What is the play here?

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Answer: I9 TRIDENT is the best play. The nice thing about TRIDENT is that it leaves two in the bag. Two in the bag is a good number because it makes it hard for your opponent to go out in two. In this close game, whoever goes out first is likely to win the game. TRIDENT also works to shut down the last bingo lanes on the board, meaning that if Brad takes the fishing approach, it will not work unless he can open a new line and fish for 9 letter bingos ending in ATE.

My choice of E11 ENTER is close and has similar logic, but it ends up slightly worse because I can get outrun by things like 15A FIXER. Plays like TYNED or TYNDE would be poor choices because of the non negligible number of bingos they set up.

A tricky endgame with your opponent having a difficult but not impossible to play Q. Is there a win here?

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Answer: No, there is not a win here, and the best you can do is to start by blocking the 27 point QAT with 7J EWK. This spot comes up decently often in Q endgames. Oftentimes you cannot stick your opponent with the Q, but you are in no rush to make your high scoring play because of your opponent’s relative lack of options.

If Noah plays ERK then Matthew Tunnicliffe’s options will be somewhat limited. He can try to block 13A plays but he will end up either Q stuck or slowed down significantly in the endgame. Therefore, Noah ends up better off blocking the higher scoring QAT knowing that he can wait one turn for his 13A play.

Here is the optimal endgame. GER is played first by Noah because immediate ZEX would set up MOM underneath. Therefore, he is better of setting up a second spot for ZEX and not setting up MOM. Conversely, Matthew Tunnicliffe plays QI instead of QAT in order to threaten MAM in the spot that GER opens up and to leave the A for future flexibility.

Here is the game after the optimal endgame.

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To start thinking about how to write a pairing algorithm, you need to come up with what factors are important to you when you think about what an ideal tournament pairing system is. Josh and I came up with the following factors.

Limited Repeats — From an enjoyment standpoint, it is not fun to play the same person over and over. From a competitive standpoint, it makes sense to give different players their chance at taking down the leader.

Closeness in the standings — From an enjoyment standpoint, it is not fun to play way up or down in the standings, as it is more likely to create a ratings mismatch. From a competitive standpoint, it does not make sense to pair a top contender with someone that cannot reasonably catch them.

Giving players a chance — Pairings should maximize the number of people that have a chance of winning the tournament

Giving players a chance to control their destiny — Pairings should maximize the number of people that can win the tournament by winning out.

You may notice that some of these things contradict each other. For instance, you cannot maximize both limited repeats and closeness in the standings. Once a player plays all the players near them in the standings, one of the two has to give. To deal with this issue, we use an algorithm called minimum weight matching. With minimum weight matching, you assign weights to different possible pairings based on how bad you consider them to be, and then you find the “least bad” pairings that pair everybody.

Minimum weight matching might sound like a scary math topic, but it’s a relatively simple algorithm that has a lot of real world uses. In fact, it’s what the NFL uses to pick it’s weekly schedules. The NFL’s case is slightly different because instead of using it to pair teams with each other, they use it to pair matchups with time slots.

In the NFL’s case they might want a division rivalry game between two teams that were strong in the previous year (for instance something like Rams vs Seahawks for 2026) t be in one of the special time slots (Thursday night, Sunday night, or Monday night). They would assign something like this a low weight. You might think of this as being a good thing. In terms of the algorithm, it is probably better to think of it as “very low bad” because every weight is a measure of how bad something is, but the same logic would apply. They might not want a very sad matchup in that same timeslot, (something like Browns vs Raiders 2026) so they would assign a much higher weight to that.

Back to the example of tournament Scrabble, we have to assign weights to different things that we don’t like. Repeats, distance in the standings, and ability to catch each other all get weights. If you are a contender, getting paired with someone that cannot catch you is so bad that the cop system gives it an extremely high weight so it can never happen. Repeats and distance in the standings are given smaller weights in order to tweak what is “optimal” without strictly prohibiting anything. There is one last weight that tries to stop premature pairings between the highest players in the standings in order to give more players a chance at coming back.

