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“Man Muss Immer Umkehren” And Scrabble

I like to play games - bridge, blackjack, poker, Stratego, chess, backgammon, Scrabble, rock/paper/scissors, capital markets, or essentially anything else -. Give me a set of rules, an adversary, a strategy, and a goal and I'm happy until I win, lose, or physically collapse. This past week, it has been Scrabble. Herein are a few thoughts on Scrabble and how it relates to investing.

As usual, let's start at the end. One of the great mathematician Carl Gustav Jacob Jacobi's favorite maxims was man muss immer umkehren (invert, always invert). Charlie Munger is famous for his application of this maxim to the field of investing. In the case of Scrabble, the key is to look first at the end of the game and then to look to the problems that one has at reaching it with success.

Man muss immer umkehren - Carl Gustav Jacob Jacobi

At the end of the game, all tiles are played and one player is the winner based upon points earned. The key to winning is to use all of your tiles in a given move with as much frequency as possible - 5-6 is good and it should be at least 2-3 times per player per game. Using all of your tiles adds 50 points. It is also the easiest way to bridge multiple world multipliers (I have yet to play on three word multipliers although it is possible to do so; bridging two world multipliers is relatively common unless an opponent is playing effective defense).

Every time you move, compare the expected value of a potential move in nominal points with the probabilistic impact upon going out in subsequent moves. For example, if you can add a 50% chance of going out in the next move, for .5 x 50 = 25 probabilistic points, then that combined with twenty nominal points outweighs a nominal 40 point move.

So, if the goal is winning and the strategy is to go out a lot, then how do you do that? In two words: tile management. Okay, so there are two more, but less important words: board management. Think about a frustrating game of Scrabble in which you are playing a losing strategy. What are your frustrations? The board probably feels constrained and you are probably unhappy with your letters in your hand. Both probably feel like bad luck. Neither have anything at all to do with luck over the long-term but they are the right problems to solve.

Good tile management involves planning ahead to give yourself the best tiles in subsequent moves. What tiles do you want? Well the best way to answer that is to say that you want the tiles that form seven or eight letter words. There are just about 24,000 seven letter words and 30,000 eight letter words in the English language, but these are far from random letter permutations. In fact, words of this length are not comprised of letters but of prefixes, suffixes, and other patterns. These patters allow you to learn the words, remember them, spell them correctly, and form them on your tile rack. Your first rack of letters is the only letters that you will see all game that you are not responsible for. They will be seven randomly drawn letters. After those seven, the rack will be what you make of it. Never breakup prefixes, suffixes, or other patterns. Never accept more than four vowels or consonants. Ship unusual or hard letters. Do all of this by playing the others. Limit yourself to playing only the letters that do not fit these categories, the letters that you do not want. Then, randomness becomes your friend as it works for you to reset every subsequent rack. A reasonable tempo is to play a few hands to build each hand that can go out.

A lesser but also important strategy involves sound board management. Just like the fact that you keep your good letters by playing the other ones in order to discard them, you are responsible for the board, for keeping open the real estate that you need to go out. If you are able to go out far more frequently than opponents, then keep swaths of the board open in order to do so. If you are on top of your eight letter words or even the 29,000 nine-letter words, then be sure to build a board that plays to your advantage. Lay down tiles that can be subsequently bridged to play triple-triple moves. This does not appear to be good defense, but if you can open more than one up, you may be able to out play your opponent on bridging triple-triples. This routinely adds up to several hundred points and generally proves to be decisive in the overall game score.

The more you know, the less you have to think. It is very helpful to know the 7-, 8-, and 9- letter words. You almost certainly know 90% of them, but it is helpful to know the vast majority of the rest. Of the most obscure 10% of these words, memorizing 60% is okay but 90% is really much better. However, there is a much easier route to winning most of your parlor Scrabble games: instead of killing yourself over memorizing all of the long words, simply memorize the approximately 100 2-s, 1,000 3-s, and 4,000 4-s. This is easy since you already know the vast majority. It is really very little memorization, probably 250 or so obscure ones that are easy to learn in under an hour (remember that these are all short words and are all pliable with basic mnemonics). The short words are the glue that stick your 7+ letter moves to the board. Once you know them, even if you know only 20,000 7-s, which you probably do simply from casual reading, it is a cinch to stick one of these 7-s to the board with short words by laying down the tiles parallel to existing words instead of being forced to lay them down perpendicular. An added advantage is that parallel play is more efficient in its use of the board's real estate allowing you to go out far more frequently in a given game. I would go as far as to say that mastery of the 2-s, 3-s, and 4-s should probably come before your first game.

None of this solves short-term problems but all of it is helpful for long-term success. In the short-term, point performance is misleading (especially of an effective tile manager), noisy, and pushed around by luck. Long-term, performance is everything. It is statistically significant. The noise quiets down. It becomes 100% skill. Investing, incidentally, shares all of these characteristics. With sound tile and board management, you will give yourself the gift of multiple ways to win. Since other players impact the board and remaining tiles between your moves, you need to have the flexibility that this pattern-based strategy offers. Dramatic moves such as going out on a triple triple for several hundred points will happen and then they will start to happen frequently. But they only happen when you set them up ahead of time by giving yourself the board and rack for that kind of success.