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Here is an example of how the gambling house will always win all the money from all of the players. Five players sit-in on an online poker game each with a $20 bankroll for a total at the website table of $100. Let’s say the average pot is $10 and the rake is 5% or 50 cents per hand. Let’s say 200 hands are played which does not take that long. After 200 hands, that 50 cents rake per hand totals $100 which is the entire amount that all of the players started with at the website table. Of course not all of the players go broke at the exact same time and fresh money can come into the game. But sooner or later each gambler will eventually lose their $20 bankroll every time without exception. If bringing in $20 more, that will also eventually be lost. Every amount brought in will eventually be lost through continued play. Those are the facts in a nutshell. Any honest mathematician, statistician, or numbers expert who understands the game of poker, would not dispute the example in this paragraph.



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From the first sentence to the next in the bold is where the logical fallacy occurs.