No … whether it is a fallacy or not is contextual — otherwise nobody would ever win at cards ¹.

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¹ I’ve watched people play ‘War’ in Las Vegas and … by simply deciding, on the basis of how many higher/lower cards had appeared prior to the currently dealt card, whether to leave their last winnings on the table or not … be unable to remove the last winnings faster than the new winnings were placed on the pile.