There are a lot of practical advantages to the cop system over other systems. For instance, one of the things it does right is severely limit repeats. In a normal Swiss system tournament, you set the number of acceptable repeats. If you set the acceptable repeats to one, it means that you are allowing repeats but not threepeats or higher.

This however also means that you do not care how many individual matchups within the round are repeats. If you are repeating, then anyone in the round can repeat. Swiss systems prefer a very specific set of pairings, and “explore” in a very specific order if that specific set of pairings contains unacceptable repeats. They stop as soon as they find an acceptable answer.

Cop pairings, on the other hand, minimize the total number of repeats across one round. Cop considers one single matchup that is a repeat to be bad, two to be worse, three to be even worse, and so on and so forth. Here is an example of a tournament situation where this makes a huge difference.

At this point in the tournament, Wellington, the leader, has played all of the people that have a realistic chance of catching him. Simulations confirm that Chukwudi, the highest player in the standings that Wellington has not played, has a 0.2% chance of winning the tournament. While this is a nonzero chance, I would generally recommend treating anything below 1% as not high enough.

There are two main reasons for this. For one, the more people that you consider to “have a chance” the stretchier the pairings get. This limits the ability for the “mid” contenders to get a chance to come back by knocking out the leader. The other reason is that many rounds in Scrabble tournaments are paired two rounds back to make things go quicker. For instance, these round 22 standings are being used to pair round 24. If someone is below 1% to win a tournament they likely have to win all the rest of their games in order to win the tournament. Setting 1% as a threshold helps avoid situations where someone who is a “contender” in round 22 loses round 23 and then is paired against the leader in round 24 after they no longer have any chance at all.

Because of our self imposed restraints, there must be at least one repeat matchup in order to make the pairings. A Swiss system that allows repeats but not threepeats would work as follows:

It would start by considering pairing me with Wellington, because as the only players with 17 wins we are our own group. It would not allow this because we have already played twice. It would then add Harshan and Matthew Tunnicliffe to our win group. It would favor starting with 1 vs 3 and 2 vs 4 within that group, because Swiss systems start by trying 1 vs 1 below the midpoint and 2 vs 2 below the midpoint etc. This would work and would pair Wellington vs Harshan and me vs Matthew Tunnicliffe. It would then move on to lower groups with the same algorithm. Both of these matchups would be repeats, with the Swiss system completely ignoring the fact that Matthew Tunnicliffe and Harshan have not yet played. Kevin Fraley would be paired with Winter (also a repeat) and then then players with 14 wins and less would be paired according to the same algorithm, likely creating many more repeats.

Cop pairings improves on this by avoiding the rigid groups created in a Swiss system. While Chukwudi might not be able to reasonably catch Wellington in first place, he can reasonably catch Harshan in third. There is no reason that a pairing system should prohibit that, but it would be prohibited in a Swiss system where the two players end up in different win groups. Here is a list of the pairings for round 24 that the cop system chose for the contenders, which includes Chukwudi vs Harshan.

Only one pairing in the whole round is a repeat, yet contenders are playing reasonable opponents. This is the advantage of minimum weight matching. It threads the needle as much as possible between strictly prohibiting someone from playing a non-contender while heavily favoring non-repeat pairings between contenders.

The cop system also automatically generates logs to show you why it came up with what it did. Here are some snippets of the logs used to generate the pairings for this round.

Here is a list of the possible pairings for Wellington. The pairings with an extremely high weight are the ones between Wellington and an opponent that the computer has determined has a less than 1% chance of winning the tournament. At this point in the tournament, there are only 6 players with at least a 1% chance of winning the tournament. In addition, pairing Wellington vs me gets an extra high weight because it has already happened twice while other pairings have only happened once.

