Did BODOG European Roulette rip me off?

I pretty much avoid online casino's like the plague, but iv'e been playing poker at Bodog since black friday and decided to play a little at their casino. Wizard of Odds has said BODOG casino was fair, so I decided to play some European Roulette to pass the time, never thinking I could get buried playing $20 bets on 1-1 shots (18/19 with the 0). Anyway, I'd like to know from math guru's how unlikely the following numbers are.

I played #1-9 getting 3-1 on my bets (24.32% likelihood of hitting). 63 spins - 10 wins (15.87%)

Noticing the low numbers were awfully cold, i doubled by bets and decided to play #1-10 (27.03%) Played 60 spins- 12 wins (20%)

So now I just want to win some bets so I decide to play numbers 1-18 (48.65%) at 1-1 odds. Lost 16 of my first 18 bets and ended up winning 9 out of 34 (26.47%) when I finally cried uncle and had a quick $880 haircut . (just betting $10 and $20 bets on short odds props.)

For simplicity, I decided to look at all 157 spins and see how many times the numbers 1 thru 18 hit. 55 out of 157 spins landed on 1-18. A whopping 21 off of statistical norm (76.38)

I know the sample size of 157 isn't huge, but it seems like that's quite a few spins for a near 50/50 shot to be hitting barely above a third of the time. Is this somewhat normal variance, or is this borderline suspicious?

I made a total of $2447 in bets. My expected return of course is $2381, I got back $1584
I wasn't really expecting to win or lose all that much, and figured I might drop $100 or $200 at worst, never expected to lose a whole third of my stake after 157 spins betting nearly half the board on a game with a 2.7% hold.

Courtesy stattrek.com Link.

Binomial Experiment
A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:

�¡ The experiment consists of n repeated trials.
�¡ Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
�¡ The probability of success, denoted by P, is the same on every trial.
�¡ The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

Roulette results fit nicely into analysis using the binomial distribution.

b(x; n, P) = nCx * P^x * (1 - P)^(n - x) , where nCx is the number of combination of x successes in n trials, P is the probability of success, and n is the number of trials.

For example, in roulette, where the probability of success is 18/37, over 37 trials, the odds of getting 18 successes is:

= (37! / (18! 19!)) *((18/37)^18)*((19/37)^(37-18))
= .130335

To get 18 or less successes, you have to sum up all of the probabilities.


You can stick this in excel and use the binomial distribution formula figure out the odds of getting n number of successes or less:

1. BINOMDIST (10,63,9/37,true) = .0737558.
2. BINOMDIST (12,60,10/37,true) = .1389038
3. BINOMDIST (9,34,18/37, true) = .0070532

All three separately are not likely but not proof of cheating either.

Your last claim has a probability of .00039006 (BINOMDIST (55,157,18/37,TRUE)).

The cheat line is at about .000001 or less I think, so I'm guessing very bad luck. You need more trials.

I play and practice roulette exclusively. At an online
casino, including Bodog, you'll never see a string of
outcomes that doesn't fall into the mathematical
parameters of feasability. The problem is, you'll
see far too many of these 'questionable' strings
happen online than you ever would on a real wheel.

After awhile you see that, wow, these once in a
blue moon oddball outcomes happens to me everytime
I play. Nothing that 'couldn't' happen on a real
wheel, over time. So you start to question whats really
going on with these casinos, and the conclusion is
always the same: Save your money and watch Gilligans
Island reruns..

you practice roulette???????????

Quote: appistapp1s

you practice roulette???????????

Just as he practices watching Gilligan's Island, and with the same effect on his roulette results.

This online roulette game: Is it You versus the Bodog provided simulated wheel or are there other players simultaneously betting on this wheel as well?

Your complaint seems to be that your results at the electronic roulette table were less than exactly equal to some statistical expectation that you are quoting.

Ofcourse, I fail to see how that first spin can ever be anything other than wildly off from the statistical expectation. If your first spin is a win, that 100 percent figure is way off the "expected" mark. If the first spin is a loss, then that 0 percent figure is way off the "expected" mark. So the question is How many spins constitute a valid sample? Now I'm sure the math types here can start talking about optimal number of spins and absolute certainty and all that stuff, but the question before us is how many spins are needed to reach a conclusion and how likely is it that you've reached the true and correct conclusion.

>a game with a 2.7percent hold. ???
Hold? Did you mean House Edge?

I fail to see results that are suspicious, I just see results that are a disappointment to you.

Quote: FleaStiff

I fail to see results that are suspicious, I just see results that are a disappointment to you.

I'm sure you're correct. Thats why I always advise
investing all your money in online casinos. Its
a sure thing...

I've had this conversation about online casinos 50
times in the last 6 years and I always try to wise up the
chumps. It never works. Never attempt to wise up a
chump, it just makes them angry and resentful.

Quote: EvenBob

Thats why I always advise investing all your money in online casinos. Its a sure thing...

Now don't get carried away. I've always been suspicious of online casinos particularly when there are various dubious characters and multiple entities involved in some shady vest-pocket principality somewhere wherein the gambling commission is a rubber stamp inside the casino owner's desk drawer.

Ofcourse casinos seem to make alot of money if they are "Bricks" so the fact that casinos seem to make alot of money if they are "Clicks" does not necessarily mean fraud.

We all know about butchers and thumbs on the scale. We all know that most gamblers would be alert to outright cheating its the 'little nick here and there' that makes the money.

You would never go into a bar, see a woman there who was "not a 10" and leave. You would look around at the other women and even though "not a 10" was quite frequent, you would go by what was in fact there.

The data set presented by the original poster is "Not a 10", but I'm not sure where it would be on the scale.

If there are other players at the same online roulette table, this would make me wonder how do you cheat the player betting on the first eighteen numbers while avoiding giving an advantage to the people betting on the second eighteen numbers? The only way to cheat the entire table that is betting on Red and Black is to have Green roll an inordinate number of times.

Given this one data set, I am not willing to say the player is being cheated. When a bar puts up a sign Warm Beer, Lousy Music and Ugly Girls you assume its going to be a great place. Sometimes you get in and you find it was merely truth in advertising.

One data set is not enough. I don't know if the butcher is using his thumb or how heavily he is pressing on the scale.

Quote: shakhtar

For simplicity, I decided to look at all 157 spins and see how many times the numbers 1 thru 18 hit. 55 out of 157 spins landed on 1-18. A whopping 21 off of statistical norm (76.38)

Forgive me if I just focus on this statistic.

The expected number of 1-18 is (18/37)*157 = 76.3784

The variance is 157*(18/37)*(19/37) = 39.22

The standard deviation is 39.22^0.5 = 6.26

The number of standard deviations you were short is (76.38-55)/6.26 = 3.41

The probability of being that far south of expectations, or more, is 1 in 3,120.

This could easily have just been bad luck, which is what I would claim. It is always easy to look at results in retrospect and find something that seems fishy about them.

Quote: Wizard

It is always easy to look at results in retrospect and find something that seems fishy about them.

Online casino results will always be within
the proper parameters. The fact that you'll
see these parameters stretched into the
realm of the Twilight Zone should have no
effect on a 'casino oriented' player. They're
just having another bad day.

Quote: appistapp1s

you practice roulette???????????

Depending on your exact definition, I do as well. Just yesterday I played at DublinBet (fake money) for 7-8 hours straight.

Ken

Don't bother explaining, Ken. They're far smarter
about roulette then we'll ever be. You and I will
just stumble along till we catch up to them..