It doesn't matter for this hypothetical scheme. It'll always be one or the other outcome, and you will thus look prescient to one half or the other half of the victims. Each day your pool of victims cuts in half but you don't care which half it is. The scheme works regardless of how often the stock actually goes up or down. At the end, there will always be one victim who was given exactly the correct series of predictions by you ahead of time.

One way to overcome this is to calculate the percentage change of a stock compared to the percentage change of the median performing stock in the market. 50% will be perform better than the median stock while 50% will perform worse.

I've never looked into this, but I'd assume that a stock's price being the same as it started on any given day is one of the rarest results.