Friday, January 8, 2016

Will there be a Powerball Winner on Saturday? - And, What is the probability there will be?

The Powerball jackpot for tomorrow night's drawing (Saturday January 9 2016) has just been increased to $800 million for the annuity value, and to $496 million for the cash value. Based on this, we are estimating that around 400 million tickets will be sold in total for the next drawing.

Since the total number of combinations is 292.2 million, one would think that the jackpot will be won for sure (because 400 is greater than 292).

But you would be wrong.(See Probability of Winning the Lottery)

The real probability that the winning ticket will be sold is only:

a 74.6% probability that Powerball will be won 
(if 400 million tickets are sold).

This means that there is a 25.4% chance that there will be no winner, and that the jackpot will continue to grow!

The explanation for estimating this lower probability lies with the principal of randomness and duplicates.

Since every combination is randomly generated independently from another, the chance that a newly printed number set is a duplicate increases as the number of combinations are sold. Eventually, it becomes more likely that new combination is a duplicate, rather than being a unique combination.

According to the LottoReport.com website, approximately 176 million tickets were sold in the Wednesday January 6th drawing and there was no jackpot winner. This is not surprising because there was only a 45.3% chance that a winning ticket would be sold.

Likewise, when 200 million combinations are sold, there is only a 49.6% chance of winning; and when 300 million combinations are sold, there is a 64.2 chance of wining  (but more than 1 in 3 chance of losing).

You can access our:

page to analyse the chances of winning the Powerball and other lotteries based on the number of tickets sold.

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