Thoraiya DyerBeauty of Maths, Part 3: Winning Lotto
April 21st 2008 23:18
Part 3 of The Beauty Of Maths aims to demonstrate that a person who buys one lotto ticket has the same chance of winning as a person who buys no lotto tickets, when rounded off to the 5th decimal place.
Item:
Two different NSW lotteries: a) Lotto and b) Lucky Lotteries. Both heavily advertised on TV and in newsagents all over the state.
What the TV Ads depict:
a) “The big red ball that makes dreams come true!”, typically accompanied by a massive truck full of $50 bills.
(Note, average dimensions of a truck that size: 14 cubic metres. Based on a measured $50 note, 15.1cm x 6.5cm, and the thickness of a 100-page stack of photocopy paper, 5.5cm, I put the estimated dimensions of a million dollars at only 0.01 cubic metres.)
b) “You ought to buy yourself a lottery ticket!”, typically accompanied by a fuzzy cat puppet and scantily clad models.
What it actually offers:
Everyone knows that lotteries are games of chance.
If you check the details in the How To Play sections on theNSW Lotteries site, the two lotteries are remarkably frank about your ludicrously poor chances of winning.
Buying an 18-game, $5.40 Lotto ticket gives you a 1 in 452,503 chance of winning a share of the minimum $1 million (Monday) or $750 000 (Wednesday) Division 1 prize.
Buying a $5 Lucky Lotteries ticket gives you a 1 in 5,963,196 chance of winning the entirety of the minimum $1 million jackpot.
Both of these lotteries have additional prizes of lesser amounts, but Lotto’s TV ads don’t mention the Division 5 prize. Nor does the man in the fuzzy cat suit surrounded by models make the claim that you can visit the Playboy mansion after you’ve won one of 3,700 $10 prizes.
Outcome:
Oh, no, which one to choose? Decisions, decisions.
Statistically, if I definitely want to win the Lotto, I’ll have to buy 452, 503 tickets. That’s a bargain basement price of two million, four hundred and forty-three thousand dollars.
BUT, I might have to share my one million dollar prize if someone else picks the same numbers. Would I be better off buying 5 963 196 Lucky Lottery tickets? That would cost twenty-nine million dollars, but I’d get to keep the jackpot all for myself.
I know, maybe I won’t waste money on either one!
The fact is, a person who buys a Lotto ticket with an eye for the Big Red Ball has a 0.000002 chance of winning. Rounded off to the 5th decimal place, that’s 0.00000 – or NOTHING!
So I don’t see how I’m any worse off, not having purchased a ticket at all.
Similarly, a person keen to buy a spangled suit and romp with half-naked babes who buys a Lucky Lotteries ticket has a 0.0000002 (one extra zero squeezed in there) chance of winning the jackpot.
Here’s some free advice from me.
Unless you are from the future, a psychic or a dodgy employee of NSW Lotteries, YOU OUGHT NOT TO BUY YOURSELF A LOTTERY TICKET!
Item:
Two different NSW lotteries: a) Lotto and b) Lucky Lotteries. Both heavily advertised on TV and in newsagents all over the state.
What the TV Ads depict:
a) “The big red ball that makes dreams come true!”, typically accompanied by a massive truck full of $50 bills.
(Note, average dimensions of a truck that size: 14 cubic metres. Based on a measured $50 note, 15.1cm x 6.5cm, and the thickness of a 100-page stack of photocopy paper, 5.5cm, I put the estimated dimensions of a million dollars at only 0.01 cubic metres.)
b) “You ought to buy yourself a lottery ticket!”, typically accompanied by a fuzzy cat puppet and scantily clad models.
What it actually offers:
Everyone knows that lotteries are games of chance.
If you check the details in the How To Play sections on theNSW Lotteries site, the two lotteries are remarkably frank about your ludicrously poor chances of winning.
Buying an 18-game, $5.40 Lotto ticket gives you a 1 in 452,503 chance of winning a share of the minimum $1 million (Monday) or $750 000 (Wednesday) Division 1 prize.
Buying a $5 Lucky Lotteries ticket gives you a 1 in 5,963,196 chance of winning the entirety of the minimum $1 million jackpot.
Both of these lotteries have additional prizes of lesser amounts, but Lotto’s TV ads don’t mention the Division 5 prize. Nor does the man in the fuzzy cat suit surrounded by models make the claim that you can visit the Playboy mansion after you’ve won one of 3,700 $10 prizes.
Outcome:
Oh, no, which one to choose? Decisions, decisions.
Statistically, if I definitely want to win the Lotto, I’ll have to buy 452, 503 tickets. That’s a bargain basement price of two million, four hundred and forty-three thousand dollars.
BUT, I might have to share my one million dollar prize if someone else picks the same numbers. Would I be better off buying 5 963 196 Lucky Lottery tickets? That would cost twenty-nine million dollars, but I’d get to keep the jackpot all for myself.
I know, maybe I won’t waste money on either one!
The fact is, a person who buys a Lotto ticket with an eye for the Big Red Ball has a 0.000002 chance of winning. Rounded off to the 5th decimal place, that’s 0.00000 – or NOTHING!
So I don’t see how I’m any worse off, not having purchased a ticket at all.
Similarly, a person keen to buy a spangled suit and romp with half-naked babes who buys a Lucky Lotteries ticket has a 0.0000002 (one extra zero squeezed in there) chance of winning the jackpot.
Here’s some free advice from me.
Unless you are from the future, a psychic or a dodgy employee of NSW Lotteries, YOU OUGHT NOT TO BUY YOURSELF A LOTTERY TICKET!
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