Buy, match, merge, then repeat
Pickaxe Tycoon's official description says players buy pickaxes, mine ore, convert ore into money, and merge pickaxes into better ones. It does not publish the full roster, prices, or a permanent merge ratio.
Open the live merge interface and note how many same-tier pickaxes it requests. Use that observed number with the merge calculator. This approach remains useful if the developer changes the balance because the calculation starts from what your server currently shows.