Author |
Topic: Casino Scam (Read 790 times) |
|
Nick
Guest
|
Consider a standard game of roulette. 38 spaces on a wheel. Numbers 0, 00(green), and 1 through 36 (alternating black and red). While only betting on a color (red or black) using an amount from 5.00 to 1000.00, what method would yield the most income, and have the least risk involved? What is the least ammount of money required for a certain method? What is the expected profit/loss assuming the wheel is spun once every 2 minutes? I've calculated my own "theory" on how to guarntee a profit, adn was wondering if any could come up with somethign better.
|
|
 IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender: 
Posts: 13730
|
 |
Re: Casino Scam
« Reply #1 on: Jul 7th, 2003, 2:32am » |
 Quote  Modify
|
Since there is a betting limit there is no way to guarantee a win, the expected 'gain' is always negative. So the safest bet is putting your money in a bank account.
If there wasn't a betting limit you can start betting some amount, and if you loose bet double, and do that untill you win. And that's why every casino has a betting limit, they want the customers (or suckers) to loose on average.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Casino Scam
« Reply #2 on: Jul 7th, 2003, 6:52am » |
Quote Modify
|
towr,
A betting limit doesn't change the expected payout. The casino still expects to win the same amount of money. Without a betting limit, however, an arbitrarily large portion of betters can win money, with the rest of them losing a huge amount of money. The "average person" still loses, because the average of these huge negative sums of money and a lot of small positive sums of money is still negative.
The problem with letting this happen is that the people who lose in this case wouldn't be able to pay up. Only then does the casino lose money!
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Casino Scam
« Reply #3 on: Jul 7th, 2003, 7:09am » |
Quote Modify
|
on Jul 7th, 2003, 6:52am, James Fingas wrote:towr,
A betting limit doesn't change the expected payout. |
|
I never said it did.
Except that you can do this.
bet 1 dollar
win -> one dollar gain
loose -> bet two dollars
win -> one dollar gain
loose -> bet 4 dollar
win -> 1 dollar gain
loose double bet again repeat till you win.
using this process you allways gain 1 dollar given sufficient time. Unless there's some point at which you can't double your bet any more, a betting limit.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Casino Scam
« Reply #4 on: Jul 7th, 2003, 8:44am » |
Quote Modify
|
You can increase your chances of getting one dollar to a value arbitrarily close to one, but your average return is still negative.
The casino doesn't care if most people win, as long as they still make their money. The betting limit is imposed because the losers can't pay, not because the expected return changes.
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Casino Scam
« Reply #5 on: Jul 7th, 2003, 9:06am » |
Quote Modify
|
on Jul 7th, 2003, 8:44am, James Fingas wrote:You can increase your chances of getting one dollar to a value arbitrarily close to one, but your average return is still negative.
|
|
If you take the limit to infinity the value is 1, and the return is positive.
In any case, in reality it doesn't matter anyway.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Nick
Guest
|
My dad and I discussed this on a road trip once, If you were to find the probability of losing on a color,(20/3 which is 53% for any given spin. But in conjunction, the probability of losing twice in a row would be 27%. 3 times would be 14.5% and so on and so forth. Spinning 8 times and not winning would only occur .005% of the time. If you were to start your bet at 5 dollars, and double it for each loss, at 8 losses in a row, your last bet would be 640 dollars. If you were to lose that bet, you could not bet enough to recoupe your losses. Assuming 30 spins in an hour, you could expect to win 47% of the time. which is a little more than 14 times. With each win, you should regain what you have lost prior, plus 5 dollars. Where your average winning would be 70 dollars per hour. I know my job doesn't pay that much. Is it really this easy, or is my logic flawed?
|
|
IP Logged |
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Casino Scam
« Reply #7 on: Jul 7th, 2003, 1:47pm » |
Quote Modify
|
The first problem I see with this is that you're understating the probability of losing. On average, you'll lose 0.00623 of the time, which is 0.623%, not 0.00623%. When you lose, you will lose big ($640). Sure, if you don't lose, you'll make 70 dollars an hour, but there's only a 92% chance you'll make it through the hour without losing. If you try and make any serious money on it (let's say, playing for 10 hours straight), there's only about a 40% chance you won't lose at all (for a payout of $700). There's about a 24% chance you'll lose only once (for a payout of $60). There's roughly a 14% chance you'll lose twice (losing $580), and you could easily lose a whole lot more than that.
