I think the equation is going to be exponential, because on average, for each coin toss, you'll have 1/2 heads and 1/2 tails. That is, the number of coins that you remove for each round is going to be, on average, half of the coins you tossed. It's exactly like the exponential decay of radioactive materials. So I would assume a function of the form

where

is the number of coins remaining at toss

, and

is the initial number of coins. You already know

. The trick is to figure out the

. I would probably use a

least squares fit procedure. That is, try to minimize the error of

Set

and off you go.

Another equivalent approach would be to plot the logarithm of your data (essentially, you're plotting on a semilog plot). Then you can fit a straight line to the data. Theory:

and therefore

So, if you define a new variable,

then you've got yourself the equation

You can fit a straight line to that from your data, which is quite straight-forward to do in Excel, for example, and from that you can get your

. This is probably the easiest way to go.