Mathematical Proof that English Harbour is cheating

[spearmaster]

Originally Posted by erp1

The Holy Grail for fairness in a card game is that each not exposed card has exactly the same probability to be the next exposed card.

We should not focus on regrettable but inevitable programming errors. We ought to focus on system errors.

According to the information we have now, the bonus game that apparently caused the biased result produced those biased results exactly because the game was meant to deal the cards weighted. We still don’t know exactly how and why the code for the bonus game in test mode influenced the doubling feature for games played in production mode.

What stands is that Spearmaster in detail has exposed that they deliberately were manipulating with the Holy Grail for fairness in a card game.

Add to that an unbelievably break of some of the fundamental guidelines for programming.

I think we should all thank Spearmaster – not attack him. He has helped us to gain a reasonably balanced insight in the events. We can now discuss and interpret based on facts.

Thanks to Spearmaster we now know that the biased outcome of the doubling facility in the second half of April is the consequence of a combination of inevitable bad programming praxis and manipulation with the Holy Grail for fairness in a card game.

Again, the card game itself was not being manipulated, nor was the doubling game (not intentionally). It was a bonus game/event which was to be randomly triggered on a doubling WIN, allowing the player to win a multiplier of the value of the doubled win. The multiplier ranges from 0.5x (meaning you'd only win half of the double - but still a win nevertheless) to 10x.

[spearmaster]

For the record, my lunch consisted of a crappy hamburger, some fries and a couple of beers Meister, though, went whole hog... he had pasta with asparagus and a couple of beers And he mooched some of my fries...

The discussion was very frank and open - they are obviously concerned that they are getting the cold shoulder even though they admitted their mistake and paid 120% of any ties or losses - and naturally they are anxious that this issue should be cleared up.

I told them that the best I could do was provide as detailed an explanation as I could and they were satisfied with that.

Mitch - in answer to your questions, the glitch affected all EH group casinos, and possibly a small number of bets elsewhere, as the gaming server is the same. All coding is controlled by the software provider and the casino operators do not have access to this code.

One more explanation - the first statement they made was based on a testing of all results from January to May 2 - and because of this the results were very close to normal despite the period during which the new code had been introduced.

It was only after they examined the logs on a daily basis, rather than over a specified period of time, that they discovered the problem - and this is why the first statement appeared to be a rash, knee-jerk statement. I know that they regret not having done more comprehensive testing for daily results but as it stands they must accept sole responsibility for that statement and the subsequent uproar that ensued.

[erp1]

Originally Posted by thelawnet

What has been described is a cheating game. A broken cheating game, stuck in by mistake, yes, but still a cheating game.

I agree. That is excatly what has been exposed.

The cheating game might well have been stuck in by mistake. But it doesn't mean that the affair is forgivable because of lack of intention. Odds On/ English Harbour has in praxis demonstrated that they find it's ok to develp card games that break with the founding principle that each not exposed card has equal probability to be the next exposed card.

We must as players in praxis demonstrate that we have no tolerance for software providers and casinoes that is willing to break with the most founding principles of fairness in a card game.

[thelawnet]

Originally Posted by spearmaster

For the record, my lunch consisted of a crappy hamburger, some fries and a couple of beers Meister, though, went whole hog... he had pasta with asparagus and a couple of beers And he mooched some of my fries...

The discussion was very frank and open - they are obviously concerned that they are getting the cold shoulder even though they admitted their mistake and paid 120% of any ties or losses - and naturally they are anxious that this issue should be cleared up.

I told them that the best I could do was provide as detailed an explanation as I could and they were satisfied with that.

Mitch - in answer to your questions, the glitch affected all EH group casinos, and possibly a small number of bets elsewhere, as the gaming server is the same. All coding is controlled by the software provider and the casino operators do not have access to this code.

So why did it not affect Hot Pepper Casino, as we found at the time?

That does not make sense.

[spearmaster]

Originally Posted by erp1

I agree. That is excatly what has been exposed.

The cheating game might well have been stuck in by mistake. But it doesn't mean that the affair is forgivable because of lack of intention. Odds On/ English Harbour has in praxis demonstrated that they find it's ok to develp card games that break with the founding principle that each not exposed card has equal probability to be the next exposed card.

We must as players in praxis demonstrate that we have no tolerance for software providers and casinoes that is willing to break with the most founding principles of fairness in a card game.

I want to correct this apparent misconception. Thus I will illustrate in a text manner what happened, though obviously I will work on a flowchart later.

Player has winnings, and chooses to double.
Dealer is given one random card.
Four random cards are drawn from which player selects one.

If player loses, end.

If player wins, random bonus game may be triggered (as the game is in testing mode 100% of wins will initiate bonus game).

Player is given choice of whether they wish to play the bonus game or not (as the game is in testing mode assumes player wants to play bonus game).

Four random cards are drawn from a weighted deck. Information is supposed to be written to "bonusgame" array, but instead is incorrectly written to "double" array.

Game malfunctions and returns null because certain other objects and properties are non-existent.

Error is trapped - and goes back to compare the normal doubling game - only now the four random cards have four NEW random, weighted cards in the array.

