By the way, Here in Texas we had a fluke where because of a disaster of the flight 800 the people chose 800 in Pick 3 lottery. That number came up and it broke the lottery. They don’t have enough money to pay it out.
In that case, the winning combination got a set amount regardless of the pool. It’s a different situation.
I submit that you like to feel superior for some reason. Almost everyone gets the lottery at some level even though they couldn’t calculate the exact odds. A few waste too much money on it but most like the tiny chance of a life changing event. I only play when there’s a pool at work and I get five dollars worth of fun being part of the group and joking around with everyone. Thinking that roulette is a better option is absurdly missing the point.
I play only a dollar a game on Texas Two Step. I buy my tickets $10 at a time for ten drawings. As it happens I won $20 on the first drawing. I have 3 drawings left on this ticket.
I understand people wanting to dream about “a tiny chance of a life changing event”, as you put it. But some strategies are better/worse than others. And some games are worse than others. Anyone who takes a serious look at the facts would see that the lottery (as it is run in America) is one of the worst ways to gamble.
- Many casinos brag about 97% or 98% payouts. The lottery pays out 40%.
- In America, state-run lotteries routinely misrepresents the size of the prize, in three ways.
a. They are “estimating” a prize whose value is in flux, and the final result is almost always lower than the estimate.
b. They are actually offering an annuity but they don’t state the Present Value of the annuity, they state the Future Value. For example, when they say the pot is 25 million, they are actually offering you an annuity which has a cash value of about 15 million.
c. The rules provide for splitting the prize with all the other “winners”.
OTOH, when you go to a roulette wheel in a casino and bet $100 on 22, you know in advance that you will win exactly $3,500 (plus you get to keep your original $100) if it lands on 22. That’s not an estimate based on how many tickets they think they will sell. They actually give you $3,500 cash right now, not $175 a year for the next 20 years. And if someone else also bet on 22, you don’t have to share your prize with that other person.
If a casino in Las Vegas ran their gaming tables the way the government runs the lottery, they’d be shut down by the Nevada Gaming Commission in a heartbeat.
Don’t get me started on the fact that the USA taxes lottery winnings (other countries don’t), or the fact that most lottery winners end up more miserable after winning the lottery than they were before, or why it’s illogical to apply Pascal’s formulas for Expected Value without taking into account the limited utility of huge sums of money. Just compare the lottery to other forms of gambling. You’d have to search far and wide to find a worse game.
I propose a game. You could win $14. You give me $1 to play the game. I roll a pair of dice. If it comes up double sixes, you win! (your chance is 1/36). Actually you don’t win $14, you win $12. And you have to split it with all the other people who won today. So you get $6. And it’s not really $6 either, you just get a coupon which says I promise to pay you 30 cents per year for the next 20 years. If you don’t want the coupon, I’ll give you the cash value of the coupon, which is $4.73, and then I’m gonna take taxes out of that. And oh by the way you don’t get your $1 back either. Wanna play?
I don’t need a lecture on probability. I have a masters degree in engineering and I do complicated statistical analysis every day in my career. You are still missing the point. Any casino gambling, with the possible exception of poker, is idiotic. Almost no one who buys lottery tickets is doing it as a gambling strategy. It is a different animal than casino games. My guess is that the average casino gambler in Vegas loses more in a day than the average lottery player does in a year.
Your chances of winning are the same for any combination. Your expected winnings drop if that combination is played by many people.
Don’t know where you’re getting that from. I have said absolutely nothing about the probability of winning the lottery.
Props for having an advanced degree. I’m not sure why you’re bringing that up. Is it because I said people who play the lottery can’t recognize a good strategy from a bad one? I guess that sounded insulting and you took it personally. I apologize. I take it back.
I was trying to say that the lottery goes to great lengths to disguise just how unfair the game is, and it’s really really hard to look past the hype, even for people who are very smart and/or know a lot about math. It has been said that the lottery is a tax on people who are bad at math. I think this is absolutely untrue because it implies that people who are good at math are immune to the lottery’s trickery. And that’s not the case.
And I certainly admit that people can know that the lottery is unfair but still enjoy it anyway because they have fun dreaming about being a millionaire. In that case, it’s not that they can’t recognize a bad strategy. They know it’s a bad strategy and they don’t care because they have other motives.
I’m curious as to why you think casino games are “idiotic” but you appear to be defending the lottery. Do you not agree that some games are more fair than others? By any definition of the word “fair” that I can think of, the lottery is much less fair than just about any other form of gambling.
Now, if you feel that casino gambling isn’t as much “fun” as the lottery, well, that’s an opinion. Go with what you enjoy.
Personally, I find digital slot machines to be no fun at all. But that’s just my opinion, and has nothing to do with whether the machines are fair or unfair.
Edit: I’m not actually promoting casino gambling. I was just using it as a point of comparison.
They are both idiotic and they are both fine if people get enough enjoyment out of it to be worth the cost. From a statistical point of view, roulette and black jack are better. From a dollar cost point of view (and amount of time wasted), lottery is better. As far as how they are marketed, both are evil.
