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If you flip a coin and it comes up heads, the probability will remain 50% on the next flip.

I think there was a case at a casino in Montreal where the numbers in a keno game were chosen by computer which automatically reset after a power failure and generated the same numbers when it did (due to the fact that the backup battery was dead). The pseudo-random number sequence was randomized to the time which always reset to zero. Some observant patrons made some money off this.