[HN Gopher] Lottery Simulator (2023)
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Lottery Simulator (2023)
Author : airstrike
Score : 193 points
Date : 2024-09-10 21:09 UTC (1 days ago)
(HTM) web link (perthirtysix.com)
(TXT) w3m dump (perthirtysix.com)
| airstrike wrote:
| Now I just need to scrape the data on all major lotteries
| worldwide, plop them all into the simulator, make some
| assumptions about exchange rates and figure out where in the
| world I should bet on the lottery to get the best payout!
| ISL wrote:
| No need to simulate. It is generally straightforward to compute
| the odds directly from the rules.
| airstrike wrote:
| For sure, but not as fun to watch!
| jamesfinlayson wrote:
| Australia's Saturday Lotto is one of the better ones I believe
| (1 in 6,000,000 or so I think).
| itake wrote:
| the expected value of each ticket is negative, but going from 0
| tickets to 1 ticket, increases your chances of a big win by
| infinity.
|
| Going from 1 to n tickets, isn't necessarily wise
| caseyy wrote:
| 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.
| BizarroLand wrote:
| I think the saying goes buying a lottery ticket only marginally
| increases your chance of winning.
| BigParm wrote:
| 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?
| web007 wrote:
| Odds for N tickets as odd(N):
|
| odd(0) = 0
|
| odd(1) = X, so odd(1) / odd(0) = +Inf increase in odds of
| winning vs 0
|
| odd(2) = 2X, so odd(2) / odd(1) = 2x increase in odds of
| winning vs 1
| ff317 wrote:
| 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.
| seagullriffic wrote:
| This is almost exactly how I think about it too - a good
| repeatable mental model is "infinite upside / near-zero
| downside".
|
| These massively asymmetric choices occur elsewhere in life,
| e.g. "asking them out on a date"; "asking for a raise", and
| are good to look out for.
| cwillu wrote:
| Dunno, seems wild to compare positive-but-still-unlikely ev
| things with straight up negative ev things like gambling.
| avidiax wrote:
| There's a near-zero possibility that the next potato chip in
| the bag has been laced with cyanide. But if you never eat any
| potato chips, there's a definite 0% chance that you'll die of
| cyanide-laced potato chips.
|
| This kind of thinking never holds up when it's a small chance
| of a horrible outcome.
| ryanjshaw wrote:
| How many potato chip killers have there been?
|
| How many lottery winners?
| krisoft wrote:
| > However, if I never buy a single ticket, there is a
| definite 0% chance I'll ever win the big prize.
|
| I'm not sure about that. There is some chance of someone
| random buying a ticket and gifting it to you and then that
| ticket winning. Not a big chance. But it is not 0.
| petesergeant wrote:
| 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
| GrantMoyer wrote:
| 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.
| nine_k wrote:
| 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.
| TheDong wrote:
| 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.
| ldbooth wrote:
| Very cool visualization. This will save me a few bucks next time
| I think about playing.
| Aeolun wrote:
| I think this lottery simulator is a scam. I played a hundred
| thousand games and never made my money back.
| madamelic wrote:
| You obviously haven't played enough. You stopped right before
| you hit it big!
| frogpelt wrote:
| You were due for a big win.
| phs318u wrote:
| You forgot the /s.
| zzanz wrote:
| I used to work at a lotto counter in my towns supermarket. When I
| started I noticed alot of older regular buyers, a weekly lotto
| purchase like the daily newspaper. However, as the younger
| generation started bringing in kids I didn't see this habit,
| instead just an occasional purchase for a birthday gift or
| rolling the dice because the jackpots gotten big enough (funnily
| enough the time when the chance of winning is actually lowest).
|
| Overall I would consider lotto small next to the scratch cards
| (our countries version at least). I have never seen a more
| predatory marketing strategy, and completely swept under the rug
| next to lotto being berated with anti-gambling campaigning. To be
| fair, lotto is bad, but scratch cards are much, much worse.
