define compute-ev-probabilites (state-probs)
    probs = make-array 0 .. 538
    probs[0] = 1
    foreach state-prob in state-probs
       fold-into probs state-prob.votes state-probs.probability

  define fold-into (probs votes prob)
    for i from 538 downto 0
      probs[i] = probs[i] * (1 - prob)
      if (votes <= i)
        probs[i] = probs[i] + (prob * probs[i - votes])

So far so good. Now I'd like to add this function which can back out
the effects of a single state:

  define back-out (probs votes prob)
     for i from 0 to 538
      if (= prob 1)
        probs[i] (i + votes) < probs.length ? probs[i + votes] : 0
      else
        if (votes <= i) probs[i] = probs[i] - probs[i - votes] * prob
        probs[i] = probs[i] / (1 - prob)

Mathematically this works--I've actually implemented this in Common
Lisp and when I use arbitrary-precision rational numbers it works
perfectly. But when I use floating point numbers the computations in
back-out get wildly out of whack. As best as I can tell this is
because small errors introduced because (x * y) / y isn't necessarily
exactly x get propagated throughout the whole array of probabilities
and perhaps amplified by inaccuracies in the subtraction. (I can't
just use rationals because I'm actually implementing this in
Javascript whose only numeric type is double float.)

Is there some obvious way to write this so I can still use floating
point numbers but have back-out work properly. I'd be happy to trade
some precision for reversibility.