In any game of chance, the value of a prize is normally in direct proportion to the odds of winning that prize—the greater the odds, the more valuable the prize. Here I use “greater odds” to mean “less likely to win.”
The odds of winning the Lotto is 3,392,928-to-1. The odds of picking five correct numbers (without the powerball) is 376,992-to-1. In other words, if you have picked the first five numbers correctly, your chance of winning the Lotto is 1-in-9 (the probability of choosing the correct powerball from nine balls).
The previous week, when the jackpot was $25 million, two people matched five numbers to share a total purse of $97,769.20, again nothing close to the expected $2.8 million.
The release also stated, “One hundred players matched four numbers and the powerball number to win $797.44.” That’s a total purse of $79,744. This is where it gets even more interesting.
The odds of matching four numbers and the powerball is 530,145-to-1, which is greater than the odds of a five-match (376,992-to-1). So the purse should be more than that of the five-match. But it’s less.
In a fair game, you would expect that the prize for matching five numbers would be roughly one-ninth of the big prize. So if the jackpot is $30 million, a five-match should be worth about $3.3 million, especially if no one won the jackpot.
So I was a bit shocked to read the NLCB release which stated, “Five players matched five numbers without the powerball to each win $21, 619.60.” That’s a total five-match purse of $108,098, nothing remotely close to three million.
Clearly, the NLCB does not use probability theory in determining its prizes, to the detriment of the playing public. It would be interesting to hear what formula they do use for the lower prizes.
In the meantime, you might get a fairer deal from the bazaar huckster playing “over, under and lucky 7.” At least, his prize structure accords with probability theory more than the NLCB.
Noel Kalicharan