Since entropy is such a new concept, many people have errant beliefs about entropy. The most common misnomer is that entropy measures the propensity to score, rather than the propensity for the score to change. Positions where both players will often score well does not imply a high entropy. Here are some basic misnomers about entropy:
• Entropy measures the propensity to score. Entropy is not a measure of the ability to score points: it is a measure of the propensity for the score to change. Decreasing scoring spots usually does not decrease entropy: in fact, it often increases entropy by polarizing both players’ score on future turns. Positions where both players will often score well does not imply a high entropy: high entropy positions are positions where both high and low scores are possible, but not much in between.
• “Taking a shot to end the game” or “Taking a risk because you can afford it”. These ideas are completely wrongheaded and are diametrically opposed to what you should be doing whenever you have an advantage. When ahead, you want to minimize risk and decrease entropy, and when behind, you want to encourage risk and increase entropy.
• All strong bingo racks have high entropy. Extremely strong racks or strong racks on poor scoring boards actually have a fairly low entropy, since a bingo is extremely likely or failing to draw a bingo is insignificant. High entropy not only requires the possibility of extremely good outcomes: it also requires the possibility of bad outcomes.
• All scoring racks have low entropy. Especially when there is one difficult, high scoring spot or significant bingo potential, scoring racks can often have lots of entropy. This is especially true with setups or fishes where you need one tile to hit a very high scoring play.
• Entropy is a concept stemming from fear. While many players may go overboard and block bingo lines, X spots, and higher scoring plays out of fear, entropy is still a real, mathematical concept used in many games and sports. While it might not be pleasing to fans and spectators, entropy is simply part of basic game fundamentals.
• Entropy is a concept for special situations. Entropy is not a concept: it is a metric. Just as one considers the equity of every play, they should also consider its entropy. While large differences in equity usually overrule equity, 5 or 10 point equity differences can easily be made up for if the entropy is more desirable.
• Blocking scoring spots decreases entropy. While this is sometimes true for short term entropy, entropy is not a measure of the ability to score: it’s a measure of the “variance” of one’s ability to score, and often times scoring spots decrease that variance, since they serve as a stopgap between bingos and ugly racks. Blocking scoring spots usually does not decrease entropy: in fact, many times it actually serves to increase entropy.
• Entropy only is based on score. Controlling entropy depends on other factors such as your tiles, the tile pool, and point spacing (which will be discussed in a future article). The potential of attaining a 70 point bingo is far more significant when the average non-bingo scores 20 points rather than 40 points.