The Break-even Algorithm
The break-even algorithm instructs you to rent for 9 days and buy skis on the morning of day 10 if you are still up for skiing. If you have to stop skiing during the first 9 days, it costs the same as what you would pay if you had known the number of days you would go skiing. If you have to stop skiing after day 10, your cost is $19 which is 90% more than what you would pay if you had known the number of days you would go skiing in advance. This is the worst case for the break-even algorithm.
The break-even algorithm is known to be the best deterministic algorithm for this problem.
Read more about this topic: Ski Rental Problem