Here are the possible pairings for me. As I am in second place, there are more people that have a chance of catching my position. I have already played all of them except for Thomas Reinke. The cop algorithm would strongly prefer that I play Thomas, because it is fairest to give him his chance at catching me when all other contenders have already gotten their chance. It does so by assigning 5 digit weights to all of my other possible opponents and a much lower 729 weight to Thomas.

Going down the line we see more repeats being avoided. Harshan has three contenders possible that he has not yet played. Kevin Fraley would be the “optimal” one because he strikes a balance between the relatively stretchy pairing of Chukwudi and the “too tight” pairing of Matthew Tunnicliffe that would run the risk of locking other players out. Ultimately, the cop algorithm chooses the “suboptimal” opponent of Chukwudi, likely because it helps other players avoid repeats.

Ultimately there is no perfect answer to what the pairings should be. Different people prioritize different things in the pairings and that is fine. I do, however, believe that cop is a distinct improvement on systems like Chew pairings and Swiss pairings because it produces far less repeats while also avoiding situations where a player is matched with someone that has no reasonable chance at catching them.

It is important to remember that Chew pairings and Swiss pairings are both a product of their time. They were both made in the 20th century when computers were much slower than they are today. The fact that they had “stop” conditions that stopped running the pairing algorithm once they found something that worked would’ve been more important in the 20th century. The simulations used for cop are computationally expensive in a way that would’ve been difficult in the 20th century. Therefore, pairing systems like Chew pairings and Swiss pairings should be seen as products of their time rather than complete failures.

What is the play here?

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Answer: Despite my early deficit, I6 EON is the play. It is too early in the game to worry about ripping open the board. My leave of AEMNR works well with the I floater on the board. In addition, the C column provides me a second place to go for bingos. It is likely that if I open the board further, Jason will get more use of the new spot than me, because he would get first crack at it. Being patient at this game stage and not trying to forcibly rip open the board is very important.

I5 NEON would normally also be worth consideration. This time, it is a poor choice due to the fact that it reopens the H column triple that is currently inaccessible due to the floating V. My choice of I5 NEMN was a poor one for a similar reason.

Bonus content:

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1. One ply sims have no purpose. One ply sims only consider your opponent’s response. They do not even consider your reply. They are a terrible judge of a Scrabble game. Do not use these for any serious study.

2. Bogowin determines the percentages — You might be wondering how win % is calculated. After all, you do not reach the end of the game in these. The answer is that the result of the game is actually calculated as a decimal for each player. Bogowin is a giant table. You get a value for the number of tiles left and score differential. Additionally, leave values at the end of the sim are added to game scores to adjust for the win % changing due to players’ racks. You then calcuate average Bogowin across sim instead of fraction of wins.

3. There are consequences to Bogowin — Bogowin is good at a quick lookup, but it is not without consequence. Bogowin is not good at telling whether or not your leave is especially good or bad for the board. For instance, consider a position where the Q is going to be very difficult to get rid of near the end of the game. You can choose between QI for 22 and a play that scores more in the same spot but keeps the Q. A 2 ply sim will not be able to tell how bad the Q is. It will add the leave value of the Q to -7.6 to your score. When you consider how likely you are to be stuck with the Q, the Q is actually much worse than -7.6 here, and your win % will be inflated by the 2 ply sim. The 2 ply sim might accidentally favor the high scoring play when QI is actually the best play.

4. Odd number ply sims are better than even ones. This is because each sim assumes equity plays are made. Equity plays are not always correct. An odd ply sim assumes one less equity play on your part. These equity plays often get the wrong idea of what the ideas are for your leave or for the board, making the sim less accurate than the corresponding even ply one.

5. Pros and Cons to low and high ply sims. Low ply sims are fast at the expense of accuracy. If your leave is especially good or bad for the board, a low ply sim will learn the least from that. On the other hand, low ply sims are much faster, allowing you to find statistical significance for the true sim winner faster. High ply sims, on the other hand, sacrifice speed for accuracy. They are more likely to find the best play but they converge slower on the statistically significant true sim winner

6. 5 ply sims work best in a timed environment — It has been proven that if you are creating a bot that has a limited amount of time, it is best to use 5 ply sims. We have already discussed why odd ply sims work better. We have also discussed the tradeoff between low and high ply bots. A five ply sim strikes the perfect balance between the two. In a timed game, the answer cannot be to run the slow but accurate sims. A compromise is needed. 5 ply sims retain some of the speed of low ply sims and some of the accuracy of high ply sims.

