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The Economist ~ A very short article about maths.

Day 2,221, 10:59 by Iain Keers



Dear friends,

A few brief notes on probability:


The eight sided dice

Say you have an eight sided dice. The dice is weighted so every side has an equal probability of showing up.

The odds of any particular side showing up is one in eight.


The combi bet

Now say you have three of these dice. You roll all 3. The chances of three of the same side showing up (4-4-4 or 5-5-5 or whatever) is 1 in 8^3 or 1 in 512.


Independent probability

Now say instead you have just one dice, but you keep rolling it. The chance of rolling a 5 is 1/8 each time, so you should expect on average to roll a 5 once for every eight attempts, though of course you could roll it a million times and never actually get a 5.

This is how the jackpot would work in the event it is an even chance of landing on it each time. It isn't a 1/512 chance.

To put it more simply, take coin flipping. You can flip a coin a hundred times, and the chance of getting a hundred heads in a row is equal to the chance of getting any other combination. Because each time it is a 50/50 chance.

This belief that the odds "stack" is one of the most common misconceptions in probability.

Sure, the chance of the first three goes you have being jackpots seems very low, but as you are effectively tossing dice or flipping a coin each time, the chance is equal to you hitting it with any other combination (if the "toss" is unweighted). Meaning you would normally get all three jackpots with an average frequency of 24 attempts, which is about 51.6 gold.


Admins don't believe in maths

Unfortunately it is highly unlikely all of the different outcomes have equal "weight". Having played the wheel itself I got the first jackpot on my third attempt, the second on my twentieth or so roll. I guess that the jackpot becomes increasingly harder to "hit" as you click. If I was the admin I'd make the median payout for all three at around the 350-400g mark. Most people would give up before then, but that way enough people would succeed to draw others in.

To be honest I'm not sure whether it's random at all, the whole thing could be scripted.

But anyway it just annoys me when people start talking about independent probabilities like they're conditional probabilities.

Iain out





Ps. it's been 10 years (gosh really!) since I've had to do any maths in a serious way, so if I've made any mistakes lemme know and I'll fix em.
 

Comments

Igoreckkkk
Igoreckkkk Day 2,221, 11:03

first

Malkaiser Day 2,222, 06:03

Comment deleted

Malkaiser
Malkaiser Day 2,222, 06:59

eRepublik keeps eating my massive replies. I think that this could be said better. I'll go for TLDR this time and maybe try t post the detail again later.

1/512 is indeed wrong, that is the probability of rolling three 8's in a row which is a 0.2% chance. You don't need to roll them all in a row AND you can hit free roll.

If you take into account all of the possible ways of winning then you'd expect to win on average after 21 rolls rather than 512. Draw a tree diagram.

Of course it's probally not a fair spinner.

The Grumpy
The Grumpy Day 2,221, 11:03

No.

Mr Sherlock Holmes
Mr Sherlock Holmes Day 2,221, 11:04

Biased dice! \o/

Mininuns
Mininuns Day 2,221, 11:08

Miau

Igoreckkkk
Igoreckkkk Day 2,221, 11:10

Mininuns
Mininuns Day 2,221, 11:17

Hostilian
Hostilian Day 2,221, 11:09

The probability of the outcomes having equal weights is infinity^-1.

I believe this article shows us the best way to use the power spin:

http://www.erepublik.com/sr/article/-power-spin-ftfy-2354053/1/20

krispo
krispo Day 2,221, 11:13

v

vladb
vladb Day 2,221, 11:20

"if the "toss" is unweighted" -ofc it is weighted

Virotutis
Virotutis Day 2,221, 11:35

I doubt there is anything legally binding here in terms of the odds. The bias must be ridiculously high and I doubt they have considered any median payout. There is probably some gold intake quota along with player quota and once they are filled, the script will randomly pick a person, could be a player spinning for the first time or someone who spends the 500+th gold on this. the house never loses

Virotutis Day 2,221, 11:34

Comment deleted

Alina V
Alina V Day 2,221, 11:43

Hmmm, math in english must be translated
Or probability changed since I went to school.

etljo stnov
etljo stnov Day 2,221, 12:13

Voted and shouted ! o/

TigerII91
TigerII91 Day 2,221, 12:14

Voted and shouted !

