I question your detachment if you are calling gambling an "investment" at all. If you want to win at probability games, look at what any professional gambler does and stick your money down only when you can prove or reasonably expect to see a positive expected value given your odds. That's how basic strategy in blackjack and most of poker math works.
Also, I assumed ticket generation for the simple games was something brute-force-ish akin to:
1. Create your winning tickets. Fill in the rest of the numbers with things that won't cause duplicate wins on the same ticket pseudorandomly.
2. Make a random ticket. Check to make sure the ticket is not solved. If the ticket doesn't solve, add it to the stack of tickets.
Randomly shuffle all tickets. Print to rolls and cut. You could probably even get away with duplicate random "losing" tickets if you had enough of them because most people likely won't end up with the same losing ticket.
Numbers games (lotteries) are run by governments now because organized crime was running them in inner cities. People still played then. See Wikipedia: http://en.wikipedia.org/wiki/Numbers_game At least the "tax" from lottery proceeds often goes to benefit social goods like public school systems.
In other words, there are varying methods of obligation.
I would also like to recommend this PG essay: http://paulgraham.com/wealth.html
http://www.foxnews.com/scitech/2011/02/02/statistician-crack...
There was a special promotion at the racino she goes to -- you could take your loser scratch tickets in a certain game to the casino, they'd put them in a big jar, and then whoever won the drawing got a trip to Las Vegas.
She saw there weren't many tickets in the jar, so she bought about $150 of these scratch tickets (she won $80 back so these only cost her $70) and submitted them. Her mom did about half as many.
A few days later her mom gets a phone call and she won a trip to Las Vegas worth $2000. Then she goes there and does some tricks with her loyalty card and now she's on an $800 junket.
I worked it out with decision theory and found that they had played the raffle almost optimally -- it blew my mind since I figured anyone who messed with scratch tickets and video slots would have to be completely impervious to probability theory.
Raffles, in generally, are good for people who play to win. My family regularly wins multiple prizes when they have raffles at the school because we're smart enough not to put tickets in for the Battleship game all the boys want or the hula-hoop all the girls want.
There's always some prize which is cooler than the muggles think that it is, and I'll walk home with it.
Now, you never see books about "how to win at raffles" because unlike Poker and Stock Trading, there's no motivation to suck in players who are just a little bit worse than you.
Here's a great article on lotteries, particularly Cash Winfall. CWF was a particularly broken lottery. In a certain season it was possible to purchase enough tickets (say, $100,000 worth) to (almost) guarantee a profit.
https://en.wikipedia.org/wiki/Massachusetts_Lottery#Cash_Win...
I would argue that a lottery's goal is to make money while providing entertainment, and not necessarily create an "unbeatable" game.
The game was shut down because public outcry at what the public deemed "unfair" and not because it was losing money.
[1] tickets are not random but comes in batch with nearly constant amount of various outcomes: the seller, who you tipically ask for your gain, can take note of what happened in each batch and predict if its remaining part is worth being buyed by a friend. Very easy.
I'm confused about why we are supposed to believe that there is anything exploitable about this particular card?
The other parts of the world are fucked up as well. There are probably a lot of "secure" lotteries, but there are probably also a lot of insecure ones.
Even smart people using good software can make mistakes.
You can look at the $10 as being 2-3 Starbucks coffees
Just go to your local grocery store or gas station and stand next to the machine or cash register for just 30 minutes and watch the guys that buy a ticket. They're all regulars. They're all putting their hope (even if they tell themselves they're not) in this ticket being the winning ticket. They're buying 2 or 3 tickets a day which is money that most of them really can't afford to just be throwing away (and these are people that honestly would say they can't afford a Starbucks a day, by and large). It's very sad.
It's been a while since I read it, but as far as I recall, one of the hypotheses about her good fortune (other than luck and some form of inside information) is that she had analyzed how winning tickets are distributed among batches (by cracking the pseudorandom number generator), and tracking which stores are likely to get packages containing winning tickets by the shipping routes.
There are professional "cashers" that have figured out how to hack a small percentile of games in MA. They take advantage of a few things, but if you have $100k you are guaranteed to make a profit. Source: http://www.wired.com/wiredscience/2011/07/broken-lotteries/
Now this guy is a trained statistician from MIT and Stanford and has put math behind it. He figured out the tic tac toe game. Source: http://www.wired.com/magazine/2011/01/ff_lottery/all/1
So as you can see all games aren't entirely fool proof. Good luck!
Also edited to add: Even ask the dealer. He might know something -- although it'd probably be against the rules for him to say anything, even what he's seen. But maybe he can point you to customers who know.
