Archie, the archaeologist, has discovered 50 valuable gold coins, which he needs to ship to Zurich. Using an insured courier is expensive, costing $50\%$ of the shipment value. On the other hand, Archie knows of smuggler, named Smullyan, who claims to only deduct one coin as fee from a shipment of any number of coins. However, Smullyan is not only perfectly rational, but also a scoundrel, and will steal an entire shipment if he feels this is profitable.
In order to entice Smullyan into being honest, Archie makes the following promise:
"I will divide my gold into packages of size $s_1,s_2,\dots, s_n$, and tell you this ordered list. I will send the first package of size $s_1$ with you, and as long as you don't take more than your standard fee for the first $k-1$ packages, then I will let you deliver the $k^\text{th}$ package. However, if you ever cheat me, then I will use the insured courier for the rest."
Archie realizes he is promising to act irrationally, since Smullyan will always steal the last package if they get that far. Unlike Smullyan, however, Archie is an honest man, and Smullyan knows this to be true.
Smullyan replies,
"Since you are being so kind (or stupid, Smullyan thought), I will do something I don't normally do. Every time I considering stealing from you, and would gain the same either way, then I won't steal."
Archie is touched by the gesture.
How should Archie choose the sizes $s_1,\dots,s_n$ in order to minimize the amount of money he loses to theft, smuggling fees, and courier fees combined? Was this a stupid proposition after all?
Clarifications: Coins are indivisible, so all $s_i$ must be positive integers (positive so that Smullyan can deduct his fee). The reason the courier can charge $50\%$ is because the courier fee is payed legal tender, not in ancient coins. Archie is indifferent between losing coins and losing their cash value (he plans to sell them anyway).
Source: The Puzzler's Elusion, Dennis E. Shasha