This lecture was about board control (with an extra bit about bluffing and challenging - see the last few slides). The main concepts were: - Open vs. closed boards - Controlling the board's variability - Board conditions for exchanging - First move placement 1. Open vs. closed boards The overall condition of a Scrabble board can be characterized along a spectrum from open to closed. An open board is one where there are many spots to play, many playable bonus squares, and/or accessible stretches of 7 or more open squares suitable for placing a bingo (called bingo lanes). A closed board is the opposite. Generally, it's easier to score more points on an open board than on a closed board. This is true for both you and your opponent; consequently, the more open the board, the greater the variability in expected score difference over several turns. Why? Because, as we've all experienced, luck ultimately has a large influence on how many points we score. We might get great luck and play several bingos, or we might get all vowels and have to exchange for zero points. If the board is open, i.e. amenable to high-scoring plays, good luck will very likely yield high scores and bad luck will yield low scores. But if the board is closed, then even with good tiles we probably won't be able to score highly; there is less score variability based on drawing luck. Thus we say that open boards have greater score variability. Understanding, evaluating, and making plays to control this variability is a subtle but important skill for good Scrabble playing. 2. Controlling the board's variability There are several reasons why you might want to use your plays to push the board towards one end of the spectrum of open or closed (I'll sometimes use these terms adverbially and call this "playing open" or "playing closed"): 1. For one, you may just prefer to play on open boards or closed boards. If you are good at anagramming for bingos, you probably prefer open boards where there are many lanes to place bingos. On the other hand, if you know lots of short words and are great at finding compact parallel plays, you may prefer closed boards where you can utilize those skills. So your personal playing style may affect whether you choose to push the board towards being open or closed. You should also, though, think about the opponent's playing style, whether you know it in advance or you detect it by observing the way they play. Forcing the opponent to play on a board which doesn't match their preferred style could be to your advantage. 2. Your and your opponent's relative skill levels should influence how you choose to play. The better your opponent than you, in particular the greater your opponent's word knowledge than yours, the more closed you should tend to play. The more opportunities available, the more your opponent's greater vocabulary or skill will enable them to outplay you. 3. The current score should be the biggest factor in whether you choose to play open or closed. When leading significantly (70-100 points), it often makes sense to close up the board to reduce the variability. Remember that more open boards permit greater variability in score: over the course of 3 turns, for instance, you might gain 100 points over your opponent, or vice-versa. If you can instead close the board so that the greatest possible spread swing is 30, then you can essentially guarantee that your opponent will not surmount your lead. Similarly, when you're significantly behind, you should strive to open up the board to increase the variability. While this also increases your opponent's potential for scoring, it may be the only way for you to have any chance of winning the game. You should always be vigilant of the board's condition and, especially, what your opponent is doing to it. As soon as you notice your opponent closing up the board to guarantee their lead (whether it's intentional or not), you should fight with everything you have to keep it open. Once the board is very closed, it's extremely hard for the player who's behind to open it up, because any opening you try to make your opponent will quickly shut down. So what does opening or closing the board actually entail? If you understand the definitions of open and closed, this should be deducible. To open the board, strive to create hot spots and bingo lanes. To close the board, get rid of the same (preferably by using them). When opening the board, keep in mind that your opponent will get the first shot at whatever you open up. It's best if you can create multiple openings, or an opening that, if you opponent were to use it, would create another opening in the process. Understand that controlling the board is not a separate task from your usual goal of accumulating points. Ideally, you'd like to make plays that score well, yield good leaves, AND push the board towards your desired conditions. It's another factor to think about when evaluating plays, and unlike leave values, it's something that requires a broader perspective - perhaps information about the previous few turns, and predictions about the next few, as well as the score - to evaluate. 3. Board conditions for exchanging I want to particularly examine how this additional factor affects our exchange plays. Let's suppose we have a really bad rack; e.g. ACEIIRU. We definitely want to exchange. However, if the board has one particularly glaring opening, like an S on 1E with the TWS open, exchanging will mean giving this huge opportunity up to our opponent. Although exchanging would be our typical choice, with these conditions we might be forced to play something on the TWS, just to keep our opponent from fetching a huge score there. On the flip side, if the board is very closed, with few opportunities for you or your opponent to score well, then you should be even more willing to exchange. You know that your opponent won't be landing any huge plays on big openings, so there's not much loss in giving up a turn to improve your rack. One common position that's often a good time to exchange is the starting position. This may seem counterintuitive, and/or just lame to start the game by not playing any tiles, but it's often the best play when you start with a lousy rack. The starting position can be considered a pretty closed board - there's one DWS (the center square) and one DLS that can be reached, but you're limited to exactly those bonuses and no more. Once you make your play, you tend to open up several more hot spots for your opponent. Thus, the first move position is actually quite a bad one. Unless you have a play that scores pretty well and yields a good leave, it's usually better to exchange for a better rack and let your opponent deal with this troublesome position. Your opponent may very likely respond by exchanging and giving it back to you, but hopefully your exchange gives you a rack good enough to play it. If not, you know what to do... exchange again! Just keep in mind that 6 zero-score plays in a row ends the game, turning it into a "who's got lower tiles" contest, which you might win, but probably don't want to risk. 4. First move placement Assuming you get a rack good enough to warrant playing the first tiles of the game, you can follow a few rules (unusual for Scrabble, but since this position is so standard, its analysis is as well) to decide how to place your play. You have to cover the center DWS square, and whether you play horizontally or vertically doesn't matter, since the board is rotationally symmetric. The important factors to consider are the positions of the surrounding bonus squares. Generally, you should follow this thought process: - If you can make a 5+ letter word, place the highest-value consonant you can on a DLS. - Otherwise, or if there's a tie between multiple options, prefer the play which places less vowels under the two DLS near the center. Between vowels, prefer placing the harder to use ones under the DLS; i.e., prefer to place U > O > I > A > E under the DLS, if you have to place a vowel under them. Importantly, the second consideration is subordinate to the first. If you can place a high-point consonant on a DLS but it requires placing vowels under the central DLS, do it still. The defensive effects of avoiding placing vowels under the DLS is enough to be a tiebreaker, but still very small. Even 2 extra points generally outweighs it.