(Also: in Australia you usually see the next 4 tickets on the roll behind a clear display, so if you ended up with a good trick, even if it required running a script on your smartphone, you could have fun with it)
The base of my sample program [implemented in ruby] was based (in theory) of Proportional Betting "The Martingale" - http://www.bjmath.com/bjmath/progress/prog1.htm
The game I picked was "Casino War" [ http://wizardofodds.com/games/casino-war/ ], as it was very quick to implement in a few lines of code. I selected the base rules as played in Garden City Casino [Bay Area] (50c drop per every $100), and came up with the following:
Game/House Rules: - 6 deck of cards. - Played until 1/2 is gone. - 50c drop for every $100 [Example: $200 bet costs $1, $300 $1.5.]
Betting Rules:
- Base Bet is always 1% of current wallet, at starting point - $10. - If the proportional bet can not be covered by wallet, the round is surrendered and the player waits until re-shuffle. [Example: Lost up to $500, next bet is $1000, wallet has $700, game ends/waits and the player accepts a loss of $300.] - Bets are doubled on loss as defined in the Proportional betting link.
Here's my data, though I believe something is wrong due to its results:
- I ran the initial program, as is, expecting the player to play one round every day for 10 years. - Losses and earnings were added together. - The average win % went to 58.4%. - The average cash win [the times the player didn't go bankrupt] was $1590. - Max loss [consecutive] cash $2980. [Bankroll covered over multiple sessions]
* A key point here is the average cash win. It was highly consistent and never below 1500.
I then added a factor that stated in the software:
- If winnings are at $1500, the player stops, takes the winnings and waits for a re-shuffle.
* Win percentage went up to 64.8% !
If anyone is interested, I'd be happy to share/pastebin the code or similar. Overall, due to the percentages I'm assuming something is wrong with my assumptions/gameplay, but so far an interesting experiment.
[Edited for clarity on betting strategy]
Based on the comments it looks like the reliability is a little bit sketchy.
A sample of 43 observations might be reasonable if there were few independent variables and these variables had relatively few possible values.
If it's a serie of numbers you have to find out what the chances of a winning ticket in X-amount of tickets, meaning that you statistically have a chance of a price within the range of X-amount of tickets. But the way they have made it, you statistically have to spend more money than you can win in order to do so, or just about break even.
Now, the fun part is that most of these tickets (atleast where I live) come with pseudorandom serie numbers, so even finding the system in how the numbers are generated is going to be hard, if not even down-right impossible given the sample-size you will be able to buy.
And last but not least, lottery makers are not stupid. They've known about this since the dawn of time. Actually some credit the math behind statistics to gamblers. And you have so many level of pseudorandomness to crack, so, when you're done, statistically we can say that the lottery made it's money anyway, and you probably spent more than you won. And the lottery agency just have to change one constant and they are, from your point of view, totally random again. It's a cat and mouse game you cannot win.
We were told that each pack contains at least one winning ticket (it might be $5 or it might be $100K).
That's a definite weakness.
Otherwise, I do not see what that information (if it is true) would give you.
IIRC, a martingale strategy will eventually destroy you because it requires an exponentially sustainable bankroll to maintain the same risk of ruin.
Also, 3,650 hands is far too small of a sample size for a game with such a small edge and you are probably just witnessing positive variance. See where the law of large numbers leads you and run your simulation for 500,000 hands.
If you factor in the times the player went bankrupt, your win percent probably won't look so hot.
As it was run twice, it's closer to 56,940. (using two different alg.)
Rerunning it (now) produces minimal differences, even at a 1,000 year setup. (3-5% variation)
Obviously not something a person who didn't have the ability to monitor the purchases could do.
for instance, is it possible to ship 5 rolls with million dollar winnings to the same store in a week? maybe the answer is yes, but i imagine there's a reason to prevent this. in case it's not clear i am just guessing. i don't really know what i'm talking about.
That, I do not see. If there are some guarantees as to having guaranteed prices per roll, one can see the lottery as the sum of small, per-roll lotteries, possibly combined with a larger one to distribute the truly large prices. There is no reason to assume that those per-roll lotteries will be correlated in some way.
Overall; I agree [and having played my share of a variety of strategies] I found the data to be confusing, hence my peaked curiosity. :-)
The famous MIT black jack team was able to 'take down the casino' by counting cards and waiting for expected value to swing positive, and then placing large bets at that time. If the game is truly random and negative (like all well-constructed casino games should be) then there should never been an opportunity for positive expected value.
Make that $10 instead of $1 and open a "mini mutual fund" that angel invests in high risk things like new companies. $10 per "share", 100 people is a $1000 which isn't too bad of an investment to put into a local computer repair business or something.
I don't know about the legalities of something like this, though.
But if your goal is to get the people buying lottery tickets to buy yours instead, that's not going to happen. If you tell them there's a 1 in 10 chance that their money will be doubled in six months or a 1 in a million chance that they'll win the jackpot overnight, these are people that'll go for the latter every time.
On the other hand I am not even sure if lotto is really such a bad investment. I know the expected value is negative, but there is a chance to become a millionaire after all. If spending 1$ doesn't hurt you much, might be worth a try?