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morganstark

Modeling: Most Probable Drawn Numbers

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Please forgive me for any grammar mistake.

I'm a civil engineer and completed my Msc (Maths) focusing on Numerical Study 10 years ago. After my semi retirement as a result of my financial freedom, i have been studying some practical Maths problem for fun.

Recently I've been trying to model and solve a 2 digit lottery drawing game, and i failed. It's purely my imagination since i didn't see this in anywhere. But who knows it may exist? 

Suppose we have a lottery game of 2 digits, drawn from 2 separate but identical electrical drums as lottery company always have. Each drum consists of 10 balls, numbered from 0 to 9, to be drawn as a pair and the drawn balls are to be replaced. In one game, 12 pairs of numbers to be drawn as winning numbers, on every Saturday and Sunday. 

Eg
A particular Saturday: 09, 21, 04, 31, 48, 61, 00, 32, 99, 98, 11, 99
Sunday: another 12 pairs of numbers

My question is: if you have the result of last 1000 game, how do you calculate the most probable drawn numbers (one or two pairs)  for the next drawing? 

Any idea? 

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29 minutes ago, morganstark said:

My question is: if you have the result of last 1000 game, how do you calculate the most probable drawn numbers (one or two pairs)  for the next drawing

It looks impossible if numbers are random.

Unless there is a flaw in the mechanisms, how could earlier drawings have an effect on the next week’s numbers?

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Posted (edited)
22 hours ago, morganstark said:

the most probable drawn numbers 

As Ghideon said, if the draw is "fair" then no numbers are more probable than any others.
Are you thinking of something like this?

https://en.wikipedia.org/wiki/Gambler's_fallacy

 

Edited by John Cuthber

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Posted (edited)
On 6/14/2019 at 7:54 AM, morganstark said:

Please forgive me for any grammar mistake.

I'm a civil engineer and completed my Msc (Maths) focusing on Numerical Study 10 years ago. After my semi retirement as a result of my financial freedom, i have been studying some practical Maths problem for fun.

Recently I've been trying to model and solve a 2 digit lottery drawing game, and i failed. It's purely my imagination since i didn't see this in anywhere. But who knows it may exist? 

Suppose we have a lottery game of 2 digits, drawn from 2 separate but identical electrical drums as lottery company always have. Each drum consists of 10 balls, numbered from 0 to 9, to be drawn as a pair and the drawn balls are to be replaced. In one game, 12 pairs of numbers to be drawn as winning numbers, on every Saturday and Sunday. 

Eg
A particular Saturday: 09, 21, 04, 31, 48, 61, 00, 32, 99, 98, 11, 99
Sunday: another 12 pairs of numbers

My question is: if you have the result of last 1000 game, how do you calculate the most probable drawn numbers (one or two pairs)  for the next drawing? 

Any idea? 

Make a histogram and check the relative frequency. If you have something that looks like a box, then there is equal probability, if not, then you can see which ones pop up more often in the long run. Assuming a 1000 games is enough to give you an accurate picture, most lotteries will have such a span of possible combinations 1000 games may not be good enough.  So you could run some computer simulations to see just how well this approach works with your set up. 

Edited by Jeremiahcp

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You would have 1/10^24 chance of picking the right number.  The events would be independent, so the previous draw would not affect the next draw.  You would just still have the same chance of picking the correct winner.  It would take 1/10^48 to pick the correct number twice in a row.

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