On average, you'll lose 53% of what you bet. It's just as simple as that.
What bet-doubling does is concentrate the losing into a very few large bets, and spread the winning around into many small payouts (sort of the opposite of a one-armed bandit!). In order for bet-doubling to work, you have to have the betting limit high enough that most people can win all the money they want (let's say $1000) with a very high probability (let's say 90%). But this means that the remaining 10% of people have to lose at least $9000 each (for an even-money game). Since many people would go bankrupt before they could pay out $9000, the casinos could never make money doing this, so they have to limit the losses to something most people can pay.
In your case, you can win about $85 with 90% probability. So if you're only interested in $85, it may seem like a good bet. But if you're one of the unlucky 10% that loses over $700 on average, then it won't seem like such a good idea, and if you keep playing like this, then you'll end up getting at least your share of the losing. There are professional gamblers out there, but they're not usually mathematicians, because the mathematics of the game is clear: the house always wins.
towr,
I would argue that it's more mathematically valid to take the limit of the additive sum of the expected returns than it is to find the most common return, and take the limit of its probability. In the limit, the casino still makes money--from the zero people who lose an infinite amount. As an individual gambler, however, you can be sure you're not going to be one of those losing players!
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Casino Scam
« Reply #8 on: Jul 7th, 2003, 1:57pm » |
Quote Modify
|
The more you bet, the more you stand to loose. 5 dollars isn't going to cut it unless you're guarenteed to win, and that guarantee only exists infinitely past the betting limit.
I'd suggest running a computer simulation of what happens before trying it in a casino.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Casino Scam
« Reply #9 on: Jul 7th, 2003, 2:01pm » |
Quote Modify
|
btw I thought casino's didn't allow non-covered bets anyhow. As far as I know you have to buy the chips to bet with beforehand with real money, and not on credit.
So there shouldn't be a problem with people not paying up.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Kozo Morimoto
Junior Member
Posts: 114
|
|
Re: Casino Scam
« Reply #10 on: Jul 7th, 2003, 9:04pm » |
Quote Modify
|
I think gaming theory saids that for a negative expected return game (like our roulette), you should bet once, and bet big - i.e. all your money on the first game. Of course, not playing would be the most optimal...
For a slightly positive expected return game (properly counted blackjack, for example), you should bet little each game and play for a long a time as possible for as many games as possible (like in a team of a dozen over different tables with pooled resources).
|
|
IP Logged |
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Casino Scam
« Reply #11 on: Jul 8th, 2003, 1:25pm » |
Quote Modify
|
on Jul 7th, 2003, 1:57pm, towr wrote:The more you bet, the more you stand to loose. 5 dollars isn't going to cut it unless you're guarenteed to win, and that guarantee only exists infinitely past the betting limit.
I'd suggest running a computer simulation of what happens before trying it in a casino.
|
|
Actually I did just this. You get a nice even line for your money that increases as 18/38*(your initial bet)/(#of bets). The only problem is that you have to cover the sometimes dramatic downswings. So long as you have a bankrole capable of it and you don't have the bad luck to hit a long series of failed bets in a row you will make money. The problem is that if you lose, you have lost everything. Your chance of coming out positive in the end greatly depends on the ratio of your bet to your bankrole.
For example, betting one dollar per spin and playing 50 rounds one case gives you ending with $22 extra in your pocket and having to be able to cover $5 in the hole. Then again another simulation ends with +$27 and a maximum loss of $17. Of course, to have gotten out of that hole would require you betting $16 when you were already down $17.
The bottom line is, on average if you randomly determine when to stop you should lose money, but if you can decide to always end after a winning round, and you have the cash to cover it, you will win.
|
|
IP Logged |
|
|
|
James Fingas
Uberpuzzler
Gender:
Posts: 949
|
|
Re: Casino Scam
« Reply #12 on: Jul 8th, 2003, 1:56pm » |
Quote Modify
|
Aero Guy,
I'm skeptical. Can you give more details on your simulation? Are you just running a large number of test runs at the roulette table where you follow the doubling strategy starting with $1? If so, you will have to run a large number of tests before getting an accurate average. A few tests will probably only show that usually you make a small amount of money. The problem is, as you say, when you lose, you lose everything. Your probability of losing everything is based on (desired winnings)/(initial bankroll). You need a surprisingly large bankroll to get a high probability of winning even a modest amount of money.
