Although my return is well within statistical expectation – 0.5 SDs – I remain very much unconvinced that this game is dealing in random manner. The whole nature of the game has seemed, from the outset and for want of a better word, wacko. It feels like a blackjack slot machine, delivering winning and losing runs far greater than a genuine game.
I decided to try and test this contention, by comparing randomly chosen 2000-hand samples against a 2000-hand sample that I would deal manually (yikes). I would compare them by noting all the non-winning and non-losing sequences, from sequences of four upwards.
An example of a 4-hand “non-win” is: L/P/L/P
An example of a 4-hand “non-lose” is: P/W/W/P
Two winning splits count as two wins, and vice versa.
A W/L split counts as a push, so a sequence of win / win / win / lose-win split counts as a 4-hand non-lose.
I could explain this in more detail – and in fact there are several more explanations necessary to give an accurate account of my tracking system – but the only really important matter is that the criteria are applied consistently.
I have to date tested five randomly chosen 2000-hand samples of the Pharoahs game, in addition to noting all the above sequences in my 2000-hand manual sample. I will not detail the numbers for each sequence of each sample, as it would be unnecessarily cumbersome. I’ll post some relevant summaries.
NL = “no lose”, and NW = “no win”
TOTAL SEQUENCES:
My sample:
NL = 51
NW = 90
Total = 141
Boss sample 1:
NL = 75
NW = 84
Total = 159
Boss sample 2:
NL = 67
NW = 98
Total = 165
Boss sample 3:
NL = 65
NW = 85
Total = 150
Boss sample 4:
NL = 70
NW = 92
Total = 162
Boss sample 5:
NL = 66
NW = 78
Total = 144
The immediate conclusion here is that my manual sample contains fewer overall runs than ANY of the Pharoah’s samples.
It’s also noteworthy that there are less WINNING runs in the manual sample than any of the Pharoah’s samples.
The next example is details of the most prolific runs, the shortest, ie. the 4-hand sequences, and these are quite extraordinary:
My sample:
NL4 = 17
NW4 = 31
Total = 48
Boss sample 1:
NL4 = 43
NW4 = 32
Total = 75
Boss sample 2:
NL4 = 23
NW4 = 31
Total = 54
Boss sample 3:
NL4 = 36
NW4 = 52
Total = 88
Boss sample 4:
NL4 = 36
NW4 = 46
Total = 82
Boss sample 5:
NL4 = 24
NW4 = 29
Total = 53
The exact same conclusion here:
1) My manual sample contains less 4 NW / NL sequences than ANY of the five Pharoahs samples to date tested.
2) Although the losing sequences are there or thereabouts in relation to the manual one, the winning sequences are off the scale, being double the random amount on two out of the five, and just under TREBLE on one occasion.
This evidence supports my contention, it cannot be denied. Of the six samples, the random sample is far and away the least “streaky” (hate that word).
The question is: I know there are going to be calls from the “random brigade” that this is insufficient testing, that the fact that the Pharoahs game fails spectacularly on all fronts over the five test, five tests (or 10,000 hands) is not enough.
So how many tests would you like? I would like Ken to answer this question. I have about 180 pages of 200-hand data, and hence I could conceivably run 170 tests, pages 1 – 10, 2 – 11, 3 – 12 etc etc. I contend that each and every test will throw up results exactly in line with the above, and that not one Pharoahs sample will be less streaky than the random sample.
At what point will my results conclusively prove that this game is dealing in non-random fashion? If each and every 170 tests show sequences above my random sample, this can only be far more than sufficient evidence. Already, the five random 2000-hand tests are very damning in my opinion.
Equally, I could (painfully) produce another 2000-hand manual sample and add it to the previous one as double the genuine data for comparison with the Pharoahs data.
Opinions sought.
