Workshop › Memory › Step 12 of 25

A fair shuffle

What we are doing

Right now the pairs sit side by side. We shuffle the deck with the Fisher–Yates shuffle: walk from the last position to the first, and swap each one with a random position from 0 up to it. Every order is equally likely.

```js
// Fisher–Yates: every order is equally likely.
function shuffle(items) {
  for (let i = items.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1))
    ;[items[i], items[j]] = [items[j], items[i]]
  }
  return items
}

  const deck = shuffle([...SYMBOLS, ...SYMBOLS])
```

What it means

• i goes from the last position down to 1 (i-- subtracts 1).
• j is a random position from 0 to i: Math.random() is 0 up to 1, times i + 1, rounded down.
• [items[i], items[j]] = [items[j], items[i]] swaps the two items. The leading ; stops JavaScript from gluing the line onto the one before.
• The range must shrink with i; picking j from the whole array would be biased too.

Your turn

1. Above function newGame, write the comment and shuffle, then an empty line.
2. In newGame, wrap the deck in shuffle( ... ).

Skills: Arrays and objects, Functions

← The face of a card Which card is at a point? →

All steps

1. Get the canvas and the pen
2. The table
3. One card
4. A row of cards
5. Four rows
6. Every fruit twice
7. Cards that know themselves
8. A card's corner
9. Draw the cards from the list
10. Draw again and again
11. The face of a card
12. A fair shuffle
13. Which card is at a point?
14. Click to turn a card
15. One place for the rules
16. Two cards at a time
17. Pair or no pair
18. Count the moves
19. Show moves and pairs
20. All pairs found
21. Play again
22. A number that follows
23. Swap sides halfway
24. Animate the turn
25. Build it yourself: your best game