In addition, Nick is probably starting at $5 because that's the minimum bet (but I don't know that for sure).
|
|
IP Logged |
Doc, I'm addicted to advice! What should I do?
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Casino Scam
« Reply #13 on: Jul 8th, 2003, 8:13pm » |
Quote Modify
|
I am running with a starting amount of $0. After each round you either win or lose the current amount of the bet and reset the bet level to 1 if you win, double if you lose. The initial amount is set to 0 just so I can easily see if you are losing money. You follow a very nice 18/38 line with the occasional spike (when looked at over a long period). Over the period of 50 rounds it is rare to have to take your bet over $32. When the number of plays is upped to 1000, we see that you win about $470, but there are the rare times when it is required to bet up to $4,096 on a single spin. Never seen it get worse than this. The real drawback to this technique is not the probable outcome, but the time required. When you consider how long it takes between spins of a roulette wheel you see that you are making less than you would at a well paying job, assuming everything works out that is.
|
|
IP Logged |
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Casino Scam
« Reply #14 on: Jul 8th, 2003, 8:16pm » |
Quote Modify
|
I think the crux of this is that any time you set a spending limit you will eventually lose. The bigger the limit, the less often you will lose, but the more you lose when you do, thus always giving you a net negative outcome. Only when you have bottomless pockets will you win in the long run.
|
|
IP Logged |
|
|
|
Kozo Morimoto
Junior Member
Posts: 114
|
|
Re: Casino Scam
« Reply #15 on: Jul 9th, 2003, 5:18pm » |
Quote Modify
|
What happens if you can set up a consortium of like 12 players over 12 roulette wheels, where winning from one person can fund the losses from the other? And because you get 12 times more spins in the same amount of time would this fair any better than the single player model? Or does this mean that you just lose money slower than before?
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Casino Scam
« Reply #16 on: Jul 10th, 2003, 1:02am » |
Quote Modify
|
no, it actually means you loose money 12 times faster (on average).
For any bet the expected gain is negative. And because of the betting limit you can't double your bets to make up the losses indefinately.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Freddy
Guest
|
ok here is something I thought up and ive tried a few times and its worked everytime
I think blackjack favors the house a little less then roullete does, so I did this playing black jack instead
ok so you play with a 1000 chips and you start off by betting 5. If you lose you double your amount and add 5 and keep doing that until you win and you once you win start again at 5 and repeat
so the betting goes like this:
5, 15, 35, 75, 155, 315, 635
so basically that means the dealer has to win 7 times in a row to stop you, that is not likely to happen but if you give him enough hands the odds of happening will not be good for you
so what you do is you set a goal of like 2000 this is what I set it at and once you reach this you stop and start over if you want
so far ive tried this 6 times and ive reached the goal 5 times out of 6.
So basically what it all comes down to is a race for either you to win 100 games(if you get black jack you profit 1.5 so this number can be less)or the dealer to beat you 7 times in a row. I think the odds now favor the player.
|
|
IP Logged |
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Casino Scam
« Reply #18 on: Nov 21st, 2003, 12:39pm » |
Quote Modify
|
No they are not. You win a moderate amount 5 out of 6 times, but you lose enough on the sixth that the house makes a profit and you lose. It is possible ot beat the house at blackjack though. If you memorize blackjack tables you can increase your odds to something ling 49. something percent. By a simple counting cards method you can increase this over 50%. The problem is that if you make any mistakes you quickly lose all the money you could have made. There are examples of people who worked in teams from MIT in the 80's I think that had this perfected. They won a sh*tload of money. The point is that you have to increase your odds to over 50%. Any betting strategy on a game with less than 50/50 odds will lose money.
It is like a perpetual motion machine. You can't get more out than you put in.
|
|
IP Logged |
|
|
|
Freddy
Guest
|
how did the house make more on the 6th time? I would make 5k the first 5 times and only lose 1k on the 6th time...
|
|
IP Logged |
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Casino Scam
« Reply #20 on: Nov 22nd, 2003, 1:11pm » |
Quote Modify
|
Actually, with the way you have the problem set up you will lose far more than 1 in 6. Firstly, you do not need to lose 7 times in a row. If you lose 6 in a row without gaining too much in between you will also lose. The problem with you sim is that you do not seem to consider the many ways you can lose. It may be likely you will win 100 games before losing 7 in a row, but that is far from reaching your goal.
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print
Remove