Boxes of apples

[Guest]

Hi!

There is a game with infinite levels.
On each level, I have to choose one of a random number of boxes (between 3 and 10).
Each box has a number on it, the first box always has the number 1, the second has the number 2, etc.
On each level, there is 1 box that contains a skull. If I open that box, the game is over.
The other boxes contain apples. The numbers on the boxes represent the amount of apples I get if I choose that box.
So that suggests I always have to open the box with the highest number on it.
But the numbers also show the likelihood of opening the box with the skull. Box #3 for example, has 3 times the chance of containing the skull than box #1 has.
So if I get a level with 3 boxes, the first box has a 16.67% chance of containing the skull, the second has 33.33%, and the third has 50%.
How should I play this game to get the most apples? Is choosing box #1 on levels with 3 to 6 boxes, and choosing the box with the highest number on levels with 7 to 10 boxes the way?

Thank you!

[Guest]

Reason: There are more apples in the higher-numbered boxes, but the risk of dying is significantly larger. In terms of math, the anticipated total apples
E= (n(n+1)-2i)/2

falls as box number i rises, meaning that box 1 consistently provides the best long-term benefit.