re: 2, then 1.5, then 1, then .5, then -0 Game Over

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Every play as to take at least 1 second off the clock...

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Not every play. you could clock the ball fast enough at 4:32 in the fourth and have the clock still read 4:32. Internally the clock reads 4:32 and 9 tenths. One tenth after they start the clock it would read 4:33. But a play where the ball is snapped in the last second of a period has to take 1 second off because there are no more full seconds to be displayed.