Bitcoin Attacker Success Probability,Javascript version. Reference Satoshi Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System", 2008.

AttackerSuccessProbability.js

/**
* Reference Satoshi Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System", 2008.
* The attacker's potential progress will be a Poisson distribution with expected value.
* @param [Number] q Probability the attacker finds the next block,(double).
* @param [Number] z The attacker will ever catch up from z blocks behind,(int).
**/
function AttackerSuccessProbability(q,z){
  //p = probability an honest node finds the next block
  //q = probability the attacker finds the next block
  let p = 1.0 - q;//Binomial Random Walk
  let lambda = z * (q / p);//The average expected time per block
  let sum = 1.0;
  let i, k;
  for (k = 0; k <= z; k++){
  	let poisson = Math.exp(-lambda);
    for (i = 1; i <= k; i++)
      poisson *= lambda / i;
    sum -= poisson * (1 - Math.pow(q / p, z - k));
  }
  return sum;
}

///Running some results, same as the paper.
let P,Q,Z;
Q=0.1;
console.log(`q=${Q}`);
for(Z=0;Z<=10;Z++){
	P = AttackerSuccessProbability(Q,Z);
	console.log(`  z=${Z} P=%s`,P.toLocaleString(undefined, {minimumFractionDigits:7,maximumFractionDigits: 7}));
}

Q=0.3;
console.log(`q=${Q}`);
for(Z=0;Z<=50;Z+=5){
	P = AttackerSuccessProbability(Q,Z);
	console.log(`  z=${Z} P=%s`,P.toLocaleString(undefined, {minimumFractionDigits:7,maximumFractionDigits: 7}));
}

console.log(`P < 0.001`);
for(Q=0.10;Q<=0.45;Q+=0.05){
	Z=-1;
	do{
  Z++;
  P = AttackerSuccessProbability(Q,Z);
  }while(P>=0.001);
	
	console.log(`  q=%s z=${Z}`,Q.toLocaleString(undefined, {minimumFractionDigits:2,maximumFractionDigits: 2}));
}