**Echip**

Action–Duration|$2

+e Cards.

+1 Action.

Strictly better than Laboratory

But requires you to destroy some cards *and* make good estimates of what 0.718 of a card is.

*Toss up your thousand Echip tokens. If 718 or more of them landed heads-up, draw a card.*

Yeah, as others also pointed out, that’s not even 2.718 cards, more like 2.00000000000000000000000000000000000000000000923322 cards. (It’s very unlikely that 218 out of 1000 more fair coins than expected come up heads.)

Here’s something elegant you could actually do with expected number of cards drawn of e: Keep picking uniformly random numbers between 0 and 1 until their sum exceeds 1. Draw a card for each number that takes.

You could even approximate this by spinning an object (e.g. a pen or bottle) on the table and tracing the places where it stops around in clockwise order. When those make a complete loop, stop and draw a number of cards equal to the number of spins it took.

(Proof: The probability that k numbers is not enough is the volume of the region in the first orthant of k-dimensional space such that x1 + x2 + ... + xk < 1. You can either do the integral by induction or notice that the partial sums x1 + ... + xi are also distributed uniformly and independently mod 1, and all of them are less than 1 if and only if mod 1 they are in increasing order, which happens with probability 1/k!. Then you sum this from 0 to infinity, getting e.)