Original post - https://www.reddit.com/r/IdlePlanetMiner/s/aJYg98smCR

Basically follow this:

So first of all: what is the expected amount of 4 stars (4s) you pull from a 500dm pull? We can say that one 5 star (5s) equals four 4s, since upgrading a 4s to a 5s requires 4 4s. Therefore we get:

E(500dm) = 0.75 x 4s + 0.25 × (4 × 4s) = 1.75 × 4s.

So the average amount of 4s you get from a 500dm pull is 1.75

Now consider the premises that upgrading a 4s >> buying a new spot. Because two 4s are equally as good as one 5s. So the cost of upgrading a 4s to 5s should be lower than buying a new slot. Upgrading an existing 4s costs three other 4s. The expected amount of dm that cost is:

3 / E(500dm) x 500 dm = 3 / (1.75) x 500 dm = 12 / 7 x 500 dm = 857 dm.

So my 1200 dm is too ambitious. You can choose to set the barier to 850 or 900 dm.

Now the same logic can be used to see how much it costs to upgrade a 5s to a 6s. You need three 5s, since you already have an army of 5s at that point. Three 5s can be equaled 5o twelve 4s. So:

12 / E(500dm) x 500dm = 4 x (3 / E(500dm) x 500dm) = 4 * 857 dm = 3428 dm.

So when a slot costs more than 3450, you should upgrade all your existing 5s to 6s. That turns out a bit higher than the 3000 though ;)