Average cost of an item from container with different chances

Question

i need to find average cost for every item in container. It costs 50 currency to open one. I have following chances for items:

• lvl-1: 58%
• lvl-2: 24%
• lvl-3: 12%
• lvl-4: 6%
• and lvl-5 is not included in it.

The thing is that i can get N lvl item by merging two N-1 lvl items. So lvl-5 is obtainable only by merging two lvl-4 items.

What is the right way to calculate average/expected cost of each item?

Answer 1

From comment:

If you were allowed to swap either way at no cost between $k$ items at level $n$ and $2k$ items at level $n−1$,

then in a sense you expect to get the equivalent of $1×0.58+2×0.24+4×0.12+8×0.06=2.02$ level $1$ items each turn at a cost of $50$,

so with an effective cost of $\frac{2500}{101}\approx 24.75$ per level $1$ item,

with each higher level being double the effective cost of the previous level.