts 4494

:O. how do u get a number from an equation with n in it and n isn't defined. It isn't 1.

there is no trick here but most people find the answer to be quite unexpected.

Oh yes 1 is a silly answer when the player wins a minimum of 2!

So if you sum the ev over all possible outcomes (n=1 to infinity) you get the same cancelling and end up with the divergent series 1+1+1+... which implies you should pay any amount asked! If that’s right this time that is indeed a very cool problem!

Researchers used brain scans to show that when straight men looked at pictures of women in bikinis, areas of the brain that normally light up in anticipation of using tools, like spanners and screwdrivers, were activated.

On October 30 2019 21:34 Nitewin wrote:
Raul Oly ...?

EV = 1 yes

Not him. I used to post here a fair bit a long time ago but I stopped playing professionally years ago but still occasionally surf liquipoker as the habit seems deeply ingrained. I’m so old school I played the original Party Poker Monster days. 3betting JJ+ was cutting edge.

Researchers used brain scans to show that when straight men looked at pictures of women in bikinis, areas of the brain that normally light up in anticipation of using tools, like spanners and screwdrivers, were activated.

Stroggoz New Zealand. Oct 31 2019 13:01. Posts 4494

On October 31 2019 11:03 Oly wrote:
Oh yes 1 is a silly answer when the player wins a minimum of 2!

So if you sum the ev over all possible outcomes (n=1 to infinity) you get the same cancelling and end up with the divergent series 1+1+1+... which implies you should pay any amount asked! If that’s right this time that is indeed a very cool problem!

yup, exactly right. It's called the St petersburg paradox

Change the problem to the following and it becomes something fun to solve (this way is trivial as the answer is 2*.5+4*.25+8*.125+...=1+1+1+1...= infinity):

You play a game where a fair coin is flipped until it comes up tails the first time. After each heads flip, you win back $n, where n is the number of times the coin was flipped thus far. How much should one be willing to pay for each game to still be +EV?

ex: H +1, H +2, H +3, H +4, T end and receive $10

NewbSaibot: 18 TIMES THE SPEED OF LIGHT. Because FUCK YOU, Daut

Last edit: 01/11/2019 03:24

Stroggoz New Zealand. Nov 01 2019 04:50. Posts 4494

On November 01 2019 04:43 Stroggoz wrote:
nice proof, can use that same kind of argument to prove that 1+2+3+4+5...=-1/12

Been about 15years since I tutored Calc 2, but I believe you can only use that method for series that converge (otherwise S doesn't have a value that we can multiply). And I want to say the smallest same sign series that diverges is 1/n, so any monotone series that shrinks faster than 1/n converges. Gets much trickier with series that alternate signs.

NewbSaibot: 18 TIMES THE SPEED OF LIGHT. Because FUCK YOU, Daut