Lottery Odds
 

I have a friend who plays the lottery. Each week he buys a ticket playing the exact same numbers he always has. He believes that doing so somehow improves his chances of winning because, to paraphrase, "odds are, the numbers will come up eventually!"

I disagree, and my contention is this: each lottery drawing is a separate, self-contained incident. Previous incidents have no bearing or effect on the current incident, and the current incident will have no relationship whatsoever to the next incident. So trying to locate a pattern by examining history is, in this case, a waste of time. In my mind, there is no pattern, and can be no pattern without removing the fundamental randomness of the lottery. My understanding of statistics is admittedly very very basic, but this seems like common sense to me.

Am I wrong? Are your odds improved by playing your (un)lucky numbers every week versus letting the machine pick new ones for you each week? Opinions? Facts?

You are correct, assuming sufficient randomness on the part of the lotto. Which is probably a decent assumption.

If certain numbers come up, they are not then retired until all other combinations have been used.

On the other hand, psychologically, if you play the same numbers for years, then try something new, and that's the day your numbers come up, you'd feel much worse than if you just continue to lose with the same numbers.

He's suffering from a well known logical fallacy, if I could remember the name I'd find the wikipedia page on it. Gambler's something.

In fact with lotto, buying a ticket does not statistically increase your chances of winning it's so minor.

Each drawing is independent - there is no carryover. Think of it this way - if the assumption were true, then every number not drawn became more likely not just your buddy's. It is easy to see that all combinations (all possible outcomes) less one can't become equally more likely. Odds are a zero sum game - they must total 100%.

The source of the fallacy comes from the following scenario. The odds of flipping a coin to heads ten straight times is very low - odds are that it will not happen. Now, if you flip nine straight heads, there is a temptation to think that the odds of yet another head are less than 50% (a carryover from the previous nine flips) when, in fact, it is exactly 50% (provided the coin is not biased, etc.).

Your friend's odds of winning are the same regardless of whether he sticks to the favorite numbers or chooses new numbers each time. But, as someone pointed out, if you have a lucky set, always play it - buy a second ticket with random numbers because if the lucky set is a winner and he didn't buy it, then he's gonna be in a bad way for the rest of his life. Most lottery's offer an option for them to automatically play the same # for you each time without having to buy the ticket. If he's that superstitious perhaps he should explore it.

Yeah that reminds me of a Dilbert strip where Dogbert is selling discount lottery tickets... "they're half price, but the chance of winning is only 1/ in 1,000,000,000 lower." "Hey wait a minute, these are a week old!"

Having said that.... assuming the odds of any one number coming up are identical on each day... you do increase your odds by playing on successive days as compared to playing on just one day. For example let's take a lottery where there are 100 possibilities. Your chance of winning if you play one day are 1%.

Now lets look at two days. The total possible outcomes for those two days are 10,000 (since each day has 100 outcomes and they are independent of each other, you multiply 100 x 100). If you play the same number both days, there are 100 combinations where you win on day 1 (your number on day 1, plus any of the 100 numbers on day 2), and 100 where you win on day 2 (vice versa), for a total of 200--except you subtract one case which you counted twice, the possibility that your number hits on 2 consecutive days. So your odds on scoring either one of the days are 199 out of 10000 or 1.99%.

I'll leave the further iterations as an exercise for the class, because I don't feel like working it out myself.

So yes, playing on successive days increases your chances of winning, but not that much. (You've doubled your investment of cash, but only increased your chances of winning by 99%.)

You can't improve your odds of winning (without buying more tickets), but you can improve your expected payout. Numbers from 1 to 31 tend to be picked more because people like to play anniversaries, birthdays, that kind of thing. So numbers above 31 are picked by less people, which means if you do win with those numbers, there is less chance of someone else also holding those numbers.

Playing the same numbers week after week does not increase your chance of wining, but does make it easier to see if you've won anything. :)

I was a casino craps dealer, boxman, floorman, pitboss, and surveillance over a period of 7 years and we used to have a saying.

The dice don't have a memory.

But you can tell your friend that with each ticket they buy that has different numbers, thier odds increase slightly. Actually they'd double if they purchased 2 tickets instead of 1, but they'd still have a 1 in a million shot if they were lucky.

I forget if you mentioned that before. I'm curious about one thing and that is: how much contempt do the dealers actually have for the players?

OK three things. What was the longest winning roll you ever saw? And the longest losing.

OK five things: what was the best cheat you ever saw? How often did you see cheats?

