Last post wins.

Kamikaze28 · 07-04-2012, 08:25 PM

(07-04-2012 09:52 AM)Solan Wrote: also to phrenikos... what would be the difference in how much i'd pay for the game? does the pot start at how much i pay or something? o jjust 1 dollar every challenge?

The game always starts with a pot of $1. The paradox is this: probability theory tells you that this game has an expected winning amount of ∞ (infinity), yet most people will only pay a small price to play it.
This is paradoxical because most of the time, the expected winnings is close to your gut feeling. For instance, say I roll 2 D6 (6 sided dice) and pay you the amount of dollars that the sum of both dies show (so between $2 and $12). The expected winnings are $7, and that'll be what most people will be willing to pay.
Here's the Wikipedia article for detailed information and most importantly all the nicely-formatted formulas to understand the paradox.

Solan · 07-04-2012, 08:35 PM

ooh ok, so it's like how much i'd pay to do that challenge. sorry i was kinda confused. I feel like i'd pay a good amount... although that paradox does sure sound true.

phrenikos · 07-04-2012, 10:11 PM

(07-04-2012 02:15 AM)Kamikaze28 Wrote: That's clever - the computer science part of me calculated the expected winnings and therefore wants to play at any cost, because the expected winnings is infinite. My gut however wouldn't pay more than $8. And in reality, I don't gamble for money and wouldn't play at all.

Good answer Kami! I got this as an interview question once - they had me stumped until I realized they weren't actually looking for a numeric value, but how'd I approach the problem.

Kamikaze28 · 07-04-2012, 10:48 PM

(07-04-2012 10:11 PM)phrenikos Wrote:
(07-04-2012 02:15 AM)Kamikaze28 Wrote: That's clever - the computer science part of me calculated the expected winnings and therefore wants to play at any cost, because the expected winnings is infinite. My gut however wouldn't pay more than $8. And in reality, I don't gamble for money and wouldn't play at all.

Good answer Kami! I got this as an interview question once - they had me stumped until I realized they weren't actually looking for a numeric value, but how'd I approach the problem.

My first response was "hey, this can easily be simulated" - and I wrote 20 lines of C. Then I noticed that with increasing iterations, the average winnings increased and it dawned on me. Once you formulate the expected value, it's clear as day that this is fishy.

Here's another interesting thing, maybe you've heard it already but don't spoil the experience and google it!
A man walks into a bar and asks for a glass of water, the barkeep takes out his trusty shotgun and closely misses the man. The man then pays the barkeep, thanks him and leaves. What happened?

knighthalo123 · 07-05-2012, 05:01 AM

(07-04-2012 10:48 PM)Kamikaze28 Wrote:
(07-04-2012 10:11 PM)phrenikos Wrote:
(07-04-2012 02:15 AM)Kamikaze28 Wrote: That's clever - the computer science part of me calculated the expected winnings and therefore wants to play at any cost, because the expected winnings is infinite. My gut however wouldn't pay more than $8. And in reality, I don't gamble for money and wouldn't play at all.

Good answer Kami! I got this as an interview question once - they had me stumped until I realized they weren't actually looking for a numeric value, but how'd I approach the problem.

My first response was "hey, this can easily be simulated" - and I wrote 20 lines of C. Then I noticed that with increasing iterations, the average winnings increased and it dawned on me. Once you formulate the expected value, it's clear as day that this is fishy.

Here's another interesting thing, maybe you've heard it already but don't spoil the experience and google it!
A man walks into a bar and asks for a glass of water, the barkeep takes out his trusty shotgun and closely misses the man. The man then pays the barkeep, thanks him and leaves. What happened?

ITS A BANDIT, jk the guy has hiccups

aaronINdayton · 07-05-2012, 11:47 PM

(07-04-2012 01:46 AM)phrenikos Wrote: I've got one for you non-stat majors (St. petersburg paradox):

Let's say I offer you a game: A coin is tossed at every stage. The pot starts at 1 dollar and is doubled every time a head appears. When a tail appears, the game ends and you win the money in the pot.

(i.e. You win 4 dollars if two heads appear, and then a tail appears after)

How much are you willing to pay for this game?

To give a realistic answer, you'd need more information. Such as: how long does it take to play a game? How long will I be able to play? How much money do you have to give me? Etc.

According to the wikipedia article linked: "It follows that, in order to be reasonably confident of achieving target average per-game winnings of approximately W (where W > $1), we should play approximately 4^W games. This will yield a finite contribution equal to W. Unfortunately, the number of games required to be confident of meeting even modest targets is astronomically high. $7 requires approximately 16,000 games, $10 requires approximately 1 million games, and $20 requires approximately 1 trillion games."

Realistically, you wouldn't have time to play and make money unless you paid less than $3 a game. And even then, you'd probably make more money just getting a job.

Kamikaze28 · 07-05-2012, 11:51 PM

There are those capable of interpolating from incomplete data and ...

aaronINdayton · 07-06-2012, 02:26 AM

Continuing with the St. petersburg paradox, because it's super interesting, I wrote a simulator to test my above theory.

Assumptions:
You have $10,000 you can play the game with to begin with.
It takes exactly 30 seconds to complete the game.
You play 8 hours a day, for 30 days.

Findings:
Betting $3 every game yielded higher results than I expected. I ran 10 separate simulations of 30 days and only once did the player end with less money than starting. On top of that, the first simulation ended with an average gain per day of $2200! Averaging the 10 simulations resulted in making about $121/hr.

Betting $4 every game was different. Six of the ten 30 day simulations when bankrupt before the 30 days completed. For the remaining four though, the average money made was about $40/hr.

Conclusion:

Realistically, hypothetically, unless you've got the bank roll, I wouldn't recommend playing for more than $3 per game, based on my roughly put together simulator, the accuracy of C#'s Random class, my limited testing, and all the mistakes I made and didn't catch. ;]

brayton · 07-10-2012, 10:57 PM

We are on the internet.
How much would the internet trade in US dollars.
I mean through games, jobs, ads, surveys, blogs, providers, servers, everything but computers

Kamikaze28 · 07-10-2012, 11:01 PM

(07-10-2012 10:57 PM)brayton Wrote: We are on the internet.
How much would the internet trade in US dollars.
I mean through games, jobs, ads, surveys, blogs, providers, servers, everything but computers

Servers are computers. Also: the internet consumes an enormous amount of energy. It has cost a lot to lay all these transatlantic cables and other lines of communication. I think it's safe to say, that the internet's net worth is outside our combined fiscal capabilities.