I would very much like to see an even faster "turbo" option because even though the current max speed of 1,000 tickets a second really drives home the point of how long it would take to actually win, I still want to see the simulation hit the jackpot a few times.

Reading people’s replies it seems like many are misunderstanding the expected value of a ticket. You may want to add another column to the table of odds showing what percentage a ticket’s hypothetical payout is from each prize, or just what the average loss per ticket is.

Also, at one point I messed up which pattern on Mega Millions tickets were winners. Something about that big X in a separate column just subconsciously seemed like it was showing winners. Perhaps dashes vs checks or groupings winning and non winning tickets together.

I noticed that when you select pick random numbers, it only picks it once. Can we run the simulation where it picks new numbers every time? I would love to see if that would make an impact on the odds.

Can you track how many people have hit the jackpot? Or how long folks stuck around to see if they hit the jackpot?

Really good tool, I made a very basic text one and showed a few friends and it put them off the lottery.

One suggestion I would make is allowing the random numbers selected by the user to be random for each draw. I understand in the scheme of things that it doesn't make difference to your odds but that's a strategy that some people play.

It would also be cool to track how many other people chose the same numbers that you did and then divide the jackpot winnings by that amount of people.

Another thing (I'm really just giving you a todo list of things that I had) was to organise the number selectors to mirror the pattern on the lottery tickets. People have very different approaches, picking columns, going over 31, sequences and you could track the user behaviour behind number selection.

Select random numbers greater than 31, and run them against past winning numbers, using the actual prize pool payouts (histories available for all major lotteries). Repeat millions of times. You'll be amazed how much more money you win. ;-P (And how much money you still lose even with this impressive advantage).Unfortunately, there aren't enough historical draws to determine whether there are more fine-grained statistically-significant differences. My tests were actually run on first-half vs. last half. But > 31 seems like a defensible rule as well.

What probability distribution are you using for the random numbers?

I expected the "Winnings:" mouse-over on the frequency chart to tell me the total amount won on that $ category (count*single winning). On MS Edge it just shows "Count: 4033\nWinnings: $2"

It might just be me, but it took me awhile to even realize there were interactive components on the page. Something about it made it seem like they were screenshots.

I never use Lotteries, but I was curious and wanted to test a domestic one, however the bonus number can be from 1 to 5, but I cant put it lower than 10 on your page :'(

Custom option needs more options: some big lotteries use two extra numbers (e.g. Euromillions). Other lotteries just pick up a single number from 00000 to 99999 (or even lower).

The site's newsletter module is broken. Won't accept my email.

wow, it's really good and the rest of your site is even better

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> funnily enough the time when the chance of winning is actually lowest

Not really?

The odds of winning are the same regardless, because you need to match every number to get a jackpot. Really, there is just an increased chance of splitting a jackpot with another person when the prize gets really large, since more tickets are generally sold. But I imagine EV of a lottery ticket with a $1B jackpot is still higher than the same lottery ticket when the jackpot is $100M.

And now we also have the long-term effects of online sports betting to look forward to.

Because you shouldn't use the simulator to calculate the EV, or said differently your n=1000000 is too small.

Assuming you used the first lottery example (Mega Millions), the EV is easy to calculate directly and is -$0.66/ticket, ie -33%

The jackpot is a whole $1 of that EV! Without it, the EV is -$1.75/ticket, ie -87%, which is closer to what you got in the simulation.

>On that train of thought, what prevents a new lottery from coming in and offering a _generous_ -50% lottery, offering ~5x as much money as before?

federal-level gambling syndicate isn't something that a private party can easily jump into.

so the answer is : a mix of 'grandfather'd-in' and protectionism, if we're talking U.S. here.

> What accounts for this payout discrepancy

Mega lotteries draw once every 2-8 days. Slot machines / video poker / etc are happy to draw as fast as you can push the button. They are designed to take your money, but their rewards systems are completely different.

Also, the mega lotteries benefit from viral marketing, “earned media”, and water cooler talk. Slot machines are just a way for bored people to pass the time, much like video games or doomscrolling.

In the US at least they're a state monopoly

Because a lot of the proceeds go to school districts.

You obviously haven't played enough. You stopped right before you hit it big!

You were due for a big win.

You forgot the /s.

On the other hand, if I don't buy a lottery ticket, I have no chance to waste my money on the lottery, but if I do buy a ticket, the odds of wasting money are infinitely higher.

Estimated monetary value might be a wiser metric to use :)

Going by the calculator, EMV of going from buying 0 tickets to 1 is -$1.85 for Mega Millions, same as going from n to n+1; n >= 0. The first ticket is the first one you lose with, statistically.

That's kind of how I look at it, in practice. I get the mathematical reality that buying lotto tickets is a financial waste. However, if I never buy a single ticket, there is a definite 0% chance I'll ever win the big prize. Whereas if I play at all, at least there's a chance, however remote, of a quite life-changing positive event happening. So, therefore, it makes sense to put a very small amount of totally throw-away income into big-prize lotto tickets, just so you're in the game at all.

Based on this kind of thinking, my personal rules are: never spend more than 0.1% of take-home pay per time-period buying tickets, and only buy big-prize lotto tickets that have potentially-life-changing payouts.

In the real world, there's a non-zero chance that someone purchased a ticket on your behalf without you knowing, so you're never quite at 0

Your chances were 0, you buy a ticket, and now your chances are x. Where x is not infinitely greater than 0, it's x greater than 0. Pretty sure your proposition implies that 2 tickets provide the same odds as one ticket (2 infinity vs 1 infinity).

I haven't gotten into the discrete math in many years. If you're right do you mind explaining please? I can intuit what you're getting at. 0 odds * inf < (odds with one ticket). Is that a decent description?

This is nonsense if it's meant to be interpreted as anything but a joke, or as a way to maximize your own personal fun.

If you send me $20k of bitcoin and a UUID, I will run 'crypto.randomUUID()', and if I get the same UUID as you I'll send back $40k.

If you don't send me any money, you have 0% chance of winning, but if you do send me $20k, you have a mere 1 in 2^122 chance of winning, an infinite increase in your chance of winning, so surely it is rational to do so.

If you truly believe what you just wrote, I'll await my $20k.

I like that logic

But does that mean you only buy 1 lottery ever in life or one each lottery?

I think the saying goes buying a lottery ticket only marginally increases your chance of winning.

To believe that you take a chance and you suddenly get the prize, despite statistics, is to believe that you're special. Maybe some people try such things to return the warm feeling of the early pre-school years.

Interesting. You got it at 11.6M tickets... I got it at 10,847,948.

https://archive.is/G5Ctz

I could never do that. Imagine the devastation of getting all of them right.

So, for Mega Millions:

For 1-70: Consider numbers above 31 (days of month)

For 1-25: Similarly, numbers above 12 might be less common (months of year)

What other numbers above 31 would you want to avoid? 33, 44, 50, 69, 70? And you might want to avoid sequences as well.

There was a Romanian economist who was able to exploit several lotteries around the world. He essentially bought every combination to lotteries where the payout was higher than the cost. Logistical nightmare.

https://thehustle.co/the-man-who-won-the-lottery-14-times

Unless you're buying a meaningful fraction of tickets, the EV/ticket will be similar to uncorrelated tickets.

If you're buying all the tickets, well, the math is real easy. (and occasionally profitable, see 1992 in Virginia)

Yes I was interested to see how different the simulation would be.

No need to simulate. It is generally straightforward to compute the odds directly from the rules.

Australia's Saturday Lotto is one of the better ones I believe (1 in 6,000,000 or so I think).