# Probability and Scrabble

Using Probability to Improve Your Scrabble Game

Most people think of Scrabble as a word game; however, it has enormous mathematical aspects to it as well. The use of math is not just for adding up the scores too. While it is critical to have fast arithmetic skills to simply figure out what words provide the highest possible point totals, the other aspect is about understanding the likelihood of drawing certain tiles or what tiles your opponent has at key points in the game. Quite simply, Scrabble is actually a game of probability, especially when it comes to the end game.

Most good Scrabble players readily know the tile distribution, especially for key tiles. For example, there are four Us in the game. If you hold the Q, it is critical to know this so you can understand if there is a chance of pulling a U from the bag. There have been occasions when I’ve discarded the Q towards the end of the game since the Us and blanks had already been played and there were no immediate opportunities to play the Q off. By exchanging the Q for another tile, I hoped that my opponent would then draw the Q and be stuck. Should I be able to play off all my tiles and my opponent is stuck with the Q that is worth 20 additional points. Alternatively, if I have the remaining U and know my opponent has the Q, I am very reluctant to play that U to prevent my opponent from having the chance to play off the Q.

While playing Scrabble, score sheets often include the full list of tiles. This allows players to mark off letters as they are played. This constantly gives the player an understanding of what tiles are remaining as well as the likelihood of drawing any given tile after a turn. It is shows whether the bag is becoming more concentrated with vowels or consonants. To the astute player, this is valuable information. While it might seem laborious to keep track of each tile played, it provides enormous benefits during the end game. At a minimum, serious players monitor the high point tiles since these can have a game changing impact. For example, QI scored twice with the Q on a triple letter score can result in 64 points, as much as a low scoring bingo. In order to combat this, players should be extremely reluctant to place an I adjacent to a triple letter score square. This play can be repeated with the X to form XI. My previous article on two letter words highlights the power of this play. However, as the game progresses and these high scoring letters are played out, it is less risky to make plays that result in this set up. As important as it is to score points, the goal is simply to score more points than your opponents.

Knowing what tiles remain, hence the probability of drawing a certain tile is valuable when exchanging tiles as well. Clearly this becomes easier towards the end of the game. An ideal situation is when you know perhaps that there is a blank and an S left and you have a bad rack. If you exchange enough tiles, there is a good chance that you can draw the S or the blank or perhaps both. It should be noted though that this will cost you a turn.

Knowing the tiles remaining in the bag and consequentially which tiles your opponent has is critical in the end game. As you examine the board looking for places to score points, you should also be considering the plays that your opponent can make. The better your word knowledge is, the more valuable this becomes since you can anticipate your opponents plays and seek to maximize points from your counter. I’ve often made different plays than I would have by knowing what tiles my opponent has. Also during the end game you can actively seek to block your opponent if they have a difficult to play letter such as a V or C. If your opponent cannot play, you potentially have the opportunity to make two plays in a row. This is also a tremendous advantage. Close games are often won or loss simply by understanding what tiles your opponent has at the end and then playing accordingly.

So when looking at Scrabble, don’t believe it is just a word game. It is a word game with significant mathematical underpinnings. A good understanding of probability can readily be used to your advantage to draw out close wins.