Result is evaluated again - thus automatically making all wins be re-evaluated against the new player card - and of course there is a slightly increased chance of a loss because of weighted distribution - BUT what is worse is that 100% of wins are now re-evaluated and thus many will be returned as loss or tie.


At no time is the doubling function weighted - it performs exactly to normal standards. If a player were to have the ability to choose whether or not to play the bonus game (which is what is intended but for testing the choice was assumed to be yes), and the player were to decline the opportunity to play the bonus game, everything would have been just as normal.

[spearmaster]

Originally Posted by thelawnet

So why did it not affect Hot Pepper Casino, as we found at the time?

That does not make sense.

As I pointed out, a small number of results at other casinos were affected. I presume that you tested in free play mode - and thus this would not have been recorded in the logs.

So yes, it did affect Hot Pepper Casino as well.

[spearmaster]

The problem with the bonus game is that they chose to use cards - but for all intents and purposes they could have used 52 different symbols like star, ball, square etc. with different colors red, green, blue etc. and because there were 52 elements, the exact same thing would have occurred because the same number of elements are present in both the doubling and bonus games.

Had there been fewer elements, losses would have been greater.

[thelawnet]

Originally Posted by spearmaster

One more explanation - the first statement they made was based on a testing of all results from January to May 2 - and because of this the results were very close to normal despite the period during which the new code had been introduced.

NEE NAW

BAD ANSWER

They lose.

Let's go back and look at the logs

The game was playing fairly from April 1 to April 12th, and for this period there were a total of 11,293 wins, and given that it was a 50/50 game, a similar number of losses. After April 12th the number of wins dropped sharply, because people lost all their money and also sensed the game was unfair

From January 1st - April 12th there are 31 days + 28 days + 31 days + 12 days = 102 days

Given 11,293 * 2 win/losses in 11 days, then in 102 days there are 11,293 * 2 / 11 * 102 = 209,434 wins and losses. You would expect:

104717 wins, 104717 losses.

Then for April 13th - May 2nd, there were 2,626 wins and 5,166 losses.

So from January 1st to May 2nd there would be a total of

104717 + 2626 = 107,343 wins
104717 + 5166 = 109,883 wins

out of
107,343 + 109,883 = 217,226 trials

The mean number of wins (for a fair game) from 217,226 trials is 217,226 * .5 = 108,613.

The standard deviation (for a fair game) is given by sqrt(npq) = 217,226 * .5 * .5 = 233

The actual result, around 107,343, is no less than five and a half standard deviations from the mean.

This is a probability of 0.00000025 (40 million to one against) of being from a fair game. THIS IS NOT VERY CLOSE TO NORMAL. It is not even in the same ballpark as normal.

Given that during the rigged period the number of wins was 1270 less than expectation, to have a 'close to normal' result, let's say 2 standad deviations (which is actually a generous standard to them, as when you have been presented prima facie evidence of cheating, any kind of result below the mean should make you examine things *very* closely) away from the mean, a sample size of 1270 / 2 = sqrt(n * .25)
n = 635^2 = 403,225 would be required for the period.

That would mean roughly 4,500 wins & losses per day for all of January, February and March (for which logs have not been provided). This is over double the number they were getting at the start of April. This is not plausible.

Fact is, that the claim that when you mixed in the bad results with a few months good data it looked 'normal' is crap - it actually would have looked very abnormal, because you had 5.5 -ve sds from the rigged period. Not quite winning the lottery five weeks in a row bad, but certainly far more than bad enough not to issue the kind of bullshit statement they put out.

How can we trust them given this?

It was only after they examined the logs on a daily basis, rather than over a specified period of time, that they discovered the problem - and this is why the first statement appeared to be a rash, knee-jerk statement. I know that they regret not having done more comprehensive testing for daily results but as it stands they must accept sole responsibility for that statement and the subsequent uproar that ensued.

[Vesuvio]

Originally Posted by spearmaster

The weighting would have only been on the bonus game. The doubling game itself would still have been normal.

That's exactly what I assumed, but as I understand it this bonus game would still have functioned by dealing weighting cards. Whether it's a doubling game or a bonus game weighted cards are going to deceive the player. If they were going to use this game fairly they'd have to announce that they were dealing weighted cards... but then the players would have no confidence in their other card games. Therefore no sane casino would ever introduce such a game. Therefore the overwhelming likelihood is that they were just planning a way to cheat players. Whether they introduced it deliberately or accidentally would surely be irrelevant.

[Vesuvio]

Originally Posted by spearmaster

The problem with the bonus game is that they chose to use cards - but for all intents and purposes they could have used 52 different symbols like star, ball, square etc. with different colors red, green, blue etc. and because there were 52 elements, the exact same thing would have occurred because the same number of elements are present in both the doubling and bonus games.

Had there been fewer elements, losses would have been greater.

This is beginning to border on the comical! Did you perhaps consider why they chose to use cards instead of random symbols. Might it possibly have involved the fact that the player assumes cards will be dealt with natural distributions rather than weighted!??