That doesn't seem correct. For the second case, where the mine contains $220M in deposits, shouldn't it be:
-$100M cost to build mine
+$220M revenue from sale of deposits
------------------------------------
$110M profit
That leaves you with $220M from the sale of deposits less $55 million for the 50% tax on the $110M profit, so you end up with $165 million.
So, starting with $100M to invest, half the time you end up with $0, half the time you end up with $165M, giving an average outcome of $82.5M, for an average return of -17.5%.
Without a tax, half the time you end up with $0, and half the time you end up with $220M, so the average outcome is $110M, for an average return of 10%.
So, starting with $100M to invest, half the time you end up with $0, half the time you end up with $165M, giving an average outcome of $82.5M, for an average return of -17.5%.
Without a tax, half the time you end up with $0, and half the time you end up with $220M, so the average outcome is $110M, for an average return of 10%.