Lottobuddy, I too echo prob987's sentiments and wish to thank you for posting that link.

I have always enjoyed mathematics, and this will help me immensely in understanding what expected return is all about. Thank God I had teachers and professors who instilled in us a desire to wonder and ask questions, then attempt to find the answers.

LOL...perhaps I should have titled my original post "Expected Payout". And that brings to mind another question that I am curious about. What is the theoretical payout of a given lottery in it's history. For that, I would probably need to know the number of winners for each prize tier, the number of tickets sold, whether the cash option was chosen, and, perhaps, how much was withheld to fund non-lottery related projects. Just to satisfy my own curiosity.

Again, thank you both lottobuddy and prob987 for your contributions.

Regards and best wishes,

Rick

You're all welcome.  I've been trying to find out the expected payoffs for Canada's Lotto 6/49 and Lotto Super 7.  My hypothesis is that even though they offer tax-free cash jackpots, they have never had a positive expected return because of high sales.  I am requesting if prob987 or other statistical guru can plug the numbers into their complex formula and confirm this.

The last time the 6/49 jackpot exceeded the 1 in 13,983,816 odds was for a $15 million draw back in November 15, 1997.  Looking at that payout table, there was a total payout of $26,565,427.50, but the ticket sales of 38,085,190 is I think what lowers the expected payoff to well below the $1 ticket cost.

For Lotto Super 7(/47), you get 3 plays for $2 so the odds of winning the jackpot per $1 wager is 1 in 41,927,666.  The biggest jackpot ever in Canada was for $37.8 million in the May 17, 2002 draw.  The record sales of $102,092,406 was incredible for a nation of only 30 million people, and four winners split the jackpot.

Unlike Powerball, Canada's two national lotteries have never had a single draw where the total payouts exceeded sales.  For Powerball, the total sales is usually exceeded by the cash jackpot amount when it is dventually won.  For example, in the February 4 draw, Powerball sold only $17,795,366 worth of tickets, but paid out $50.9 million (including the $46.5 million cash jackpot).

LottoBuddy,

I have calculated the expected values of the Canadian Lotto 649 and Super 7 lotteries and no, they have never had a positive expected value. The reason is as you have surmised - high sales.

The highest expected value for the Lotto 649 lottery occured on the Sept 30, 2000 draw. The expected value was 79%. The jackpot was $15 million and the sales were 28,649,988 tickets. The expected value is usually around 70% when the jackpot is $10 million

The highest expected value for the Super 7 lottery occured just recently on Jan 30, 2004. The expected value was 70%. The jackpot was $30 million and the sales were 33,834,020 tickets.

By the way, my calculations show that the Mega Millions and Powerball lotteries never have had a positive expected value. I do factor in the taxes when calculating the expected value.

Good luck,
Jake

Well that may be the key to the discrepancy, Jake, and my calculation that the MegaMillions right now has a slightly favorable expectation value.   I don't factor in taxes.  People of course pay taxes on all kinds of income and usually report their earnings before taxes when asked "How much do you make?"  They do this on stock valuations as well.  So it seems to me that the calculation of a return on the ticket should be a before tax, rather than after tax calculation. 

It is worth noting that a favorable expectation value is a rarity for gamblers.  Gambling works because of a less than favorable expectation valuation, taxes or not.  Including a tax valuation reduces all gambling expectation values.

For the record, I will be more than happy to pay the taxes on any jackpot I win.  In an ideal world, taxes are simply the price you pay for living in a civilized world.

prob987,

I agree taxes are something we have to live with. But, nonetheless, I believe it is important that the tax factor is used to calculate the expected value. It is the after tax money that you truly "win". It is for the same reason that we use the cash value rather than the annutiy value to calculate expected value.

You are correct in stating that a positive expected value is a rarity. One lottery that currently does have a positve expected value is the Mass Millions with a jackpot of $48.5 million. With very low sales, one can reasonably expect to not have to share the jackpot if won. If I lived there, I would only buy tickets for this lottery to the exclusion of all other lotteries until the jackpot is won.

Good luck,
Jake

And you'd be smart to do it.

Quote: Originally posted by Jake649 on February 18, 2004

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The highest expected value for the Lotto 649 lottery occured on the Sept 30, 2000 draw. The expected value was 79%. The jackpot was $15 million and the sales were 28,649,988 tickets. The expected value is usually around 70% when the jackpot is $10 million

The highest expected value for the Super 7 lottery occured just recently on Jan 30, 2004. The expected value was 70%. The jackpot was $30 million and the sales were 33,834,020 tickets.

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Thanks for the replies.  For the 6/49 Sept. 30 draw, the prizes given out totaled $23,839,799.3, so with sales of $28,649.987, the actual return was 83%.

For Lotto Super 7, you get 3 plays for $2 so there were actually 101,522,391 "tickets" in play for January 30.  If we value the free plays as $2, the actual return for the $25 million bonus draw on January 23 was 84.6% ($46,517,297.30 / $54,964,354).  For Jan. 30, the potential return was 83% had the $30 million bonus jackpot been won ($56,317,199.5 / $67,681,594).

LottoBuddy,

I am using the term expected value. It is not calculated by simply dividing the amount of money paid out by the number of tickets sold. The reason is that the money paid out is based upon someone winning the jackpot, this is not a given. Expected value calculations does not depend upon the jackpot being won, only the probability that it is won and by how many tickets. In performing expected value calculations, you need to calculate the probability of no jackpot winner, 1 winner, 2 winners, etc. These are the calculations that prob987 has been posting.

I am sticking with my previous calculations.

Good luck,
Jake

I have reviewed lottobuddy's paper posted earlier.  As I surmised in my conversation with Jake, the issue comes down to taxation.  An expectation values you may have seen from me or will see from me do not include taxes.

Are you calculating for the government?I am surprised you guys are so fond of it..so whats the point?