gistfile1.txt

<?php

$packs = [];
$swaps = [];

const ATTEMPTS = 5000;
const CARDS_PER_PACK = 5;
const TOTAL_UNIQUE_STICKERS = 680;
const COST_PER_PACK = 50;
const COST_PER_MULTIPACK = 275;
const PACKS_PER_MULTIPACK = 6;

for ($attempt = 0; $attempt < ATTEMPTS; $attempt ++) {
    $packs[$attempt] = 0;
    $swaps[$attempt] = 0;
    $duplicatesInSamePack[$attempt] = 0;
    $stickers = array_fill(0, TOTAL_UNIQUE_STICKERS, false);
    while (in_array(false, $stickers)) {
        $packs[$attempt] ++;
        $thisPack = [];
        for ($j = 0; $j < CARDS_PER_PACK; $j ++) {
            
            do {
                $r = rand(0, TOTAL_UNIQUE_STICKERS-1);
                if (isset($thisPack[$r])) {
                    $duplicatesInSamePack[$attempt] ++;
                }
            } while (isset($thisPack[$r]));
            
            $thisPack[$r] = true;
            
            if ($stickers[$r]) {
                $swaps[$attempt] ++;
            } else {
                $stickers[$r] = true;
            }
        }
    }
}

$averagePacksBought = (array_sum($packs) / ATTEMPTS);

$multiPacksRequired = floor($averagePacksBought / PACKS_PER_MULTIPACK) + ($averagePacksBought % PACKS_PER_MULTIPACK == 0 ? 0 : 1);

$costBuyingMultiPacks = ($multiPacksRequired * COST_PER_MULTIPACK);
$costBuyingSinglePacks = ($averagePacksBought * COST_PER_PACK);

echo "Average packs bought = " . number_format($averagePacksBought) . PHP_EOL;
echo "Average duplicates rejected per attempt = " . number_format(array_sum($duplicatesInSamePack) / ATTEMPTS) . PHP_EOL;
echo 'Cost (buying multipacks at ' . number_format(COST_PER_MULTIPACK / 100, 2) . ' for six packs) = ' . number_format($costBuyingMultiPacks / 100, 2) . PHP_EOL;
echo 'Cost (buying single packs at ' . COST_PER_PACK . 'p each) = ' . number_format($costBuyingSinglePacks / 100, 2) . PHP_EOL;