## Why don't they sell scratch cards in betting shops?

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### Re: Why don't they sell scratch cards in betting shops?

laklak wrote:It's a tax on stupid. But hey, somebody's gotta win. The scratch card games have much better odds than lotto. The current big scratch card in Florida is "Monopoly", with a \$2,000,000 prize. Odds are 1/2,500,000. Odds in Florida Lotto are about 1/14,000,000, and odds in the Megamillions are about 1/320,000,000.

Where have you got those odds from and have you factored in the stake?

The odds on scratchcard grand prizes are typically orders of magnitude worse than that would indicate.

Thommo

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### Re: Why don't they sell scratch cards in betting shops?

Is it this? I think it's this:

There are 12,103,014 possible combinations of the first five numbers ranging from 1 to 70. Multiply that by the 25 options for the final ball and you get a total of 302,575,350 possible Mega Millions draws. That means any given ticket has a 1-in-302,575,350 chance of winning, or about a 0.00000033% probability.

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### Re: Why don't they sell scratch cards in betting shops?

I think I might be tired, but I'm not sure what you're asking, sorry!

Laklak was talking about the odds on a scratchcard, as opposed to a lottery draw, typically those are much more opaque and the companies (like companies who run other addictive forms of gambling like slot machines, fruit machines and FOBT machines) try to disguise what's going on within the letter of the law. The percentage of the total prize fund that goes into the jackpot (as opposed to lesser wins and free plays) tends to be in the single digits, but varies from game to game.

I can see nothing wrong with the calculations present in the article you linked, as far as it goes though.

Thommo

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### Re: Why don't they sell scratch cards in betting shops?

Oh, right. I didn't read the question properly. As you were!
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### Re: Why don't they sell scratch cards in betting shops?

Ooh, here's a prize structure. No idea how it's worked out, though:
Odds of Winnings

Prize Amount Odds of Winning
\$2,000,000 1-in-3,000,000
\$10,000.00 1-in-120,000
\$5,000.00 1-in-24,000
\$1,000.00 1-in-3,000
\$500.00 1-in-1,791
\$200.00 1-in-1,000
\$100.00 1-in-71
\$50.00 1-in-240
\$30.00 1-in-41
\$25.00 1-in-80
\$20.00 1-in-15
\$15.00 1-in-20
\$10.00 1-in-9

Overall Odds: 1-in-3.44

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### Re: Why don't they sell scratch cards in betting shops?

Thanks that's perfect, it's exactly what I couldn't find.

So consideration of the jackpots alone (which doesn't reflect the expected value of the bet, for which you need to sum the expected values of every prize level) shows that \$1 in the Florida lotto gives you a 1 in 22,957,480 chance (calculated from the simple formula for number of combinations N!/(N-k)!k! ) of winning a minimum of \$2,000,000 shared among the number of winners, I can't find the statistics on that either, so I'll just assume it's about 2 on average (which would represent sales of ~23 million tickets per week). This means the jackpot gives you an expected return of \$-0.956 per dollar wagered.

The scratchcard costs \$10 to play and so has an expected return per dollar from the jackpot of of \$2,000,000/10x3,000,000 = \$-0.933 per dollar wagered, which is worse. Again note, that's only considering the jackpots.

The megamillions costs \$2 to play and so has an expected return from the jackpot of \$-0.939 per dollar wagered, again subject to the assumptions of about 23 millions tickets sold (the more sold the more likely you are to share your jackpot) and no rollover jackpot.

So the best bet depends on ticket sales, and rollovers. It's likely that the least worst option is to play only when there's a large rollover in either the lotto or megamillions draw, and the best option is not to play. The article mentioning that the megamillions jackpot had reached \$1.6bn would make the draw worth playing if few enough tickets were sold (although business insider point out in another excellent article that because of taxes, it's probably still not worth it).

I do seem to recall a few years ago there was a huge rollover in the UK national lottery draw that made it *almost* worth playing. I think this has been made less likely by more people playing "lucky dip" tickets with randomly generated numbers in recent years.

PS: All of that does assume you choose your numbers randomly, if you do something daft like pick 1,2,3,4,5,6 or your family's birthdays you drastically increase the chance of sharing the jackpot and make your chances worse.

Thommo

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### Re: Why don't they sell scratch cards in betting shops?

Chasing the link chain further, this made me laugh:

There actually is a precedent for someone buying every ticket in a lottery, thus ensuring that the person would be holding a jackpot-winning ticket. The Romanian mathematician Stefan Mandel managed to win the lottery 14 times in the 1980s and '90s through a scheme similar to the one considered above.

According to a profile of Mandel in The Hustle, he recruited investors to put up the money needed to buy every ticket in the Virginia lottery. Once the jackpot grew to \$27 million in February 1992 — high enough to make the plan theoretically profitable — Mandel used a bank of computer printers to print out every combination of numbers from that lottery. A group of couriers then dropped off thousands of tickets at a time at lottery retailers around the state.

Though logistical snags prevented all of the combinations from being entered in time, the consortium still won the \$27 million prize.

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### Re: Why don't they sell scratch cards in betting shops?

N!/(N-k)!k!

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### Re: Why don't they sell scratch cards in betting shops?

Thommo wrote:Where have you got those odds from and have you factored in the stake?

The odds on scratch card grand prizes are typically orders of magnitude worse than that would indicate.

http://www.flalottery.com/remainingPrizes

You have to click on the individual games to find the odds.

Easy to calculate for scratch cards, they know how many they've printed and how many prizes there are.
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laklak
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### Re: Why don't they sell scratch cards in betting shops?

Thanks. It's the \$10 price that makes the odds look better.

Thommo

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### Re: Why don't they sell scratch cards in betting shops?

They should sell \$100 cards for even better odds.
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