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I can go several different routes here. I can take equity with 14A PEE, prioritize turnover for an S with O4 UPTAKE, or block the S hook with something like F13 LEU. What is the play?

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Answer: The best plays prioritize blocking ERGATOIDS. LEU edges out the sim over LEE in the same spot, likely because LEE is not a thorough block. My lead is not huge, but it is big enough and the board is tight enough that a sacrifice to block ERGATOIDS is necessary. Note that while prioritizing turnover is usually a bad idea with two blanks already on the board, UPTAKE still ends up simming relatively well because of how important it is to draw an S if I do not end up blocking row ERGATOIDS. PEE is a poor choice because it sets up a scoring spot that does not require an S.

Ultimately, this position shows several things about closed boards. For one, a scoring spot that mostly only allows 40 point plays can suddenly be a big deal. This is especially true with how close the game is. Caring about blocking a spot for 40 point plays is usually silly on a wide open board, but it’s very important here.

Second, turnover can be important even with 0 unseen blanks. This is because the esses, and possibly the Z, are hugely important here to who might win the game, and I need to try to get my hands on one. UPTAKE does not end up being the right play, but it does do much better than its equity value because it prioritizes turnover.

Third, the risk of setting up a new spot shoots up. If Laurie does not have an S, she cannot do much here. If I play PEE, she has all sorts of new ways to score 40. Even something like ANI scores 30, which is a huge score on this board, and probably much higher than I would be able to muster afterwards. Therefore, PEE is a very bad play.

Sim results showing just how bad PEE is.

Longer sim showing LEU edging out LEE with statistical significance.

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What is the best way to approach this endgame? My opponent cannot bingo, but there is still a lot of value in blocking AIOLIS. I also need to make sure I get rid of my high pointers in a timely manner because I could get stuck with one if she goes out in two.

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Answer: 14B JAG is the correct play. JAG does not fully block the triple (it’s not really possible anyways) but it does reduce Laurie to much worse plays on the triple, such as AIS or ISO as opposed to AIOLIS, a much higher scoring out in two.

The interesting thing about JAG is that I willingly get Q stuck. This works because it is going to be impossible to get rid of all of my high point tiles. In a situation like this, it is less of a big deal to willingly get Q stuck. The fact that JAG leaves me with E10 XU is more important than the fact that it Q sticks me. After my choice of 14A QUAG I am setting up QI and allowing myself to get hit by a much better slow play sequence by Laurie that involves QI and OILS.

After JAG the best sequence goes like this.

The final game looks like this

After QUAG the optimal sequence goes looks like this

13L AI is necessary to block RAJ and set up an out in two with high scoring plays

QUAG ends up worse even though I get rid of all of my high point tiles because of the high scoring possibilities Laurie has.

Making a deliberately imperfect bot is a different kind of challenge. It is not difficult to make a random 2000 skilled bot. Hastybot is already probably 2200 skilled. In order to make Hastybot 2000 skilled you just pick random turns and have Hastybot deliberately make inaccurate plays. Calibrate the bot so that it is even money against 2000 players and there you go.

The real challenge is in making a 2000 bot that feels like you’re playing a human. Nobody wants to play a 2000 bot that randomly passes 10% of the time. Even if this bot is 2000 skilled, it doesn’t feel like a real game of Scrabble.

The same issue happens in chess. Old school 2000 bots (much further from the top than in Scrabble) would simply make a blunder at random intervals. Some human players discovered that if you closed the board and shuffled pieces for long enough, the bot would eventually have to blunder because of the way it was coded. Eventually Lichess created Maia with machine learning to be more “human like”

Here is one example of a position in Scrabble that would be hard to code.

