New Game Probability Formula

gameprobability · 2014-10-18 20:06:37

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

bobbym · 2014-10-18 21:48:28

Hi;

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

gameprobability · 2014-10-18 23:44:37

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

bobbym · 2014-10-18 23:45:52

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

gameprobability · 2014-10-18 23:51:23

Good news bobbym,

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

Thanks again

bobbym · 2014-10-19 00:25:05

Hi;

I am getting so far:

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

gameprobability · 2014-10-19 00:32:41

Hi bobbym,

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

Thanks

bobbym · 2014-10-19 00:39:03

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.

bobbym · 2014-10-19 01:43:52

Hi;

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

gameprobability · 2014-10-19 02:07:23

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

bobbym · 2014-10-19 03:19:22

Do you program?

gameprobability · 2014-10-19 03:53:02

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

Thanks

bobbym · 2014-10-19 05:12:38

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.

gameprobability · 2014-10-19 07:17:12

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,

bobbym · 2014-10-19 09:08:54

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

Math Is Fun Forum

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

New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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

Re: New Game Probability Formula

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