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Message: [QUOTE="Four Dogs, post: 709442, member: 2668"] Hi Rick. I appreciate your interest in this thread and I am willing to consider any advice or criticism you or anyone else may have to improve it, but I'm not sure I follow what your saying. Are you suggesting that in order to prove conclusively that the software is working correctly one would have to check all the tables simultaineously? This is a just a sampling. The larger the sample, the more representative of the truth the results should be. Because the number of cards in a deck is static, there are a discrete number of outcomes. In a 5 card hand there are 2,598,960 possible outcomes, and only 4 of those make a Royal Flush. In order to validate the accuracy of a shuffling algorithm by determining the deviation of expected royals to actual royals we would probably need a sample of several billion hands. I'll get back to this. We can simplify things by only considering starting hands in which case there are 1326 separate possibilities and each possibility is a fraction of that number.The starting hand AA (or any 2 cards of the same rank) can happen 6 different ways out of that 1326 or expressed as a percentage .4525%. But even though the number of possible outcomes is quantifiable, the possibility of any part of that whole is still a random event, like flipping a coin, therefore some degree of variability or spread, is inherant, and the presence of some deviation expected. Our sample so far is only a small fraction of all the hands that have ever been played on-line, so how can we assume it's accurate, even if the result we've achieved is very close to that which we expect? After all, if we flip a coin twice and get each of the possible results, our deviation from the expected result is zero, but we really haven't validated the legitimacy of the coin, have we. We validate by having a sample size that is sufficiently large not in relation to the number of possible flip attempts which is infinite, but rather in relation to the the number of possible outcomes. In the case of our coinflip we flipped the coin twice and there are in fact only 2 possibilities, so the relationship of our sample to possible outcomes was 1:1. Very poor reliability. In the case of our AA rigged test we have about 400,000 hands from PokerStars. This is about 300 times greater than our possible 1326 2 card starting hands. 300:1 with a deviation of less than 2.5%. I'd say this is accurate and would be very surprised if the next 400,000 hands didn't sharpen our confidence. Our sample from iPoker is very small in comparrison therfore the deviation is not surprisingly larger. 16,000+/- [SIZE=3]÷ [/SIZE][SIZE=2]1326 or 11:1 with a deviation of 4.9%. A pretty useless sample if you ask me. [/SIZE] One last thing just for fun. Remember our Royal Flushes? In order t0 recieve the same degree of accuracy using a Royal as we have achieved with AA we would need a sample size of about 780 billion hands. I douubt that many hands of poker have ever been played in all the history of the game. Not to mention that most of the time you'd need to go to showdown. lol So Rick. Did that answer your question?:rolleyes: [/QUOTE]

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