Modeling: Most Probable Drawn Numbers

[morganstark]

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?

 

[JeffM]

If the machines were and remained perfectly random, then, by definition, you could not predict the future outcomes from amy number of past outcomes.

Of course, even when brand new, the machines will not be perfectly random. Moreover, over time the machines will experience wear so that the bias will change discontinuously. Furthermore, every time the machines are maintained, the bias may be altered, again discontinuously.

Your question is unanswerable unless you can specify the initial degree of bias, the mean number of uses between incidents of degradation from use and time, and the mean number of uses between incidencts of maintenance.

 

[pka]

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.

I mostly agree with what JeffM wrote. But our state gaming commission might have trouble with some of it. It is true that the forced air models as used in the megamillions lottery are closer to random. Assuming randomness the events are independent. Therefore, there is now way to predict.

 

[JeffM]

I mostly agree with what JeffM wrote. But our state gaming commission might have trouble with some of it. It is true that the forced air models as used in the megamillions lottery are closer to random. Assuming randomness the events are independent. Therefore, there is now way to predict.

I doubt we disagree on much of anything except the honesty and mathematical competence of state gaming commissions in most states. I am sure that such commissions will state under oath that their machines are perfectly random and unbiased at all times. I am also sure that such statements are false.

The point on which I am sure we agree is that if such statements are true, then the OP cannot do what he wants to do.

The point on which I suspect we agree is that if the machines are close enough to being unbiased and whatever small bias exists is changing by small increments in a discontinuous and unknown way, the OP cannot do what he wants to do.