Topics relating to this question:
Why is the number of times to get up after having fallen down for seven times counted as eight instead of seven?
- Opinion 1: Seven and eight are used to express large numbers, not intending to express logical numbers, and seven and eight sound better 語呂｛ごろ｝がいい than seven and seven when read continuously.
- Opinion 2: At first, the state before falling down is counted for one time.
(This interpretation is already written in Tommy's answer) - Opinion 3: Under the influence of a proverb 「転{ころ}んでもただでは起{お}きない / 転{ころ}んでもただでは起{お}きぬ」, the last state to get up is counted for two times at a time.
The meaning of 転{ころ}んでもただでは起{お}きない is as: To learn something even from a mistake. To turn anything into profit. Even if you may fall down many times, each time you get up with picking up something in taking advantage of the opportunity.
In the case of 七転び八起き, the person gets up with picking up another count except for himself at the last time.