The “did we cross zero?” logic

The first step is “up”. For each consecutive step, as long as the cumulative proportion of “ups” remains ≥ 50% then you have NOT crossed zero.
At each step, ask “is the the proportion of up moves by the ith period >50%?” If that ever happens then we’ve crossed zero. Translating to Excel logic:
notion image
If the proportion of ups by the ith step is ≥50% then we answer “yes” or 1. If not, we answer “no” or zero.
When we multiply all the responses, any zero will make the answer to the whole question of whether we crossed zero an affirmative.
This is path #21 which did not cross zero.
notion image