Two lottery enthusiasts suing Loto-Québec

Here is an article someone sent to me: Two lottery enthusiasts suing Loto-Québec. Here is the executive summary:

1. The Quebec lottery has an "extra" game. The player must pick 6 digits from 0 to 9, and order matters. Players can either right to left or left to right.
2. As with most lottery games, there is a "quick pick" option.
3. If player elects a quick pick the first and last digits are not randomized. I don't know exactly how it is done, but if the player buys 10 quick picks, he will get each digit 0 to 9 as the first pick, as well as the last pick. I believe the middle four digits are chosen randomly
4. This semi-random method of choosing quick picks results in the same expected value, but less volatility for purchases of 10.
5. A player noticed said pattern on his ticket and sued the lottery for $20,040,000 because he wanted volatility.
6. Lottery is fighting the lawsuit.

What do you think should happen?

Lottery makes the rules, you either play by their rules or don't play. It's a Hobson's choice but a choice none the less.

Was it deceptive to say that Quick means Fully Randomized? Did they ever say that?

I think they have a legitimate gripe. The way they assigned the numbers completely takes them away from 'gambling' for the smallest and most common prize. They are guaranteed it on one ticket, and don't have a chance on the others. The expectation is different: Any other lottery obviously allows you to win multiple small prizes with multiple tickets.

With that being said, is it worth 20 million? No. It's not even worth $200. It has a very small effect and there was no hardship endured by the players. But the case will probably focus on the somewhat non-randomness of the game, no matter how benign, and whether that is worth punitive damages.

I hope these guys don't cash in on this. But I imagine they may get a small settlement, and if it makes the lottery change their way that is okay by me.

Quote: pocketaces

I think they have a legitimate gripe. The way they assigned the numbers completely takes them away from 'gambling' for the smallest and most common prize. They are guaranteed it on one ticket, and don't have a chance on the others. The expectation is different: Any other lottery obviously allows you to win multiple small prizes with multiple tickets.

With that being said, is it worth 20 million? No. It's not even worth $200. It has a very small effect and there was no hardship endured by the players. But the case will probably focus on the somewhat non-randomness of the game, no matter how benign, and whether that is worth punitive damages.

I hope these guys don't cash in on this. But I imagine they may get a small settlement, and if it makes the lottery change their way that is okay by me.

I was thinking about this a bit more, and think it may be more of an issue than I thought. By raising the odds of a single small prize to be won, the lottery is benefiting from the practice where small prizes almost always turn in to re-purchased lottery tickets, rather than paying out in cash. This could be seen as a profit-raising practice at the expense of randomness.

I'm confused. The article indicates that doing this, with 10 extra quick picks, guarantees a $2 win. Does that mean exactly $2, or a minimum of $2?

If it's a minimum, what's the big deal?

And the other thing is, does the lottery declare in the rules, brochures or whatever, the method in which those extra quick picks are chosen? I gotta think that somewhere the method is disclosed. They simply assumed, and are suing over an incorrect assumption.

Sounds as though it should be the beginning of a joke:

Two lottery enthusiast sue the Quebec Lottery.
"We want our money," Jacques, the first lottery fan says. "We demand satisfaction!"
....

And so on.

Quote: pocketaces

I hope these guys don't cash in on this. But I imagine they may get a small settlement, and if it makes the lottery change their way that is okay by me.

I cannot concieve of the lottery offering any small settlement, as that would open the floodgates. If you are going to POSSIBLY be unhappy with any sequence of numbers assigned, then choose your own numbers. Duhhhhh...

Quote: SOOPOO

I cannot concieve of the lottery offering any small settlement, as that would open the floodgates. If you are going to POSSIBLY be unhappy with any sequence of numbers assigned, then choose your own numbers. Duhhhhh...

Yep this could be avoided by picking your own numbers. I initially thought this game was played like the Ontario version, which is quick pick only, but quebec does allow you to dictate your own digits. I do imagine that the vast majority are quick picks, as assigning random digits is not as interesting as lotto numbers which can mimic birthdays and such.

Perhaps more importantly, the lottery cannot be purchased without also purchasing a ticket to another game, all of which are at least $1. This means they cannot simply split the combinations in to 10 seperate tickets, or they would have to pay much more. This add-on feature also has the effect of making quick pick even more attractive, as it is a simple "yes" to the clerk on the upsell or check of the box on the selection slip.

