English Harbour casino cheating at video poker

English Harbour casino has been caught dealing non-random video poker.

A player had his suspicions that something was amiss with the double-up feature of the Tens Or Better video poker game, and so conducted a test, reporting his findings in the "mathematical proof that English Harbour is cheating" thread at Casinomeister:

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.

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.

0.0000074 equates to a 1 in 135,000 probability. Since this test was set up correctly to test the hypothesis (the video poker was cheating), the 254 hands combined with the probability give us a total of over 34 million hands required to expect one replication of this 254 hand run in an honest game.

However, the matter did not end there.

A handful of public-spirited forum members also tested the game. In total, 1537 hands were dealt, of which 522 won.

The probability of a run as bad as this is so low that it cannot be calculated in excel - somewhere in the region of 1 in 2,016,352,813,782,491,278,292,828,543,127,849,349.

This is what the original tester and another arithmetically-adept forum member had to say about this level of improbability:

The probability of winning 522 or fewer out of 1537 trials is 4.9*10^-37. It is the same order of magnitude as winning the lottery with a single ticket 5 weeks in a row.

For comparison, there are apparently 7.5x10^18 grains of sand on every beach in the world. So this is as likely as randomly picking a grain of sand from every beach in the world, and getting the same one three times.

English Harbour was contacted by Bryan Bailey of Casinomeister, and they came out with the following response:

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

Basically, this says that English Harbour believes the game is fair.

Not exactly a convincing argument in the face of the extreme evidence to the contrary.

They also claim that "small sample sets" will see varying results and are unreliable for testing fairness. Unfortunately, required sample size is in direct proportion to the improbability of the event in question. To give a graphic example: if you set out to test unfair dealing of dealer blackjacks, and your first ten hands are all dealer blackjacks, this is conclusive proof of non-random dealing, with a probability of a little under one in 14,000,000,000,000.

For this test, the 1500 hands are more than enough.

Michael Shakleford, the Wizard Of Odds, was contacted, and he had the following to say:

Yesterday, May 2, I was made aware of the issue possible irregularities in the doubling feature of Odds On software. Let me assure you that the Odds On management and myself are taking this very seriously. As soon as possible I plan to conduct an analysis of all double or nothing bets made since January 1. If necessary, Odds On will hire a third party to conduct the same study. Until we have had a chance to review the log files we can neither confirm nor deny the accusations.

I will say now that indeed I have auditing most of the Odds On casinos, including the English Harbour. Also, I agree with the original post that the probability of 84 or fewer wins in 235 resolved bets is 1 in 135929.

...see his post at Casinomeister.

Michael is in fact the official "auditor" for English Harbour:

All online games are produced using Vegas Technology and have been audited for fairness of play by an independent third party gaming expert, Mr. Michael Shackleford ASA, who's Gaming Audit practice is located in Las Vegas, Nevada.

The results of this ongoing audit indicate that the random number generator is truly random and accordingly, the game play results conform with accepted statistical norms.

To acknowledge this commitment to fairness, the "Certified Fair Gambling" seal has been applied to all games produced using Vegas Technology

Note: The most recent CFG audits are undertaken on a monthly basis

Whatever Michael's review shows, the fact remains that the results of this test were FAR more conclusive than even the results of the Casino Bar experiment, where 332 hands were tested with a probability of one in 238,000,000,000.

Over 1537 hands, the probability of a result like this in a fair game is one in 2,016,352,813,782,491,278,292,828,543,127,849,349.

English Harbour cheat at video poker.

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