Mathematical Proof that English Harbour is cheating

[Aindreas_Daoc]

This just in from English Harbour:

Thank you for taking the time to review and play our games. We take your comments seriously and as such have spent time reviewing our Video Poker game play and also await some feedback on an independent review from a 3rd party.

We have concluded our review of the game play and randomness for all Video Poker games. Although the doubling component of Video Poker is theoretically deterministic, it's common knowledge that there are varying chances for winning and losing when picking a card out of four, to play against the card that is dealt face up.

Randomness:

It's important that the frequency distribution of the cards in an adequate sample set are evenly distributed for each position in the doubling game. We have found, taking several sample sets over different and varying lengths of time, that they yield in our opinion, a non biased distribution of the cards.

Game Play:

In theory, the number of Wins versus the number of losses and (excluding ties) will converge to 50% over a sample set that is large enough. Should small sample sets be used to measure this metric, then results will vary as seems to be the case tracing through this thread.

We trust, that we have responded adequately and any doubt in peoples' mind are put to rest.

English Harbour Management

And it may be premature to say the the Wiz will be back sometime today/tonight with his results. It may be until the end of the week. We'll see.

Just as I expected: they "fixed" the problem internally then denied it happened. If the Wiz tests the software now, of course he'll find that everything is back to normal, but the data set obtained by forum members here show that at one point the game was crooked.

This whole episode left a very bitter taste in my mouth. Online you can't trust any casino. Not even big, previously reputable names such as OddsOn. Who's to say that not ALL their games are crooked? And the reason this particular crooked game was detected because they made it "too" crooked? Maybe they programmed their VP doubling with a 2.5% advantage for the house, but instead some programmer typed in 25%, and lo, you get the result we obtained. If they left it at 2.5% no one would have noticed.

This kind of deception happens online because there are no regulations, no audits, no gaming commissions, nothing. It's a big free for all. Human greed unchecked will not be satisfied just winning money with the build-in "house advantage", but also by stealing it using cheating software.

The internet gaming community needs to protect itself better against these practices.

[Linus]

I suppose English Harbour has three options -

1.) Ignore it, and pretend nothing happened.

2.) Claim it was a software error.

3.) Claim the results here are bogus, and their games have always been fair.

#3 was the worst option, in my opinion. They probly should have gone with #1.

it's common knowledge that there are varying chances for winning and losing when picking a card out of four, to play against the card that is dealt face up.
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It's important that the frequency distribution of the cards in an adequate sample set are evenly distributed for each position in the doubling game.

I can't make any sense out of this.

It sounds like they're trying to imply the results could be the due to poor picking. ??? If so, they don't understand probability.

Either that, or they're just stringing together mathematical-sounding phrases, in the hope that it'll lull or intimidate the reader.

[JohnGalt]

Their response is absolutely damning.

[jeremiahsjohnso]

Right, all.

Their denial of the doubling bias is very carefully worded and does not preclude that a bias existed in the past:

<<It's important that the frequency distribution of the cards in an adequate sample set are evenly distributed for each position in the doubling game. We have found, taking several sample sets over different and varying lengths of time, that they yield in our opinion, a non biased distribution of the cards.>>

These sample sets could have all been taken after the doubling was fixed (which occurred after it was 'fixed'.)

If the game really were never rigged, they could very easily have included such a statement. I don't accuse them of lying per se, just trying to get away with a very skewed version of the truth.

[soflat]

Right, all.

Their denial of the doubling bias is very carefully worded and does not preclude that a bias existed in the past...

Well, yes it does.

because they say:

Should small sample sets be used to measure this metric, then results will vary as seems to be the case tracing through this thread.
...
We trust, that we have responded adequately and any doubt in peoples' mind are put to rest.

In other words, they are claiming we did not have an adequate sample size to prove anything.

I'm not too surprised, but I am still disappointed we can get cheated so easily by online casinos. I mean, their reputation doesn't seem to even matter to them.

[GrandMaster]

This just in from English Harbour:

Although the doubling component of Video Poker is theoretically deterministic, it's common knowledge that there are varying chances for winning and losing when picking a card out of four, to play against the card that is dealt face up.

Can someone help me? This sentence makes no sense to me.

Randomness:

It's important that the frequency distribution of the cards in an adequate sample set are evenly distributed for each position in the doubling game. We have found, taking several sample sets over different and varying lengths of time, that they yield in our opinion, a non biased distribution of the cards.

And we have found, taking several sample sets over the past week-end, that they yield in our opinion, a biased distribution of the cards.

Game Play:

In theory, the number of Wins versus the number of losses and (excluding ties) will converge to 50% over a sample set that is large enough. Should small sample sets be used to measure this metric, then results will vary as seems to be the case tracing through this thread.

Freudian slip? I would rather hope that the ratio of the number of wins to the number of losses should converge to 1. The doubling seems to be so biased that even few hundred hands give statistically significant results.