|
| A memory that stuck for me was a customer blowing well over $100
| bucks on scratchcards over 20 minutes, just pulling over and
| over, then getting card declined at the grocery checkouts.
| IncreasePosts wrote:
| > 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.
| function_seven wrote:
| There's a balance between jackpot size and a given drawing's
| popularity for sure.
|
| There are also bad number choices and good number choices.
| 1,2,3,4,5,6 is a _terrible_ selection, for example. Not
| because it is somehow "less random", but because you're
| guaranteed to be splitting that jackpot with a 1,000 other
| nerds who were trying to prove a point!
|
| To a lesser degree, choosing numbers under 31, or under 12,
| will put you in a collision space with other players who like
| to choose birthdays.
|
| Just use the random pick and don't think about it. If you do
| win the jackpot, you have higher odds of being the only one.
| RulerOf wrote:
| > 1,2,3,4,5,6 is a terrible selection, for example. Not
| because it is somehow "less random", but because you're
| guaranteed to be splitting that jackpot with a 1,000 other
| nerds who were trying to prove a point!
|
| Uh... so at first I saw your point, but if your odds of
| winning never actually change, how is not winning better
| than splitting a jackpot?
| function_seven wrote:
| I guess if you only play one drawing, you're right.
| Winning is always better than losing.
|
| But if you play the lottery week after week, year after
| year--and you always play the same numbers--then you're
| ensuring a mediocre prize should you actually get the
| jackpot.
|
| Playing the lottery is not a mathematically sound
| decision in any case, but there's no reason to make it
| even worse by chopping your potential jackpot winnings
| down by over 99%
| bongodongobob wrote:
| The odds of winning don't change, the odds of splitting
| the pot change. Certain numbers are picked more than
| others so to have the best odds of not splitting the pot,
| random numbers are best.
| rerdavies wrote:
| Numbers greater that 31 are better. Almost 30% better!
| Because you are less likely to split a pot when you win.
| But not good enough to make playing a lottery ticket a
| winning propostition.
| jamie_ca wrote:
| Maybe, "the time when expected value is the lowest"?
|
| The BC 6/49 lottery (6 balls 1-49, one bonus ball) for
| example has 53% of the common "prize pool" split amongst all
| 4-ball matchers, so if you're not hitting the jackpot you get
| less cash out of a high-demand drawing.
|
| And given the prize pool is something like 18% of net
| receipts... yeah EV is still well in the negatives.
| euroderf wrote:
| > > funnily enough the time when the chance of winning is
| actually lowest
|
| > Not really?
|
| A big jackpot draws more players, and that reduces the
| payouts at the intermediate levels.
| krisoft wrote:
| > that reduces the payouts at the intermediate levels
|
| Which has nothing to do with your chance of winning.
| euroderf wrote:
| But has something to do with the expected winning making
| it worth the investment.
| gosub100 wrote:
| What do you mean by intermediate levels? In the 2 main US
| lotteries the only award that gets split is the single
| jackpot. Even the 2nd place award is $1 million and is not
| divided among multiple winners.
| moduspol wrote:
| And now we also have the long-term effects of online sports
| betting to look forward to.
| eig wrote:
| Cool visualization!
|
| It would've been nice to not assume only one lottery winner.
| People tend to pick numbers that are meaningful for them:
| birthdays, favorite numbers, lucky numbers. Thus it actually
| significantly increases your EV if you pick unusual numbers,
| which is not reflected here.
| hammock wrote:
| 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.
| shriracha wrote:
| Hi! I made this tool. I saw it had way more traffic than usual
| and then realized it was from HN, very cool!
|
| Would love to hear any feedback. I've been super interested in
| how well-designed web apps and visualizations can communicate
| things like probability, which I think is very hard to intuit for
| many of us.
|
| The most surprising thing I learned from the tool was just how
| bad your payouts usually were even if you cut the pool of numbers
| to pick from in half (by using the "Custom" option).
