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The final outcome looks random enough which would be the more obvious way to rig a game!
I forgot to comment this, your most obvious error.
The final outcome is NOT random. It is only random under the assumption of getting a NON-random first hand! Thus, the end result, just like the result on the first hand is NOT random. IFF the first hand would have been random, the stats indicates that the final outcome would be random, but in this case the first hand was NOT random.
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