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#1 2014-10-18 20:06:37

gameprobability
Member
Registered: 2014-10-18
Posts: 7

New Game Probability Formula

Hi,                    
                   
I am trying to create a game where a player can score between 0 and 5 in a single game with the following probabilities                   
                   
0    1    2    3    4    5
P0    P1    P2    P3    P4    P5
                   
                   
I am trying to come up with a formula that calculates                    
                   
If a players plays x number of games, what is the probability  that their combined score will be at least Y                   
                   
Example                   
0    1    2    3    4    5
40    25    15    5    10    5
                   
If a player plays 6 games what is the probability that their combined score will be greater than 5                   
                   
Any help with this would be very much appreciated.                    
                   
Thanks

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#2 2014-10-18 21:48:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

Hi;

What are the values you assign to P0, P1, etc?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2014-10-18 23:44:37

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

Hi,

Thanks for the reply,

the values assign to P0, P1, etc are the likelihood that a player gets a particular score in a single game

P0  ( a score of 0)= .40 (40%)
P1  ( a score of 1)= .25 (25%)
P2  ( a score of 2)= .15 (15%)
P3  ( a score of 3)= .10 (10%)
P4  ( a score of 4)= .05 (5%)
P5  ( a score of 5)= .05 (5%)

So every times a player players the game they have a 40% chance of scoring 0, a 25% chance of scoring 1, a 15% chance of scoring 2 etc.

My question is If a player plays 6 games what is the probability that their combined score will be greater than 5 and what formula would you use to work this out?

Thanks

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#4 2014-10-18 23:45:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

There may not be a nice neat formula, but it can be answered.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2014-10-18 23:51:23

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

Good news bobbym,

If you are able to answer it or provide guidance to help answer it, please let me know .

Thanks again

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#6 2014-10-19 00:25:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

Hi;

I am getting so far:

Please give me some time to check this before using it.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2014-10-19 00:32:41

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

Hi bobbym,

That is great, would you be able to guide me through how you got this answer?

Thanks

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#8 2014-10-19 00:39:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

Yes, but first I have to verify that answer in at least one other way. That will take a bit of time I will post it when I have the second solution.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2014-10-19 01:43:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

Hi;

This is verified by a simulation so I have 2 ways. The other involves the expanding of a probability generating function.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2014-10-19 02:07:23

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

Thanks so much bobbym.

Could you elaborate on the probability generating function? I would like to be able to calculate the probability for a number of different scores ( 4,5,6,7).  I may also end up changing the score probabilities and would like to know how to re-calculate if I do.

I really appreciate your help.
Cheers

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#11 2014-10-19 03:19:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

Do you program?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2014-10-19 03:53:02

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

I have some programming abilities, I can write VBA for excel macros for example, I can certainly understand Pseudocode.

Thanks

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#13 2014-10-19 05:12:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

It is a bit more complicated than that. You have to expand this expression.

Or you can write a little program in your favorite language.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#14 2014-10-19 07:17:12

gameprobability
Member
Registered: 2014-10-18
Posts: 7

Re: New Game Probability Formula

Very helpful again bobbym. thanks, I have one last question for you.

How did you run the simulation. Is this something I could run using excel or do you have a specific program that runs it for you?

Thanks,

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#15 2014-10-19 09:08:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: New Game Probability Formula

I do not know how to run the simulation using excel. You could run it using C, python and many others.

The expression can be expanded easily at Wolfram alpha. Go here:

http://www.wolframalpha.com/

and enter in the input box,

(2/5 + x/4 + (15 x^2)/100 + x^3/10 + x^4/20 + x^5/20)^6


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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