| is_true wrote:
| wow, it's really good and the rest of your site is even better
| BitwiseFool wrote:
| 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.
| Vullun wrote:
| 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.
| sfilmeyer wrote:
| >I would love to see if that would make an impact on the
| odds.
|
| It won't make an impact on the odds of your tickets coming up
| as winners, unless they have a bug in their simulation. In
| the real world the probability of single versus multiple
| jackpot winners might vary with number choices, but they've
| already said they're assuming a single jackpot winner.
| earle_wa wrote:
| Can you track how many people have hit the jackpot? Or how long
| folks stuck around to see if they hit the jackpot?
| Retric wrote:
| 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.
| airstrike wrote:
| I did the same when I tried to create my own lottery. Thought
| the "correct" icons were the "wrong guess" ones and vice-
| versa
| tirant wrote:
| 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).
| SillyUsername wrote:
| What probability distribution are you using for the random
| numbers?
| Popeyes wrote:
| 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.
| hakonslie wrote:
| 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 :'(
| rerdavies wrote:
| 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.
| athorax wrote:
| 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.
| fragmede wrote:
| On the subject of winning the lottery, the story that goes untold
| is of the MIT crew that gamed Massachusetts' Cash Windfall circa
| 2007.
|
| https://www.theatlantic.com/business/archive/2016/02/how-mit...
|
| There's a movie out starring Walter White, of the Selbees side,
| called Jerry and Marge Go Large, but which talks about the story,
| but portrays the MIT kids poorly for dramatic effect.
| fsckboy wrote:
| https://archive.is/G5Ctz
| islewis wrote:
| Can someone explain to me how the EV can be so incredibly low? I
| know the answer is because people will buy the tickets no matter
| what, but even compared to other losing games the lottery comes
| away looking like an absolute bandit.
|
| A run on the simulation (n=1000000) comes back with -92% EV. It
| looks like -10% [1] is a rough estimate for slot machine EV,
| which I would ballpark into the same game genre (-EV, no skill
| entertainment) as the lottery.
|
| What accounts for this payout discrepancy in what I would
| consider similar games? 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?
|
| [1]* https://www.888casino.com/blog/expected-value
| elseweather wrote:
| In the US at least they're a state monopoly
| serf wrote:
| >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.
| cataflam wrote:
| 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.
| thephyber wrote:
| Exactly.
|
| In short, the simulator doesn't buy enough ticket-draws to
| approach the Law of Large Numbers.
|
| But that's also a feature of the lottery -- most people
| overestimate their ability to win or underestimate how many
| lifetimes of consistent play is required to statistically win
| a jackpot.
| onion2k wrote:
| I don't think people actually make that mistake. They know
| the chance of winning is tiny. The point is more that a
| non-zero chance of life changing money (plus the
| entertainment of fantasising about a win) is worth more to
| them than the cost of the ticket.
| gamepsys wrote:
| Exactly, winning the lottery is massively life changing.
| This is actually something I think people don't
| understand about the psychology of lottery. In some
| regards it doesn't matter if the money is $50M or $500M
| for most players even though that has a huge impact on
| the EV.
| thephyber wrote:
| > 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.
| gosub100 wrote:
| Because a lot of the proceeds go to school districts.
| hellojesus wrote:
| Does this have any way of simulating multiple plays per draw? I'm
| curious what happens to EV when you buy X tickets per draw
| instead of just 1. And for both circumstances: (a) ensure all X
| tickets are unique and (b) random entries with replacement.
| ISL wrote:
| 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)
| russellbeattie wrote:
| Humans are so weird... No matter how simple you make a slot
| machine, for some reason it's still compelling to play.
|
| On one of my runs, I won $1 million which put my numbers in the
| green for a while before slowly going into the red again.
|
| That's going to legitimately brighten the rest of my day.
