是一级一级往上爬，还是直接跳到顶

Climbing almost always costs less in total, because the steps are priced to be affordable one at a time. What leaping buys is turns, and the page prices those turns instead of arguing about the totals.

With steps of two, three and four against a leap of twelve, climbing from the bottom costs nine and takes three turns, while leaping costs twelve and takes one.

When you are furthest behind, which is the opposite of how it feels. Leaping from the bottom buys two turns at once and spreads its premium across both; leaping when you are nearly there buys one turn and pays the whole premium for it.

In the example below the same three-point premium works out at one and a half per turn from the bottom and three per turn one step up.

Because from there both ways take a single turn, so leaping saves no time at all and there is no price per turn to quote. Putting a number there would be inventing one.

What that row does show is the premium in plain terms: paying three more for nothing but a different route.

It tells you what a turn costs, which is the half of the question that can be answered exactly. What a turn is worth depends on the game in front of you and cannot be read off any table.

A turn early in a game you are winning is worth little; a turn in a race you are losing by one can be worth any premium at all.