We trust, that we have responded adequately and any doubt in peoples' mind are put to rest.

English Harbour Management

Not my mind, but I will wait for the Wizard.

Just as I expected: they "fixed" the problem internally then denied it happened. If the Wiz tests the software now, of course he'll find that everything is back to normal, but the data set obtained by forum members here show that at one point the game was crooked.

I have not played at OddsOn for ages, but as I recall, there was some kid of a playcheck feature. It would be a good idea for players to save their play history now in as much detail as possible. Michael Shackleford should be able to test the cumulative results over the whole relevant period of time, not just whether it is fair now.

[thelawnet]

Do I understand this response correctly? Are EH in effect saying that these horrific results garnered by several players was the equivalent of a bad streak, but that over a large enough sample the doubling feature would come out at 50/50?

How large a sample? That doesn't sound like a very good bet for gamblers expecting 50/50 odds to me.

Their argument is based on confusion and deceit.

Basically the argument works like this:

You walk into a casino and play roulette. 125 spins in a row the wheel comes up red (this is roughly equivalent odds to the doubling we saw). You speak to the pit boss and say you know they are cheating and leave in disgust.

The next day the gaming control board comes back to test the wheel. The casino has by this time switched the wheel for a fair one. 1,000,000 spins are conducted and the results are roughly even with red/black (as the wheel has been replaced for a fair one), say 500,000 red and 500,000 black. Taking the 125 red spins together with the 1,000,000 fair spins, the result is 500,125 red, and 500,000 black. This is not unusual nor suspicious.

The problem being that they already switched the wheel. If they had continued with the old one the results would be the same.

But if you take a sample from a rigged game and add to it a relatively much larger sample from a fair game, the rigged sample no longer has much effect.

This nonsense about things evening out in the long run is just that.

Yes it's true that if you get four reds in a row, there is nothing unusual - the odds are only 1/16 - something that will happen fairly often. In this case you need a much larger sample to say that it is likely that the wheel is unfair. But the reason that four reds in a row is not enough evidence is not because the sample is too small, it is because 1/16 just isn't unusual at all. It is *extremely* important to realise that the thing that matters is the probabiltiy that the event could happen, not the sample size. The sample size only matters insofar as a trend demonstrated over a bigger sample will have a lower probability of being fair. The nonsense about sample sizes is a logical fallacy:

1. A trend demonstrated over a bigger sample size decreases the likelihood that the game is fair
2. Therefore in order for a game to be fair you must have a big sample

This is WRONG, WRONG, WRONG. The thing that matters is the chance that the event occurred randomly. It is already been shown that this is approximately a

2,016,352,813,782,491,278,292,828,543,127,849,349-1 (this is not the exact number but it is of the correct magnitude: I have printed the full number rather than using scientific notification to give an idea of just how unlikely it is)
shot

The sample size is not important, it is the chance that something occurs by chance.

English Harbour must not be allowed to cover this up by taking samples from a game they have fixed after being caught cheating.

Selecting the same grain of sand from every grain of sand on every beach in the world three times in a row just doesn't happen. Neither does 125 consecutive reds on roulette.

Nor do the video poker results we've seen here.

My guess is that someone at English Harbour who does not understand mathematics has allowed someone to blind them with this faux scientific explanation and thinks that everyone else will be convinced.

They are wrong.

Very foolish. English Harbour has unfortunately consigned its group of casinos to the record as the casino that fixed their games and then covered up.

I believe this fatal damage to reputation will prove much more expensive to them in the long term than the money they made from their unfair doubling game (although of course nobody knows how much that is - it could be substatnial).

[jeremiahsjohnso]

(this was in response to #145)

I think we're quibbling over the small points. The main issues as I see them:

1) Statistics from multiple sources here proved their VP doubling rigged beyond the shadow of a doubt.

2) The problem suddenly corrected itself.

3) The casino issued an "all as well" statement that definitely applies to how things stand after #2.

I see their response as implying that the "all is well" also applies for issue #1, but without actually saying it. And I don't have any respect for the response, which is very lawyerly when, if they really wanted to remove player doubt, should have been very direct.

If I had a vote, I'd vote "rogue".

[thelawnet]

I have not played at OddsOn for ages, but as I recall, there was some kid of a playcheck feature. It would be a good idea for players to save their play history now in as much detail as possible.

There is no such playcheck that I can find.

[Aindreas_Daoc]

I have not played at OddsOn for ages, but as I recall, there was some kid of a playcheck feature. It would be a good idea for players to save their play history now in as much detail as possible. Michael Shackleford should be able to test the cumulative results over the whole relevant period of time, not just whether it is fair now.

I tried looking just now, but couldn't find a history log. Live chat said that there is no play-check type feature, but that you can request play history directly from them.

Edit: I just requested the logs via e-mail. However, it is unclear whether they even record play money games. The support person terminated chat before I had a chance to ask.