Grainne Ni Mhaille
Grainne Ni Mhaille Day 2,221, 12:15

*-*

Roman Daco
Roman Daco Day 2,221, 12:37

odds are weighted the same way the bazooka parts odds are. good luck wasting your G. I will be there selling it for you when it will go ridiculously high ; )

Iain Keers
Iain Keers Day 2,221, 14:10

I don't think running out of money is a major concern for me...

Roman Daco
Roman Daco Day 2,221, 15:39

It was a collective "your", and in average (since we are doing some math here) it may be a concern. In fact I have already seen some playing till running out of gold stories on my wall.

For you personally, have fun spinning the wheel!

Detharon
Detharon Day 2,221, 13:39

"Meaning you would normally get all three jackpots with an average frequency of 24 attempts,"
21 attempts. You forgot about the "spin again" reward, which alters the probabilities a bit, and in fact they're conditional in some sense.

1/8 is the chance of getting a jackpot, and 1/8 is a chance of rolling again, therefore the probability of finding a jackpot is equal to a series:
(1/ + (1/^2 + (1/^3 + ... + (1/^n as n goes to infinity. It's 1/7.

"which is about 51.6 gold." Also wrong, even with 1/8 you cannot calculate it from the following formula: (1.0 + 3.3) / 2 * 24, why?
Because the cost function is not linear, for example, if f(x) is the cost function and its argument is the number of trials:
f(23) = 48,3,
f(24) = 51.6,
f(25) = 56.25

avg(f(23),f(25)) = 52.275.
To make matters worse, this isn't even a normal distribution, so I have no idea what approach to take except bruteforcing it. So here is it, an algorithm of simulating the power spin game written in java http://pastebin.com/zTUZ94tN easily adaptable to other programming languages. Anyway, the results are as follows:
Average cost after 10000000 tries: 48.3028846
Average number of tries: 21.0010793

So on average, with unweighted roulette wheel, 48.3 gold and 21 trials are needed to get the 500g reward, which is obviously unreal, and such great odds make it look pretty phishy. So instead I think I'm gonna grab a combat stash for myself, which is apparently new (because otherwise, why would anyone add a "new" label on it?), and its price has been lowered from a whopping 87eur to just 9.9eur! Or not.

cc1432
cc1432 Day 2,221, 13:59

it's weighted for sure. if the weight of each possible event is preditermined and static, or it is scripted and dynamic to satisfy some specific conditions is to be determined.

Furio
Furio Day 2,228, 04:49

Too much math, you never win against the house should suffice xD

The Norfolk
The Norfolk Day 2,221, 17:15

The chance of three 8-sided dice getting the same value is 8 in 512 (512 combinations but 8 different combinations that win) aka 1 in 64.

candymanson
candymanson Day 2,221, 18:58

*tips hat*

Tony Clifford Day 2,221, 22:55

Comment deleted

Mr Woldy
Mr Woldy Day 2,222, 18:24

Ha, well said

You may call me V
You may call me V Day 2,223, 03:23

Try and have fun and stop over analyzing everything, I can imagine you would be a loads of laughs standing next to a fruit machine

Iain Keers
Iain Keers Day 2,223, 04:04

Laughing at the people who still use fruit machines in 2013 maybe

You may call me V
You may call me V Day 2,223, 04:32

I haven't in about twenty years.

Paddy OBrien
Paddy OBrien Day 2,223, 10:31

I could be wrong about this

I thought most coins, American at least, were actually weighted a bit more on the heads side. That would increase the odds of a tails result, wouldn't it, as the extra weight would tend to land on the bottom?

 
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