Is there a random element to the Stack Egg game?

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Is there some element of randomness to the Stack Egg game? If so, what is it? If not, is it then possible to determine the exact effects of each action and therefore construct an optimal path to minimize score?
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Egg Russian Roulette with Ryan Reynolds
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: jovan curayag, Caleb Oquendo, Olga Lioncat, João Vítor Heinrichs