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 04-22-2017, 09:06 AM #1 Lampinjon stranger   Join Date: Apr 2017 Posts: 2 Probability calculation in a simple game Hi guys! I know it's poker forum but still I hope someone will help me with a probability calculation in a simple game: What are the chances that a ball fall to a box on the bottom marked from A to R? How many combinations there is? Ball is dropped from the top and each step have 50% chance to go to left or right Example for two balls with same result:
 04-22-2017, 12:48 PM #2 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 3,894 Re: Probability calculation in a simple game Look up Pascal's triangle.
 04-23-2017, 02:10 AM #3 Lampinjon stranger   Join Date: Apr 2017 Posts: 2 Re: Probability calculation in a simple game Thank's for tip So this is exactly the same as my picture above: If I get it right...the number of all combinations is to sum lowest line (1+16+120+560...)= 65536 total combinations For a ball fall into the middle line (12870) it has 19,63806% chance or 1:5.09215 Is this correct?
04-23-2017, 01:27 PM   #4
statmanhal
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Re: Probability calculation in a simple game

Quote:
 Originally Posted by Lampinjon 1) If I get it right...the number of all combinations is to sum lowest line (1+16+120+560...)= 65536 total combinations 2) For a ball fall into the middle line (12870) it has 19,63806% chance or 1:5.09215 Is this correct?
Yes but instead of creating a triangle,

1) The sum of row n is 2^n, the total number of combinations of n trials with 50/50 occurrence of yes-no, heads-tails, left-right, etc.

2) This can be gotten directly using the binomial distribution.

04-25-2017, 09:49 AM   #5
heehaww
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Re: Probability calculation in a simple game

Quote:
 Originally Posted by statmanhal 2) This can be gotten directly using the binomial distribution.
And since these are 50/50 events, that amounts to using combinations.

combin(n, r) / 2^n

How many ways are there to pick 8 objects from a set of 16?

 04-26-2017, 10:43 PM #6 akkopower1 enthusiast   Join Date: Feb 2017 Posts: 80 Re: Probability calculation in a simple game Thats a Galton box. The probability of landing in the kth box follows a binomial probability mass function.

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