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showed a very small chance the results were by chance.

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Probably true, small sample size notwithstanding.

Can't help you with the statistics lesson you ask for, but you can find all the answers to your questions with simple internet searches and some ingenuity. I have no doubt that AS A WHOLE you will conclude that internet games can not be trusted. And furthermore, I am quite certain that some sites have fair versions and "cheating" versions. There are some sort of criteria about how you play (quality of your play and the size of your bets) that will get you switched from fair program to cheating program. Others just cheat you all the time. This is probably especially true if the games are offered as a "side light" to the main business of being a sportsbook.