Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ernest****Member**- Registered: 2005-11-14
- Posts: 1

I have a problem unable to solve. I am not an expert in maths, if possible, PLEASE provide an explanation. Any comment(s) greatly appreciated.

there are 4 possible outcomes 1 to 4, results are independent to each other and drawn randomly (suppose to)

BUT the EXPECTED percentages (from computer) are as follows:

1 = 20%

2 = 22%

3 = 33%

4 = 25%

The ACTUAL percentages (in last 500 draws) are: (which is very close to expected)

1 = 21%

2 = 22%

3 = 32%

4 = 25%

The Actual percentages (in last 50 draws) are:

1 = 26%

2 = 22%

3 = 22%

4 = 30%

The ACTUAL percentages (in last 10 drawss) are:

1 = 20%

2 = 10%

3 = 30%

4 = 40%

and the history for the last 10 drawings are as follows (left=most recent):

3, 4, 4, 4, 2, 3, 4, 3, 1, 1

and i want to predict which number will be picked next

OR able to find the probability of next picking a 1 , 2, 3 and 4.

I believe that Poisson distribution is relevant because it can predict probability of a certain outcome which relies upon knowing historical data. i.e. in excel "=((POWER(historal average,wanted outcome))*POWER(2.718,-history average))/FACT(wanted outcome)"

BUT it does not take into consideration on counting specifically - the order of the last 10 or so results to calculate (which i believe is most important).

Please also note that the law of large numbers/averages would NOT help here, because I am predicting the NEXT result and not the results in the long run.

Perhaps somehow combing with break-even analysis, maximum same number draws or something else.. i am not sure

Break-Even Analysis: =(log2/((log a)-(log(a-1)))) where the probability of the outcome is 1/a

Maximum Same Number Draws: i.e. in excel "=ROUND(((LN(no of throws))/(-LN(1-probability of occuring))),0)"

Any comments?

Thanks

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,591

If the results are independent of each other, then the next drawing will *not be affected* by the previous drawing. And hence will not be affected by the previous 10 drawings, right?

So, there is no "memory" in the system. It doesn't know what has come up before.

But there is some built-in bias (for example, one ball is heavier in a lottery) and that is shown by your long-term results.

So, just choose a random number between 0 and 1, and if it is between:

0.00 → 0.20 then choose 1 (=20%)

0.20 → 0.42 then choose 2 (=22%)

0.42 → 0.75 then choose 3 (=33%)

0.75 → 1.00 then choose 4 (=25%)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline