[GrandMaster]

Originally Posted by thelawnet

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.

I would use the chi square test. These data give a chi square value of 19.95 with 2 degrees of freedom. The probability of a chi square value being at least this much is about 0.000047 or 1/21500. This could just be bad luck, but then we have the next sample.

Originally Posted by 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.

Chi square value 20.06, probability 1/22700. This is not looking good for English Harbour. If we combine the samples, the chi square value is 37.77, probability 1/159000000.

Originally Posted by thelawnet

Actually my analysis was spot on, it was not basically spot on.

The binomial distribution is the distribution of n trials of a 2-valued event with probability p.

The result you have used is the normal approximation to the binomial distribution. The only reason to use the normal distribution for this is if it is inconvenient to use the binomial distribution (which it is not if Excel calculates it for you). The binomial distribution is exact.

As you say, it does not make much difference, but the binomial distribution is the better one to use here.

This is totally correct.