Wow. I took this to the nth degree to convince a colleague. Very little variance between biased and unbiased figures:

    [javascript]
    var sim = () =>{
        var percentChanceOfHeads = 99;
        var getRandomArbitrary = (min, max) => {
            return Math.random() * (max - min) + min;
        };

        let heads = 0, tails = 0;

        for (let i = 0; i < 100000; i++){
            var test1 = getRandomArbitrary(0,100);
            var test2 = getRandomArbitrary(0,100);

            if (test1 > percentChanceOfHeads && test2 > percentChanceOfHeads) continue;
            if (test1 <= percentChanceOfHeads && test2 <= percentChanceOfHeads) continue;

            if (test1 <= percentChanceOfHeads) heads++;
            else tails++;
        }

        let total = heads + tails;
        
        let heads2 = 0, tails2 = 0;

        for (let i = 0; i < total; i++){
            var test1 = getRandomArbitrary(0,100);

            if (test1 <= 50) heads2++;
            else tails2++;
        }

        var distanceClosed = Math.abs(heads-tails) - Math.abs(heads2-tails2);

        return distanceClosed;
    };

    for(let i=0;i<10000;i++)temp.push(sim()); console.log('avg variance:' + temp.reduce((a,c)=>a+c)/10000);