This article is the fourth post in my series “No Tile Left Behind” focusing on leaves. For a list of articles on this topic, click here.
You might be thinking to yourself: “Okay, great, all this data is fine and dandy, but how does this help me? I’m not going to memorize all of this information, and I don’t have access to all of this data in the middle of the game.” And you’d be absolutely right: no one in any game would take the time to memorize all of this data. Instead, we memorize individual data points and use general heuristics (or rules of thumb) to approximate this data until we get an innate sense of leave in our minds. At some point, the notion of leave becomes so internalized that we aren’t even aware of our calculations.
The best way for most people to evaluate a leave is by using a heuristic called anchoring and adjustment. Anchoring and adjustment makes a rough approximation on the average worth of a leave and then adjusts that approximation based on the current position. Players try to approximate the value of a specific leave on all boards and then adjust their approximation based on the options available. In practice, players have different ways of performing this heuristic. Some people use strict mathematics to find an anchor: they add up each tile value, quantify the synergy, and numerically adjust their leave based on the board. Others use a more intuitive assessment to acquire a “feel” to assess the worth of a leave.
At first, the best way is to develop a rote, somewhat robotic way of understanding leave values. As you gain more experience, then you can develop more sophisticated and intuitive ways of thinking about leave. Here is the checklist every new player should go through to calculate leave:
1. Memorizing an anchor by adding up all the tile values. Players usually memorize a list made from books, websites, or computer programs such as Quackle.
AINU = 0 – 1 + 0 – 6 = -7
2. Adjust that anchor based on basic metrics such as synergy, vowel-consonant ratio, and duplication.
-7 – 4 (V/C) + 1 (UN synergy) + 1 (AI synergy) = -9
3. Adjust the anchor by looking at the characteristics of the board. There are two major ways that this works: the specific synergy between your tiles and the board, and the general characteristics of the board. A -10 leave on an average board where the average score is 35 points is going to be usually worth -14 on a board where the average score is 49 points, and could reduce its worth by even more if the tiles don’t conform to the specific board’s openings. (the leave reduces your average score by 2/7 in both cases).
In this case, the board is good for your leave, because of the Q in the top left and (to a lesser degree) the L in the bottom right, which can help you make vowel dumps.
-9 + 5 (board) = -4
4. Adjust the anchor based on the remaining tile pool.
Tile pool: AAAEEEEEIIIILMOORRRSSTVZ?
-4 – 4 (pool: vowels and duplication) = -8
By using these steps, you can gain a much better idea of your leave’s worth by narrowing down and attempting to pinpoint exactly what the Scrabble distribution for your leave looks like as well as determining where you are on that distribution (in terms of the X-coordinate of average points) relative to an average rack.