# math nerds only

As an aside, it turns out it’s not very painful to pay hundreds of
dollars to one’s own startup. I’ve lost \$110 on my own yellow brick
roads so far. I should probably go back to selling my contracts to
friends, or do things like pledge the money to whoever catches me off
my road, a la blog.bmndr.com/rails . The rest of you shouldn’t have
that problem though, in theory.

So, here’s the cost of going off your yellow brick road the ith time:

f(i) = \$0 if i=1
f(i) = \$5 if i=2
f(i) = f(2)23^(i-3) otherwise.

Robbie Clarken rightly asks, why not just use 3^i?
Well, I was a little fixated on the constraint that whatever amount
you currently have at risk, the sum of the previous amounts you lost
is half that much.
The above formula is the only way to achieve that.
But if we just went with f(i) = 3^i then the ratio of previous total
lost to current amount at risk would start at 1/3 and asymptotically
approach 1/2.
That’s arguably even better and certainly makes for an elegant formula.
Of course, we need f(1) = \$0 so some inelegance has to creep in.
I’m thinking 3^i but rounded to the nearest \$10: f(i) = 10*round(3^i/10).

That gives this:

f(1) = \$0
f(2) = \$10
f(3) = \$30
f(4) = \$80
f(5) = \$240
f(6) = \$730
f(7) = \$2,190
f(8) = \$6,560
f(9) = \$19,680
f(10) = \$59,050
f(11) = \$177,150
f(12) = \$531,440
f(13) = more than it’s possible to charge to any credit card

Obviously unless you have a major equity stake in Beeminder you won’t
ever be willing to get very deep into that fee schedule.
But the choice of f(2) matters a lot.
Do you all have opinions about whether the first amount at risk should
be \$5 or \$10 or something else?

I’m getting the impression that the real hurdle is not the amount but
putting in your credit card at all.
Some of that is uncertainty about our credit card processing so we
I’m not sure how quickly we’ll do that though so I’d like to convince
at least you harder core fans in the meantime that our current credit
card processing is very safe! I added a little more to the FAQ at