Good point on the settlement, but lotteries have found ways to settle with whistleblower-types for a secret amount before and not pay out anything else. This happened in Ontario. These guys seem to want a hell of a lot more though. That's what makes me hope the lottery wins.

Quote: DJTeddyBear

I'm confused. The article indicates that doing this, with 10 extra quick picks, guarantees a $2 win. Does that mean exactly $2, or a minimum of $2?

If it's a minimum, what's the big deal?

In this case, unless the player wins a larger prize in a different category, they would be assured exactly one $2 win. No more, no less. In essence, they give you every combination and then take their cut, leaving you with a guaranteed loss. This process wouldn't be considered gambling, and would be like the wizard's example of a net loss of $500 above, or betting on every number in roulette. This is a troubling aspect. However it doesn't cost the player any EV at all, only volatility.

Quote: pocketaces

In this case, unless the player wins a larger prize in a different category, they would be assured exactly one $2 win. No more, no less. In essence, they give you every combination and then take their cut, leaving you with a guaranteed loss. This process wouldn't be considered gambling, and would be like the wizard's example of a net loss of $500 above, or betting on every number in roulette. This is a troubling aspect. However it doesn't cost the player any EV at all, only volatility.

That's messed up.

But, if that's the way it is, and properly publicized as such, then the Lottery should win.

Quote: SOOPOO

If you are going to POSSIBLY be unhappy with any sequence of numbers assigned, then choose your own numbers. Duhhhhh...

I just checked, and I was correct initially before I edited my post. Quick pick is in fact the only option. The only bit of control you have is that you can choose to replay the same previous quick pick number when redeeming a ticket.

DJ, the main write-up on the website for this game refers to the game as "computer-generated", but does not use the term "random". The wording may be the key to the case.

I'm not sure how things work in Canada, but if it were the US, all lottery players would receive 1 free quick pick ticket, and the lawyers would get 20 million for their work.

Two unemployed guys, suing for eight digits... can't.... pre.... judge... must... stick to case facts.... expected value variance definition of randomness... CANT DO IT ITS TOO PAINFUL BWAAAAH

Quote: FinsRule

I'm not sure how things work in Canada, but if it were the US, all lottery players would receive 1 free quick pick ticket, and the lawyers would get 20 million for their work.

If the players were lucky. Another possibility is that the lottery would promise to change its system, but no players would get anything; however, the lawyers would still get their 20 million.

As for the original problem, if the players want volatility, why don't they just play 10 separate one-ticket slips? It seems to me that the desired volatility exists, if the players want it, so they don't have much of a case.

The prize structure for Lotto Quebec on the Quickpick is such that the last matching number wins $2, so yes, a $2 winner guaranteed on the ticket if 10 quickpicks are taken.

Prize structure is:

Complete number: $1,000,000
Last 6 digits: $25K
First / Last 5 digits: $500
First / Last 4 digits: $50
First / Last 3 digits: $20
First / Last 2 digits: $5
Last digit; $2
First 6 digits: $10,000

You can play up to 10 on one ticket. You cannot pick the number drawn, but you can replay the same extra numbers with a repeat drawing.

Payout is 45.55% according to the lottery site with odds of winning 1 and 9.1

I'm trying to figure out why they're suing for a nubmer that's 20x the grand prize.

I think that complainants have a case. Nowhere is it stated that the extra numbers are non-random. I think rather than paying out $20M that they simply mail out a free extra coupon to all Quebec residents and make the generator random. Given that the 1st and last digits are not repeated, the complainents are correct that they can only win on two of the 10 tickets, and to me, that doesn't seem right.

Here are some statistics on the game:

Expected return: 0.447400
Total standard deviation with 10 individually purchased Extras: 1002.845
Total standard deviation the way Lotto Quebec does ten tickets purchased at once: 1002.833

So, the way Lotto Quebec does it, the standard deviation is 0.0011% less only. Why?, you might ask.

The reason is 99.4% of the variance is in the form of the jackpot. Whether the player has 10 shots at 1 in 10,000,000 or a 10% chance at 1 in 1,000,000 it doesn't matter much in terms of variance. The way Lotto Quebec does it, the player can't win the jackpot twice, but those odds were 1 in 2,222,224,000,001 with 10 independent tickets, so eliminating that possibility has little effect.

Quote: ThatDonGuy

As for the original problem, if the players want volatility, why don't they just play 10 separate one-ticket slips? It seems to me that the desired volatility exists, if the players want it, so they don't have much of a case.

They can't. This is an add-on only game, so they would have to also buy 9 more standard lotto tickets, costing them almost double.