Thursday, March 12, 2009

What are the odds?

Lotto Game Lotto 6/42 MegaLotto 6/45 SuperLotto 6/49 Power Lotto 5/55 +Powerball
Numbers in Pool
42 45 49 55
Chosen 6 6 6 5+1
No. of combinations 5,245,786 8,145,060 13,983,816 34,787,610
Amount needed to bet for all combinations 52,457,860 81,450,600 279,676,320 1,739,380,500

The biggest lotto jackpot ever (around PhP350M) has been won recently by two lucky bettors. Conspiracy theorists who say the usual suspects were busy defending themselves against World Bank charges that's why they haven't won the big thing yet.

Just what are the odds of getting six numbers correctly from a pool of Lotto numbers? Using basic prob formulas and a spreadsheet, we compute the odds presented in the table above. For the ordinary Lotto (6/42) alone, the number of possible combinations is more than 5.2 million. For the Megalotto (6/45), the number of combinations is more than 8 million and for the Superlotto (6/49), the combinations total just under 14 million.

From 1:5 million to 1:14 million. Statistically, that is how hard it is to guess the winning numbers. At the ticket price of PhP10 per combination, you have to invest PhP52 million (for Lotto6/42, PhP81M for Megalotto and Php280M for Superlotto) to bet for all the possible combinations. Even more staggering is the odds for the Powerlotto, where you have to invest PhP1.7 Billion to be assured of the Php50 million jackpot. The latest big jackpot is big enough for someone bold enough to bet for all combinations. But imagine the logistical nightmare of filling up all those tickets. Hahaha.

But Filipinos are so good in getting the lotto jackpot that whenever it is won, it is often shared by 2 or more winners. Statistically, having one winner is hard enough. But getting two or more? The biggest lotto prize ever was won when the World Bank controversy waned. Just what are the odds of 2 winners sharing the PhP350Million? Go figure. Conspiracy theorists may have a point.

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