I was trying to simulate the Secretary problem in JS, expecting to get a value of 1/e (~37%), but what I am getting is much less (~10%), and it was changing, increasing people would decrease it.
This is what I tried, I think the error might be the let x=new Array(people).fill(0).map(e=>Math.random()) . I was expecting 37%, but got ~10%
//number of people, and also number of results
let people=100
//multiple trials to smooth data
let trials=1000;
let results=new Array(people).fill(0);
// creates a percent, i/people, for each initial group that is "turned down"
for (var i=0;i<people;i++) {
// runs a few times to smooth data
for (var j=0;j<trials;j++) {
//x is new random set of people, values in [0,1]
let x=new Array(people).fill(0).map(e=>Math.random());
//"rejected set"
let min=Math.max(...x.splice(0,i));
//select the first person better than the "rejected" set
let select=0;
let selected=false
for (var k of x) {
if (k>=min && !selected) {
select=k;
selected=true;
}
}
//increase results by selected or last person
results[i]+=select!=0?select:x[x.length-1];
}
}
//strategy to get highest average score
console.log("Best strategy: "+(results.indexOf(Math.max(...results))/people*100)+"%");
I also plotted some of the data on desmos here.
I don't understand how you count the number of successful trials to compute the probability. Try to replace the counting logic as follows.
for (var k of x) {
if (k > min && !selected) {
select = k;
selected = true;
} else if (k > select && selected) {
selected = false;
break;
}
}
//increase results by selected or last person
results[i]+= selected
Basically, your trial is successful only when the first higher than min value is the total maximum. This gives values close to 1/e*100 for me.