Professional gamblers aside, people go to the casino to dress up, hang out, and play at the casino. The true value of something as intangible as entertainment is a fascinating question, but not one we can answer via simple combinatorics.
Long ago when I had a Commodore 64 I wrote a program that made a graphical representation of the winning numbers on the play slip. I made a database of the past winning numbers to date integrated in the program.
When I ran the program it ran through the winning numbers on the slip and showed it on the screen. I saw something interesting. A lot of randomness yes but it showed a pattern of migration. I used it to pick my numbers and I got a lot of 3 number hits and one 4 number hit.
Without it I didn’t do too well. I don’t know how to write one on my PC. The C64 was the coolest toy I ever had. 
note: the Texas Lotto (6 numbers 1-50)
In the long term, this won’t work too well.
In the short term, a truly random lottery would be expected to produce results like this purely by chance.
There’s a story I like about teaching combinatorics. A professor assigned a class a homework assignment to flip a coin 200 times and record the results. The following day, the professor examined the results one by one and put a mark on their pages or not. The professor asked, because the assignment ended up not being graded, who cheated and just wrote random results and who actually did the assignment as requested. The ones with marks on their pages all faked the results. How did the professor know? When you flip a coin 200 times, there is a high, bordering on certain, probability of seeing at least one run of 4-5 heads or tails in a row. But when people try to fake coin flips, they alternate heads and tails more often than realistic and avoid putting runs of the same result several times in a row.
We’re remarkably bad at producing truly random results and pretty good at seeing patterns, even when there is no underlying pattern. We’re good at seeing things like those runs of 4-5 and ascribing a pattern even when it’s to be expected from a set of truly random experiments.
This brings another interesting observation, the machines. How do they make the machines random? Do they load the balls in scrambled order or in numeric order? Are the machines random in opening the gates to let out the balls?
If the machines run the exact same every time and the balls loaded the same, would there be a bias?
Here in Texas we have the Lotto machine that drop the balls through the hole toward behind the machine and appear at the side. I can’t help but think that the machine could be rigged since the balls disappears for a moment.
At least for Lotto Texas, there is a check for randomness. Part of this involve having several different machines and different sets of balls.
There’s also the historical database of results which can be analyzed for draw bias. It’s certainly not impossible to rig a single game but a long term set of rigged games would be more difficult to produce because those types of statistical anomalies can be looked for.
To evaluate a gamble properly, you need to consider both the vigorish and the payoff. For example, an even-money bet with 2% vigorish consumes 3.96% total vigorish if you want to quadruple your money. (Your $1 is subject to 2% vigorish on the initial bet and, if you win, your $2 second bet will be subject to an additional 2% vigorish.) If your intent is to play at that 2% vigorish even-money table and keep doubling up until you’ve either lost your $1 or won $130,000 then the aggregate vigorish will be 29%.
This is not to say that lotteries are good gambles. But it’s not sound to compare their vigorish directly with that of a low-payoff game.
I was just pointing out that each number of the first 5 have to be unique; I didn’t feel like giving the whole explanation.
I don’t get why you brought up this stuff about vigorish at all. State lotteries do not do vigorish. The standard casino games (slots, roulette, blackjack) do not do vigorish. These aren’t bookies here.
Expected return is expected return. Casinos generally take a far smaller amount than state lotteries. If casinos are available to you and you like to gamble away money, then they are a Mathematically better option.
I’ve thought of “vigorish” as a generic term for the average percent of action which is not returned to gamblers. Perhaps I’ve been misusing the term.
Wikipedia at least agrees with your usage (for example, that the 0 and 00 in roulette are the vigorish). I’m not sure how you’d ever separate one type of house advantage from another, anyway. It all just gets rolled into the payout table.
In an hour of playing craps with some fixed amount of money on the pass line, you will bet a very large multiple of that amount, each bet of which is subject to the house edge, because you will routinely win a good number of your bets and instead of pocketing the bet and winnings, gamble them some more. While an individual bet at the pass line has around a 1.4% house edge IIRC, if you make 20 bets an hour at $5 per bet, you’re down $1.40 in an hour. If you play the 40% EV lottery for $5 once a week, you’re down $3 over a week, which is very roughly 50 cents a day or 2 cents an hour. Obviously no one plays craps continuously, but the rate at which you lose money is probably faster than playing small amounts at the lottery.
Craps can be a lot more entertaining in the moment, but you won’t get rich unless you own the casino, while you can get rich if you play the lottery, simply because in order to win enough at craps to win as much as you’d win from the jackpot of the lotto starting from the same bet, you’d be making a much larger number of bets than the lottery player, and each of those bets is subject to the house edge.
Maybe someone more inclined can run a simulation or even crunch the numbers directly on playing a 1.4% vig $1 coin flip vs. a 1:200 million chance to win $80 million or some such, and see how likely you are to reach $10 million.