SkillOnNet software - Non-random/Not Fair

First published in August 27th, 2012

After receiving requests from a couple of casinos utilising SkillOnNet software for reviews we agreed and began our review procedures. During the discovery process (that’s where we research the casinos at various player resources to try and find out if any other players have been having difficulties) we came across this thread from 2009 on CasinoMeister - http://www.casinomeister.com/forums/online-casinos/31741-u-casino-eu-casino-video-poker-double-up.html - detailing problems with the SkillOnNet video poker double up or gamble feature, where after generation of data the CasinoMeister members had shown with a very high degree of certainty that SkillOnNet’s Video Poker gamble feature was non-random. Despite the fact that one of the main contributors to the CasinoMeister thread was aka23 – the owner of Beating Bonuses and an expert in the field of game analysis - as this thread was now several years old I decided that it would not be fair to draw any judgement from it. Instead I asked one of my reviewers to sign-up and play at a SkillOnNet casino and together we would conduct our own test.

Unfortunately the results of this test confirmed the worst. In of 301 gambles we experienced 193 losses and only 108 wins. Worse than that, of the 22 gamble sequences that resulted in a third gamble, we did not experience a single win.

I should explain a few things before we go any further; firstly the gamble feature. When playing most video poker games, at the completion of a hand if the player has experienced a win it is standard to provide the option to gamble the winnings. This is a completely separate bet where the winnings of the video poker hand are wagered on what the colour of the next card will be. As the card should be dealt from a full deck – with jokers removed – it should be a 50/50 chance of receiving a red or black card, giving the casino no edge over the player. In fact the gamble feature is normally the only wager you can make in a casino where you have the same chances as the casino, every other game most casinos offer will provide the casino an edge over the player.

Now if the gamble feature is in fact fair, the odds of winning should be 50% and we should have seen somewhere around 150 win and 150 losses. Alongside this a sequence of 3 wins should have occurred approximately once in every eight sequences. In 193 separate sequences, we did not see a single three win sequences.

All of this may seem fairly damning or inconclusive depending on the levels of your mathematical knowledge. For this reason we need to run some statistical analysis of these figures to determine how conclusive they really are. Firstly to check how far away from the average result we have fallen from the average result we use a measurement called Standard Deviation (SD). We calculate the number of SDs away from the average result we are by taking the difference between the expected results and actual results and dividing by the Standard Deviation (SD) across the full events. The SD of 301 binomial events is

SQRT(n*p*(1-p)) = SQRT (301*0.5*0.5) = 8.67

Where n is the number of trials and p is the probability of a loss (or win – as they should be equal it makes no difference).

For the 193 losses (or 108 wins) out of 301 event, the number of SDs calculation is

(193 - 150.5) / 8.67 = 4.9

A 4.9 SD event is extremely rare so we now have evidence to suggest something is wrong, but we need to know just how rare so we’re going to use the Binomial Distribution. The simplest way to do this is to use the BINOMDIST function in Open Office which takes the form of “=BINOMDIST(n; t; p; 1)” which you enter into the formula bar where n is the number of wins, t is the number of trial and p is the probability of a loss. Entering these figures we get

=BINOMDIST(108; 301; 0.5; 1) = 5.50575099572453E-007 = 0.000000050575099572453

To simplify this, if you were to play 301 gambles two million times, you would only expect a result this negative once.

Now that’s fairly conclusive in itself, but one in two million events do sometime happen (approximately 1 in every 2000000 times). But we didn’t just have one extremely rare event, we had two. Two independent samples taken years apart where there was a strong correlation between the sample sets. What are the chances of these two extremely rare events happening in conjunction like this? For this we just combine the data sets and go straight back to the Binomial Distribution.

=BINOMDIST(226; 616; 0.5; 1) = 1.97595439741614E-011 = 0.0000000000197595439741614

Once again to simplify this, if you were to play 616 gambles 50 billion times (!!!) you could expect to only win 226 of them once. At this point we can safely say that it is beyond extremely unlikely that this game offers a 50% chance of winning.

