A bitcoin attacker's catching-up success probability

attacker_success_probability.js

// converted from C code from p.6 of the btc whitepaper
// tested with p.7's provided sample inputs
// q being the probability the attacker finds the next block
// z being the number of blocks the attacker is behind
var AttackerSuccessProbability = function(q, z) {
	var p = 1.0 - q;
	var lambda = z * (q / p);
	var sum = 1.0;
	var poisson;

	for (var k = 0; k <= z; k++) {
		var poisson = Math.exp(-lambda);
		
		for (var i = 1; i <= k; i++)
			poisson *= lambda / i;
		
		sum -= poisson * (1 - Math.pow(q / p, z - k));
    }

	return sum;
};