| tomthe wrote:
| HN user ggerganov made a similar tool with real historical
| numbers from Bulgaria:
|
| https://lottery-check.ggerganov.com/
| rootusrootus wrote:
| I got lucky. Won a million bucks early in the simulation and it
| took a while before the EV was negative again. Should have
| stopped right after winning a million, duh.
| hidelooktropic wrote:
| Looks a lot like https://www.adamgrant.info/heres-1m-dollars-try-
| to-win-the-l...
| kristopolous wrote:
| For years whenever I see lottery numbers announced I first scrawl
| some guesses on a piece of paper, trying to summon all divine
| power I can muster.
|
| I think I once guessed 2 of them . This way I get all the thrill
| of the game with none of the cost.
| KeplerBoy wrote:
| I could never do that. Imagine the devastation of getting all
| of them right.
| hitthejackpot wrote:
| Won the mega millions after about 1.1 million tickets. EV per
| ticket is now >$200. I think I'm taking the wrong lesson from
| this - time to get gamblin'
|
| Screenshot: https://ibb.co/6mm3hqh
| efalcao wrote:
| Hit a million dollar ticket! BRB going to buy lottery tickets!
| jackcheng1126 wrote:
| The tool has a maximum speed of 1000 tickets per second, which
| may not be fast enough for some users. Hopefully the author will
| consider adding a 'turbo' option to make the simulation faster so
| we can get more results in less time.
| dostick wrote:
| What would be super interesting is to collect all different
| lotteries from different countries and regions, and run
| simulations to find which ones are most lucrative. And you can't
| treat know how good is your local lottery in comparison.
| camjohnson26 wrote:
| There was a Romanian economist who was able to exploit several
| lotteries around the world. He essentially bought every
| combination to lotteries where the payout was higher than the
| cost. Logistical nightmare.
|
| https://thehustle.co/the-man-who-won-the-lottery-14-times
| foragerdev wrote:
| So, you will lose 1.84$ on each ticket you buy.
| mensetmanusman wrote:
| Can we add quantum suicide to this simulation?
|
| This is where you entangle your mortal soul to the lottery
| outcome and are only allowed to survive if you win.
|
| This is a cheat code for the parallel universe crowd.
| PaywallBuster wrote:
| Earnings $311,509,052 over 16,680,000 tickets
|
| Average: $18.68 per ticket
| baggachipz wrote:
| I'm the smarmy prick who, when somebody says they bought a
| lottery ticket, I say "Give me the same amount you paid for that
| lottery ticket, and if you win I'll double your winnings."
|
| Them: "there's no way you could afford to pay me!"
|
| Me: "I won't have to."
| gosub100 wrote:
| Not sure if anyone linked it here, but my favorite simulator was
| a 2D grid, with about 50 or so units per side. The computer picks
| 3 squares, you pick 3 squares. The XxY unit grid was set up such
| that if you picked the same 3 squares as the computer, it was the
| same odds as winning Powerball. Seeing how hard it was to even
| get 1 square really drove home the odds. I also did a similar
| calculation by estimating the area of millions of quarters
| (enough to represent the 1/N chance to win) and thought "ok, if I
| launched a rubber ball randomly at high velocity in this huge
| room, I would win if it landed on one exact quarter that I picked
| in advance. When I saw it like that, I realized there's no way.
| navark wrote:
| I won! That's it, the lottery is worth playing if only I can
| repeat this performance IRL.
|
| I won the $340,000,000 Powerball Grand Prize after buying
| 11,651,310 $2 tickets leaving me with a grand total of
| $319,781,766 in earnings ($27.45 per ticket).
| FireBeyond wrote:
| Interesting. You got it at 11.6M tickets... I got it at
| 10,847,948.
| thefoyer wrote:
| This is exactly why I don't play the lottery
| Idiot211 wrote:
| Any chance of multiple bonus numbers like the Euromillions
| offers?
| touristtam wrote:
| Yes I was interested to see how different the simulation would
| be.
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(page generated 2024-09-11 23:02 UTC)