The second task we needed to look at was establishing what the true chance of receiving a loss when playing the SkillOnNet gamble feature was. For this we used this article - http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair#Estimator_of_true_probability.

As the gamble feature should be the same as a fair coin, these formulas are appropriate for this circumstance. If we look at example 3, this closely resembles our situation except that where the coin was tossed 12000 times, in our data set this would be replaced with 301 and where they had 5961 heads and 6039 tails we had 193 losses and 108 wins. So;

p = h/(h+t) where h= 193 and t=108

p = 193/301 = 0.641196013

We want to use the highest level of confidence possible, so when we look at the table of possible values for Z (just above the examples) we select Z = 4.4172 – equivalent to a confidence level of 99.999%.

Now we calculate E

E = Z/(2x√n) where Z = 4.4172 and n = the number of trials = 301

E = 4.4172/(2x√301) = 0.127301587

Finally we calculate the interval within which we can say the chances of receiving a loss with the SkillOnNet gamble feature actually reside.

p-E < r < p+E

0.641196013 – 0.127301587 < r < 0.641196013 + 0.127301587

0.513894426 < r < 0.7684976

Or to simplify again – we can conclude with a 99.999% degree of certainty that the true probability of a loss when playing SkillOnNet’s gamble feature is between 54.41% and 72.21%. Once again the fair probability of 50% is not even included within this range and this time by an even greater margin.

We can now state with at least a 99.999% certainty that the game that we played was not fair.

With this information we approached SkillOnNet software and the casinos involved on Friday the 17th of February 2012, talking one of the casino representatives through the figures we’ve just covered above. The representative assured us that they were taking this issue very seriously and they were going to conduct their own test and approach SkillOnNet with this information. On Monday the 20th of February 2012 we received an email from the casino that included the results of their trial, saying that their figures seemed to fall within normal parameters and asking whether we were sure of the results we obtained.

Firstly, as I was involved in the generation of our figures of course I’m 100% sure of their veracity. Secondly, due to the reputation of the major contributor to the CasinoMeister study, I’m extremely confident of their figures.

When we conducted a second trial after receiving the casino’s response on Monday morning, low and behold, the second data set turned out to be absolutely normal. This leads to the conclusion that either both parties that conducted independent tests years apart experienced extremely unlikely and similar events during their play (that’s the 1 in 50 billion possibility) or the game had been adjusted over the weekend.

Either way the game now seems to be returning normal results – so why the blacklisting? The drastic change seen in the output of this game and the questioning of the figures we provided suggests that rather than this being a programming error – which was fairly unlikely due to the relative simplicity of programming a fair gamble feature – it would seem far more likely that the gamble feature provided by SkillOnNet software is in-fact configurable and can be set to provide the casino a range of possible advantages. As this feature should not even provide the option of giving the casino the choice to rig the game in their favour, if we conclude that the gamble feature can be configured it raises questions as to the fair operation of other games that should be non-configurable provided by SkillOnNet and testing the fair operation of the other games they provide would involve far more in-depth and time consuming processes. Alongside this, if this feature is in fact configurable it is easily conceivable that the casinos/software operators involved could adjust the chances of a loss back to the correct levels for the duration required to allow testing and confirmation that their game is fair, simply to adjust the game back to its previous non-random settings at some point in the future. This means that every customer would have to be constantly vigilant in watching for non-random behaviour.

So while we cannot say with 100% certainty that SkillOnNet offer a non-random gamble feature, we can say that there was only a 0.001% chance that the game was fair when we tested it, there was only a 1 in 2000000 chance of receiving as many losses as we did and the behaviour of the parties involved after this was brought to their attention strongly suggested that their gamble feature can be configured. This leaves the customer utterly uncertain as to whether they are receiving a fair game. Blacklisted.

I would like to thank aka23 from Beating Bonuses for his assistance with the analysis of some of this data and his critical eye as a proof reader and thelawnet for their initial analysis in the CasinoMeister thread.

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