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I am mildly worried by someone who is obviously an experienced and competent coder not understanding how pseudorandom number generators work. As they have an initial state which is often determined at program or level load time saving the state of the game means the state of the srand[1] or the 64's equivalent is stored.

[1] http://www.cplusplus.com/reference/cstdlib/srand/

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You have missed the point. The point was that it is calculated by an algorithm (presumably a RNG), not by the user. Part of the game is that you thought you could affect the value by timing when you hit jump.

I never thought I could affect the timing. I assumed that it was just an animation.

I believe that was fixed in later Mario Party games: the animation was changed to move so quick that the player has no reason to assume they could affect the outcome.

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