Code:
exports.crashPointFromHash = function(serverSeed) { // TODO: check the probablity of instant crash everywhere
var hash = crypto.createHmac('sha256', serverSeed).update(clientSeed).digest('hex');
// In 1 of 101 games the game crashes instantly.
if (divisible(hash, 101))
return 0;
// Use the most significant 52-bit from the hash to calculate the crash point
var h = parseInt(hash.slice(0,52/4),16);
var e = Math.pow(2,52);
return Math.floor((100 * e - h) / (e - h));
};
Ignore all the hash related code, all it does is generate h such that h is uniform in [ 0 , 2^52 - 1]
e is 2^52
How would I find the expected value from this algorithm?
What is the probability density function?
How would I change the house edge?
Is it only " if (divisible(hash, 101)) return 0;" that gives the house an advantage?
Initially I thought it would be exponentially distributed but it's not
When doing simulations it seems that the edge is around 2% but even when removing the divisible by 101 code, the edge is around 1% and I don't understand where it comes from
Can somebody provide a deeper math insight in this? How did they come up with this way of generating crash points?