Powerball

Tables of Frequencies of Powerball games from draw 1 held on 30/5/96 thru to game drawn on 30/03/2006.

Table of frequencies for the Powerball game.

Table of frequencies for the Powerball game by Drawn Ball.

Table of Weeks Since Last Drawn as well as product of Frequency by WSD.

Probability of getting all six numbers (no supplementary) with one game of six numbers is 1 in:

45*44*43*42*41*40! ⁴⁵C₆ = ----------------------- * 45 5! * (45 - 5)!

Or about 1 in 54 million.

This is on the assumption that each ball has an equal likelihood of being drawn as first ball. However the table above indicates that this is not the case thus far, and that the likelihood of each ball being drawn varies from ball to ball, and from their order of being drawn.

The general formula for any five numbers plus any powerball from the above table is:

Fr(n₁)*Fr(n₂)*...*Fr(n₄)*Fr(n₅)*5! Fr(pb) Pr(Any 5 + pb) = ------------------------------------- * ------------------------ (Sum of the Frequencies)⁵ Sum of the pb Freq's Where Fr(n_i) is the Frequency of the i'th number chosen from the table.

Probabilities for sytems entries:

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In systems entries we play 6 or more numbers per a game and for the first division prize hope that the five numbers drawn will be ALL amongst those 6 or more numbers we played. Only one powerball is played for any system entry.

The formula then becomes: Pr(System N) =

5!*N!*(Weighted average of the frequencies of the N numbers chosen)⁵ Fr(pb) ---------------------------------------------------------------------- * --------------------- (Sum of the Frequencies)⁵*5!*(N-5)! Sum of the pb Freq's

Take 3 and Take 4 games:

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For a Take 4 game the probability of winning the first division prize with any 4 numbers from the table is;

4! * Fr(n₁) * Fr(n₂) * Fr(n₃) * Fr(n₄) Fr(pb) Pr(Take 4) = --------------------------------------- * ---------------------- (Sum of the Frequencies)⁴ Sum of the pb Freq's

For Take 3 the formula would be;

3! * Fr(n₁) * Fr(n₂) Fr(n₃) Fr(pb) Pr(Take 3) = ------------------------------------ * ----------------------- (Sum of the Frequencies)⁵ Sum of the pb Freq's

Any errors in the above formula's please contact me

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