Rand Gambling Simulation -- Always Ending Up Positive?

This simple PHP function I made simulates a gambler going to play roulette, always picking the same color. When he wins, he stays at the basic bet (1), when he loses, he doubles it until he wins.

I tried it over 50 spins, to 1000 spins, I always end up profitable.

How is that possible? Surely I got something wrong?

<?php

// starting at a 100
$bankroll   = 100;

// our choice (one color throughout the entire session)
$choice     = rand(0,1);

// just counting how many wins and losses
$wins       = 0;
$losses     = 0;

// amount of the wager
$amount     = 1;

$output     = '';

echo 'START BR: £' . $bankroll . '<br>';

// We're playing 100 spins
for ($i=0; $i < 100; $i++) { 

    $output .= $i . '. ';
    $output .= 'Betting £' . $amount . ' (';

    // Reduce the bankroll by the wager
    $bankroll = $bankroll - $amount;

    // Checking if we won, or lost
    $result  = $choice = rand(0,1) ? true : false;

    // If we win: increase bankroll by wager times two and go back to betting one.
    if( $result ) {
        $output .= '<span style="color: darkgreen;">won</span>';
        $bankroll = $bankroll + ( $amount * 2 );
        $amount = 1;
        $wins++;
    }

    // If we lose: next bet will be the double.
    if( !$result ) {
        $output .= '<span style="color: red;">lost</span>';
        $amount = $amount * 2;
        $losses++;
    }


    $output .= ')<br>';
    $output .= 'Bankroll: £' . $bankroll;
    $output .= '<br><br>';
}

echo 'END BR: £' . $bankroll . '<br>';
echo 'DIFF: £' . intval( $bankroll - 100 ) . '<br><br>';

echo 'WINS: ' . $wins . '<br>';
echo 'LOSSES: ' . $losses . '<br>';

echo '<br><hr><br>';

// Output the log
echo $output;