In this position, the best play by far is 9G IO. I have already explained why you should strongly consider responding to QI with IO whenever it is on option. This position is no different. IO is also the equity play here, making it the best play by far.

The issue with this position for computer coding is that IO is such a great play that IOS is the second best play. No human being is ever going to play IOS here. They are either going to understand the positional nuances and play IO, or they are going to mess up and play something like 9H OY. IOS is a less “human” play because it is a clearly inferior version of IO. Humans will generally either make the correct play or they will make a completely different play. They will not slap an S onto the correct play for two extra points, barring some sort of necessary blocking reasons or a second S, because it is known to be a bad idea.

If a computer randomly rolls “mess up” on this turn, they might play IOS. This would make that computer not feel like a human. This is not the only type of position where this could happen. It also happens in positions where there are three spots for the same bingo. If one spot scores 80 and one spot scores 60, and both consist of common words, the human will always put down the 80 pointer. A computer that rolls “mess up” on a turn like that would be randomly making a play that all humans instantly know is bad and would never consider.

The solutions are complicated but doable. For instance, there is a bot on Woogles that always makes the best play that consists of common words. Most likely, a machine learning based solution will eventually be developed.

In this position, you should play G7 IWI if your rack is AEFGIII, but you should exchange if your rack is EIIIINT. This is despite the fact that EIINT is a much better leave than AEFGI. Why is that?

The answer is that there is no way to come up with a good leave with AEFGIII. You are stuck playing IWI because the exchange options are so bad. IWI is less equity in this case, but the exchange options are so poor that none of them are worth it. The best exchange involves keeping only your E, a leave that is not good enough to justify the play of IWI keeping AEFGI, a play that is not fun but better than exchanging.

With EIIIINT, EINT is a great leave. You can exchange keeping that, and it ends up being better than playing IWI, a play that scores 8 points and keeps the not so great EIINT.

Sim results after both racks.

I want to talk more about the position where you have AEFGIII because I think it is something that people struggle with. Everything about that turn is uninspiring. Your highest scoring plays (7G AGE, 9H FIG, G8 WIFIE) are absolutely dreadful, keeping awful leaves and ripping open the board. Because of this, many players often default to exchanging. The “middle ground” play of IWI just feels very sad. It scores 8 points and keeps an uninspiring leave.

Here’s the thing. Sad does not mean wrong, it means sad. IWI is sad, but if you are to compare IWI to exchanging, IWI is the scoring option. It is 8 points more than the other plays, and so it needs to be thought of as being the scoring option by 8 points. When you keep this in mind, it makes more sense to make the uninspiring 8 point play rather than the kneejerk exchange that scores 0 points.

Similar logic applies to the EIIIINT rack. Here IWI isn’t even that bad of an option, it’s just that EINT is just good enough to be worth exchanging. IWI is sad and wrong this time, but it’s barely wrong.

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What is the best way to preserve my moderate lead in this position?

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I have a smallish lead on a tight board. What is the best way to go from here?

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Answer: N5 UNFAMED is the best play. This might seem scary, because it opens up two different triples and allows Justin to make some high scoring plays. Ultimately, it is worth it because most of his sequences on the triple fall just short.

In these types of situations, you have to answer several questions. Question 1 is “how often do I win if he bingos”. I certainly have a chance given that his bingos will open the triple, but it is also likely to be too close for comfort, especially if he bingos out. Question 2 is “How do I block the D”. It is likely better to block the D with a longer play on this board. This is because longer plays require more overlaps (UNFAMED requires at least a 3 way overlap with awkward letter combos) and longer plays score more points (Justin could easily outrun me without bingoing if I play something like N9 GAD). Question 3 is “Do I win after UNFAMED if he doesn’t bingo but hits something nice on the triple”. The answer to this question is “usually, and more often than if I play something like F3 FUMED and he does bingo”.

