<ul>
<li>Use one hot encoding for each position, shape <span class="math-container">$(7, 27)$</span>.</li>
<li>Stack these two dimensions, shape <span class="math-container">$(189)$</span>.</li>
<li>Tile (replicate) this vector into images of the same resolution, now shape <span class="math-container">$(15, 15, 189)$</span></li>
<li>Stack them with your other observation, final shape <span class="math-container">$(15, 15, 216)$</span>.</li>
</ul>
<p>Another way is instead of replicating the <span class="math-container">$(189)$</span> vector along two axis, you can squeeze them into one single plane of <span class="math-container">$15 * 15 = 225$</span> values, and pad the unfilled part with zeros.</p>

CC BY-SA 4.0
2022-08-12T23:52:24.967Z
2022-08-12T23:52:24.967Z
Uduse
<p>Currently I'm trying to implement Scrabble with MuZero.</p>
<p>The <span class="math-container">$15 \times 15$</span> game board observation (as input) is of size <span class="math-container">$27 \times15 \times15$</span> (26 letters + 1 wildcard) with a value of 0 or 1.</p>
<p>However I'm having difficulties finding a suitable way to encode the player's rack of letters (Always 7 letters on the rack).</p>
<p>The available tiles are: 26 letters <span class="math-container">$(A-Z)$</span> and 1 wildcard.</p>
<p>A rack can also contain multiple tiles of the same letter.</p>
<p>Example: rack of player 1 is  <span class="math-container">$[A,A,C,E,T,T,H] -&gt; A:2x, C:1x, E:1x, T:2x, H:1x$</span></p>
<p>How can I represent a rack of tiles as a <span class="math-container">$(? \times)15 \times15$</span> (or other board size) matrix ?</p>

<reinforcement-learning><game-ai><muzero><observation-spaces><board-games>
Scrabble rack observation with MuZero
Thrusticy
# Scrabble rack observation with MuZero

(Asked by: username_0 on 2021-07-20)

Currently I'm trying to implement Scrabble with MuZero.

The $15 \times 15$ game board observation (as input) is of size $27 \times15 \times15$ (26 letters + 1 wildcard) with a value of 0 or 1.

However I'm having difficulties finding a suitable way to encode the player's rack of letters (Always 7 letters on the rack).

The available tiles are: 26 letters $(A-Z)$ and 1 wildcard.

A rack can also contain multiple tiles of the same letter.

Example: rack of player 1 is $[A,A,C,E,T,T,H] -> A:2x, C:1x, E:1x, T:2x, H:1x$

How can I represent a rack of tiles as a $(? \times)15 \times15$ (or other board size) matrix ?

**Tags:** reinforcement-learning, game-ai, muzero, observation-spaces, board-games


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## 1 answers

### Answer by username_1 on 2022-08-12. Score: 1

* Use one hot encoding for each position, shape $(7, 27)$.
* Stack these two dimensions, shape $(189)$.
* Tile (replicate) this vector into images of the same resolution, now shape $(15, 15, 189)$
* Stack them with your other observation, final shape $(15, 15, 216)$.

Another way is instead of replicating the $(189)$ vector along two axis, you can squeeze them into one single plane of $15 \* 15 = 225$ values, and pad the unfilled part with zeros.


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