Mathematical Proof that English Harbour is cheating

[thelawnet]

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Editor's Note: The following is a classic thread that takes a number of twists and turns. English Harbour had upgraded their software and had unknowingly uploaded a corrupt file thus skewing their VP in a bad way. The players caught this and when the casino was first confronted, it was a state of denial. Yet when pressed further, they relooked at the situation and indeed they had screwed up. Spearmaster and I met with the operators in Montreal and were assured that it was an honest mistake. Spearmaster was also given the code to review as well. Players were compensated but EH remained in the rogue pit under the category "Bumblings, Blunders and Negligence" for quite a while. Three years later they became accredited after assurances of proper file management and auditing had been in place.
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I was suspicious of the fairness of the doubling on English Harbour's video poker. So I deposited and carefully recorded data for over an hour, doubling after every win, except I collected any large wins, and recording for each double the result, win, lose or push.

I played until I lost all my money (playing 4 line, single coin, recording wins, losses and ties on the doubling game (I did not record the video poker itself - I was only concerned with the double).

According to my data, it is 99.999% certain that English Harbour is not offering a fair doubling game in their Tens or Better video poker game.

Although nothing is completely certain, 99.999% would be good enough to convict a man and sentence him to death, so I think it is good enough for any reasonable person in the world to be satisfied that English Harbour is a cheating casino.

Here are my results:
84 wins
151 losses
19 ties

Ignoring the ties (which push and therefore have no effect), there should be an equal number of wins and losses on the doubling game.

As you can see from 84 wins vs 151 losses, there were not: the results were hugely skewed in English Harbour's favour.

By use of the binomial theorem in Excel, =binomdist(84,84+151,.5,true), it appears that the chance of only 84 wins out of 235 trials with a fair (50/50) game is only 0.0000074.

Accordingly I recommend you AVOID this casino and the others in its group, as although I did not find any problems with the other games, I did not feel inclined to test, and a cheating casino is a cheating casino, so if they are cheating here, they could be cheating anywhere else.

[thelawnet]

Also note that I did not take a very big sample. It often requires many thousands of trials to prove a discrepancy: the fact I could show cheating with less than 250 is very telling.

Had I wanted to lose any more money, and got the same results proportion of wins over a sample twice the size, the odds that this is fair would go from 136,000-1 (such that you would expect to find such a run once in about ever 50 million 4-line hands, roughly equivalent to playing video poker 400 hands/hr, 8 hours a day for 40 years), to 3 billion - 1.

[thelawnet]

Also note that Fire and Ice Casino and Hot Pepper Casino two non English Harbour casinos accredited here, both use the same software as English Harbour.

Whether the cheating is found there or not I have not tested.

[liquidsoap]

Fixed
You need to add about 100,000 more hands if that to find out if it is fixed....

Just another loser with a conspiracy theory....
When you hit the royal flush, complain to them thats its fixed

[jonevegas]

Just another loser with a conspiracy theory....
When you hit the royal flush, complain to them thats its fixed


OUCH!!

[Linus]

I'm not enough of a mathematician to say whether your results prove anything or not. But in one respect, at least, you're wrong - the larger the sample, the more meaningful it is. It's not the other way around.

Try running it by the Wizard of Odds, and see what he says (he's busted a casino for cheating before). You might also try the "Probability" section at 2+2. There are some smart math guys there, who are very helpful.

[Linus]

Out of curiosity, does your Excel formula show the probability of getting exactly 84 wins, 84 wins or fewer, or somthing else?

[jsp377]

My post has been replaced and edited due to not thinking on my part.

liquidsoap is absolutely right that just because the probability is low, that does not mean the game is rigged. If it DID mean the game were rigged, than any small number of hands in video poker that yielded an RSF would be considered to be rigged in favor of the player.

What makes this binomial distribution different from that is the Central Limit Theorem. By the time you've got a 235-sample binomial, that makes a pretty frickin' good approximation of the normal distribution. Therefore, we can judge the likelihood of getting only 84 wins with a normal distribution of mean mu =.5*235=117.5, and standard deviation sigma=sqrt(235*.5*.5)=7.665. Now, 84 wins is (117.5-84)/7.665 = 4.3706 standard deviations away from the mean. This has a probability of .0000062, even LOWER than that suggested by the original poster. In fact, despite using a binomial distribution, his analysis was basically spot on.


To liquidsoap and his statistics-hating...
The point is not the number of trials. The point is that the probability of getting as few wins (or fewer, for you doubters!) as he did was less than a one in one hundred thousand shot. Yes, the same proportions on a larger sample would be even more damning. But the fact that the sample size is small means little.

AS AN EXAMPLE, if I had a sample size of thirty and lost every single one, that would be pretty f'in' damning...that's a one in 1,000,000 shot, and enough for me to say that the coin flip weren't a fair game, despite the small sample size.

Similarly, although this sample size is small, it is equally damning, because the results he obtained were a one in 150,000 shot. If you don't think a 99.999% confidence interval is strict enough, you have no business arguing statistics.

[Aindreas_Daoc]

Out of curiosity I tried this just now, using play money mode, doubling 1 line tens or better.

My results: 25 W, 65 L, 10 T. 100 tries total.

In my opinion, this is not a fair doubling game. Someone ought to contact Michael Shackleford (Wizard of Odds) and get his opinion.

Edit: Could other forum members give this a try too? The more trials there is, the more accurate the picture we get. Furthermore, we'll have more documented records. I did the above in less than 30 mins. Just use play money, and record your VP doubling results.

[Zoozie]

Actually my worst doubling experince also happened at English Harbour(Oddson software). I was playing doubling in the 5$-10$ range (bet size could matter).
I lost like 23 or 24 out of 25 doubles and then I busted. However this small sample size says nothing. After this happened I stopped doubling (at all casinos).

I once made a test like you did at Playtech with a larger sample size and the
results showed a fair game. (Actually I had a little more wins than looses)

However my point is, where does it say that doubling has to be a fair game at online casinos?

Because at BEST you get a fair game, but there is no garantie. There are strict rules that VP games/Dices has to be fair, but are there similar rules for doubling?

Zoozie