My most memorable time at a craps table was one where it took three of us an hour to crap out... we must have hit about 30 points and the table was as loud and happy as a table can be. My least memorable... about half of every time since then. The least memorable times are all the same: you arrive you lose goodbye.

(Aw shuddup you. The house vig is in my entertainment budget and it's as cheap as a big night on the town. And working out the house advantage in my head makes for good math skills, or something.)

Does Jacquelita know about this character flaw?

Just kidding!!!!

Depends on the players. I've had people walk up to my table and say, "I don't tip. Now give me the dice." and of course I want this kind of asshole to die. I've had really nice people who always put something down for the good guys so we could play too and we want them to win. Unfortunately it seems like the people we hate the most win more than we'd like and those we like the most lose more than we'd like.

I also hate the guy who buys a 25 cent el stinkadora, stands next to me and blows his nasty ass cigar smoke in my face. The worst is people who don't tip. I've had people who played at my table everyday for a week or two and didn't drop a single dollar. One time I was dealing at the California Hotel (Best Craps in Vegas) and I gave a guy $40,000 in 20 minutes and he picked it up and walked away without giving me a dollar.

The longest roll in history was at the California Hotel. A Hawaiian guy (they cater mostly to Hawaiians and fly them in) named Stanley (Golden Arm) rolled for 3 hours and 8 minutes without losing a point. They ran out of $500 casino checks and had to call gaming control to get permission to pay people cash at the tables to buy the checks back so they'd have something to deal. They roped off the table and wouldn't let any new players in. I wasn't dealing that night, but I know it to be true. They have a statue of a golden hand and when people roll for longer than an hour, they'll engrave your name on it.

The longest roll I ever saw was probably about 1 hr and 45 minutes. I was dealing at the California Hotel and I remember the table was on fire. I called eight hard 8's in a row. The odds of that happening are 1 in 2,821,109,907,456 (I am not making this up, I used a calculator) That's almost 3 trillion to 1.

Everyone had the table limit on the hardways and I remember screaming the numbers at the top of my lungs and the dealer across the table from me couldn't hear me. My boss told me if they rolled another hard 8, I was fired. We checked the dice to see if they were switched a hundred times. I told him I could only call the numbers on the tops of the dice.

As far as longest losing rolls, you see those everyday. You'll see a guy down to his last 5 bucks and he puts it on the passline and rolls for a half hour making everyone else at the table rich and then he'll lose his point and not even get his $5. But usually others at the table send a few bucks his way.

The best cheat I ever saw was Steve Forte. The Casinos use him to teach surveillance people how to spot cheaters. He makes video tapes you can buy on the subject. When you do surveillance, they teach you how to cheat so you can spot other people doing it.

I didn't see cheats very often except in the worst fleabag hotels. They know the surveillance in the expensive hotels will nail them and they know the weaker dealers are in the cheaper places. I did see some though and I nailed my share of them.

I used to like to play at the Horseshoe or Vegas club because you get an automatic buy on the 4 and 10 so you don't have to pay a vig unless you win. But still the California has the best dice game in town and I had the most fun dealing there. I also worked at the Gold Coast, the Sahara, the and the New York, New York. I broke in at the El Cortez (the scummiest casino in Las Vegas). You've got to pay your dues before you can work on the strip.

Re: Lottery Odds
 

"You gotta play to win!" MD State Lottery slogan (don't think they still use this one, but they wore it out years ago).

Sorry, that's the best I could do. ;)

Radar, how is it that tips are shared? Is it just the table workers that get the tips, or is it spread differently?

Actually that's the one thing I hated about the job. Las Vegas is very communist. I would work my ass off, be friendly, tell jokes, and keep people happy while others would stand around stone-faced and they'd divide the tips up at the end of the night and everyone would get the same amount. Even if they were standing around all night on graveyard doing nothing. And just like communism, the people in the high limit room didn't have to include thier tips in our pool so there was a priviledged elite. And the dealers who count and divide the tips get an extra share.

I was paying for someone else's kids new braces, I was paying for someone else's house, I was paying for someone else's car, etc. and all they had to do was stand around doing nothing.

There's a reason when you go to Las Vegas, you'll find that most of the dealer's are Asian women. The Casino feels that any money given to the dealers as tips is money they should have gotten. So they hire quiet women who work hard and aren't friendly and don't talk to customers like my ex-wife who still deals there and was one of the meanest dealers (and people) I've ever known.

Years ago some places would divide the tips on a shift for shift basis, or even a table by table basis.