Free Tarot Readings

Fair coin toss


Imagine a line of people flipping coins in order. If the first man flips heads, he wins, and the second man loses. A loser cannot flip. The first man flips again, since he won, and now flips tails. He loses and the 3rd man is the winner. The 3rd man flips… etc

This continues to the last man. Last man standing wins all.

How do we even odds so latest ones are not more likely to win.

Example: with no intervention in changing the odds, the last one to flip a coin is more likely to win than the first in line as he has challenged less people.

To make it fair to all, we need to decrease the likely hood that the next challengers odds are decrease, but by how much? By 1 divided by (number of flips + 1). So 2nd challenger (and 1st) have 1/2 chance to win. The 3rd challenger has a 1 in 3 chance to win, etc.

Javascript code

<script>

//line of people flipping coins in order. how do we even odds so latest ones are not more likely to win

var number_of_people = 10;
var number_or_runs = 10000;

var wins =[];
for (var run = 1 ; run <= number_or_runs ; run++){
        var last_winner = 1;
        for (var person = 1 ; person <= number_of_people ; person++){
                var win = Math.floor(Math.random() * ( person ) ) + 1;
                if(win == 1){
                        last_winner = person;
                }

        }
        if (typeof wins[last_winner] === 'undefined') {
                wins[last_winner] = 0;
                }
        wins[last_winner]++;
}

document.write( 'Times each man won:' );
document.write( wins.toString() );

</script>

JS output:

PHP code

/*
$number_of_people = 10;
$number_or_runs = 1000;
$wins = array();

for ($run = 1 ; $run <= $number_or_runs ; $run++){
        $last_winner = 1;
        for ($person = 1 ; $person <= $number_of_people ; $person++){
                $win = rand( 1 , $person);
                if($win == 1){
                        $last_winner = $person;
                }

        }
        if( ! isset( $wins[$last_winner] ) ) {
                $wins[$last_winner] = 0;
                }
        $wins[$last_winner]++;
}
*/