Ultimately, to solve these questions thoroughly enough to get the right answer, you do need to do quite a bit of math. The best thing you can try to do in game is develop an intuition with the exact scores of things. I do not get this right every time, but I was able to do it correctly this time in game.

Of note is the fact that UNFAMED is 10 spread points worse than F3 FUMED, but 13% better on win percentage. This is normal this late in the game when you make a bingo blocking play.

Sim details showing that UNFAMED does not really lower average opponent score at all compared to FUMED, but it drastically lowers bingo %, which is the important part.

Unfortunately, Justin had one of the better combos of tiles he could have had, and I went on to lose the game by 1 point.

This is a complicated position where I can choose to empty the bag or not empty the bag. With either of those choices, there are several viable options. What is the best path forward?

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Answer: E3 QI is the play. It looks scary because it sets up a way for Adam to make a high scoring fish of QIN or QIS. The thing is, these fishes are never the correct play for Adam. They do not bingo enough to win. With whatever rack Adam has, he will be better off fishing with something that hits more bingos in two spots. QI blocks some bingos, but more importantly, it leaves be with the option of playing 13J PREX. PREX is just enough to win against some of Adam’s lower scoring fish/bingo combinations, which is a key factor here.

There is also the question of playing PREX immediately, or perhaps something like E2 GRIP, blocking as many bingos as possible. PREX does not outrun any bingos because I have the Q. GRIP does not block enough bingos. This is because bingos like LONGIES/KYUS are a threat. The 3E QI/PREX sequence is just enough to outrun some of the KYUS bingos, which is why it is the best play.

In the real game I did in fact play E3 QI and I did go on to win the game.

Bonus Paywalled Content: On Adam’s turn, with Adam’s actual rack of EGILNOS, what is the correct play?

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The result of the game is not in question here, but we can still gain valuable spread in this Q stick endgame by playing the best sequence. What is the best sequence here?

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Take a look at this game. Here is the analyzer’s synopsis of my plays.

Now, take a look at this position

The analyzer wants me to play L1 FEWEST. L12 CORF, however, is pretty clearly the correct play. Why would the analyzer recommend a play like L1 FEWEST?

The reason involves the assumptions made in the analyzer’s logic. In non-endgame positions, the analyzer always assumes that the opponent will make equity plays. In endgame positions, there is a slightly different algorithm that prioritizes playing off more tiles due to the importance of going out in two. Both of these types of plays are not great assumptions to make, but making a different type of assumption would take a lot longer, meaning that we are stuck with an imperfect analyzer.

In this position specifically, the analyzer believes that Ben is going to play 6J QAT if he has those tiles. If he were to do that, the combination of FEWEST for 30 followed by some sort of 30+ point play on L12 would likely be enough for me to win the game.

In reality, Ben will be playing something like 12L MATE after I play FEWEST. I will then be stuck without good scoring options and I will have to block his 32 point play of QAT. Often I would not be able to win the game in these instances.

For instance, the sim thinks I will win if I play FEWEST and Ben has AMNNQTT. The sim believes that the following game will occur in this situation.

This would be the result of Ben immediately taking his highest scoring play of 6J QAT. In reality, QAT is not a good move. Ben needs to block my highest scoring play of L12 CORD.

The endgame algorithm, which is exhaustive and therefore correct, confirms that Ben can win this endgame by starting with 12L MATE. The optimal endgame for both sides would result in this game

Ultimately, there are many such endgames like this in the original pre-endgame position. Because of this, the analyzer ends up drastically overvaluing L1 FEWEST.

The sim using the analyzer’s logic thinks that FEWEST wins 90% of the time.

The exhaustive peg algorithm reveals that it only wins 39% of the time!

So, in this game, where my mistake index was 2.9 mistakes, a full 1.0 of the “mistakes” were made by making the correct play! As we will see later, this is not the only problem with the analyzer from this game.

I have a bingo here. Should I play it?

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I have a mix of good and bad tiles on my rack and a moderate lead. What is the approach to maximize my winning chances?

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