Category: Classics

N-in-a-Row Games, Part 3

This is a classic gPress post, originally uploaded October 21st, 2022.

I looked for a great Tic-Tac-Toe variant, and managed to stumble across it, thanks to the famous article on Math with Bad Drawings.

Mr. Orlin’s description of the rules of the game have no obvious room for improvement, so instead of taking the time to write a worse description, this post will build on his foundation to describe terms, openings, materials, and other items that I’ve found useful as a player.

Table of Contents
Glossary of Terms
Playing Materials
Misc. Norms, Tips, et al.
General Strategy
Openings

Glossary of Terms

The game proper is referred to long-form as “Ultimate Tic-Tac-Toe”, or as merely “Ultimate”, but we’ve taken to calling it “ULT“, a short form which distinguishes from other games (like the frisbee tossing game).

A square that keeps the play on the same board (for instance, the center square on the center board) is called a ‘home square‘.

The ability to place a piece on any board is referred to as a ‘free move‘, and a square that allows your opponent to perform this move can be called a ‘free move square‘.

There are several means of notation that I have discovered or thought of:
1) Algebraic: Like algebraic notation on a chess board, with letters corresponding to columns and numbers to rows. The bottom-left square is a1, the center square is e5, and the top-right is i9.
2) Compass: Uses directions like “NW”, “SE”, or “C”. The board picked is first, then the square on the board. The bottom-left square is SW/SW, the center is C/C, and the top-right is NE/NE.
3) Numeric : Each square has a number. The first number is the board you are playing on, the second is the square you are moving on. The orientation may vary depending on whether you are using a telephone-style keypad or a computer/calculator-style keypad; the latter is my default. The bottom-left square is 11, the center is 55, and the top-right is 99.
4) Relative : Like the compass system, but uses arrow symbols instead of letters. This can help in-person play, because the arrows will be correct from each player’s perspective. Bottom-left would be ↙↙, center would be ••, and top-right would be ↗↗.

I prefer the numeric system in principle, but my games tend to be written in algebraic notation, because I was familiar with it from chess and didn’t think of a better way to do it until after I had a large body of work in the former.

For denoting a move that wins the game, or trivially forces a win, the convention is to use # following your move, the same as in chess checkmate.

This is not standard notation, but a move that captures a board may be denoted by putting ‘[X]’ (or perhaps ‘[O]’) at the end of it. Likewise, a move that causes a free move may be noted by “FM”. If another symbol is chosen, I would recommend an asterisk [*] or perhaps an at symbol [@].

Yu can refer to a move that captures a board as being ‘3r’, and a move that wins the game as being ‘3br’.

Playing Materials

In online play, I use a spreadsheet and exchange moves with my opponent via IRC or a similar protocol. I developed a custom spreadsheet some time back, which helps keep track of free move squares, allows convenient text input of moves, and can display captured boards. Click here to download it for yourself. The first page also includes match details, useful for a series of games.

There are several computer implementations that manage the board and can help arrange online games. The most popular one used to be Bennett Zhang’s Heroku app, but it seems to be offline, as of 9/1/23. Arkadiusz Nowaczyński’s uttt.ai includes useful analysis options, as well as probably the strongest AI that exists, which plays as well as the strongest chess computers play chess. Ofek Gila’s program is older, but also features a strong AI.

For in-person play, you can either use pen-and-paper, or manufacture a board and pieces. If you don’t mind using printer ink, you can expedite the process of board-making a little bit by printing out “Game Gal’s” boards.

Misc. Norms, Tips, et al.

A player familiar with the game is able to play at a ‘classical’ level in 25-45 minutes. Two games in 60-70 minutes is a decent pace with sufficient time for thought. If a game goes on longer than an hour, someone is taking up too much time. A game shouldn’t go on as long as an hour and a half.

As in regular Tic-Tac-Toe, the first mover (by convention, X) has an advantage. Like Chess, the game is not proven to be a draw with perfect play, but it likely is. In a fair match, each player should have an equal number of games as first and second mover.

Mr. Orlin mentions a variation of the game where ‘tie’ boards are considered won for both players (whereas the norm is for those boards to be considered inert). We played this several times as “Cutthroat” (or “CUT”). Most games seem to be unaffected, but there are positions where this makes all the difference. I would stick with ‘inert’ boards for ties, on the grounds that it is mainstream and more intuitive. If you do play CUT, the norm we figured is that in the case of simultaneous opposing 3brs, the game is drawn.

Another variation is known where the play is the same, but the objective of the game is to win 5 boards. This does affect the outcome of the game, for similar reasons as why a popular vote can result in different outcomes from the electoral college. While it is ULT-like, I would not call this game “Ultimate” or “ULT”. The game seems to have been named “Tic-Tac-Ku”, and I would stick with that, for the purpose of distinguishing the two.

General Strategy

Several articles could be written on this subject, and perhaps will be in the future, but here I will try to give a brief overview.

This game is a new frontier in many ways, and there’s less known about play and principles of play than I would like. We are all students of the game, and it is best to avoid being dogmatic about an approach. A type of move that works in one case may turn out to be a disaster in another. Any advice given can only be very general, subject to circumstances.

From our earlier study of tic-tac-toe, we know that the center square is mathematically the strongest square on a tic-tac-toe board. Therefore, we understand that the center board is the strongest board in ULT. The difference is that while the center square is easily defended against in a tic-tac-toe game, good positioning on the center board can provide an enduring advantage that is difficult to offset.

Whenever you move on a square, you are giving your opponent compensating value in the board that you’re directing them to. A major principle of play is to get gain in boards you care about while trying to make sure your opponent only gets advantages in boards that you don’t. This is complicated by the possibility of your moves being ‘wasted’ by overplaying on a board that you already have a winning advantage in, or by being forced to play in boards that will lead to a good gain for your opponent.

As boards are won and the game gets to the midgame or endgame, there will be many times when you don’t want to move on a certain board, because the only squares you can move on there will give your opponent the chance to make a winning play on another board. From my experience, these positions are seldom clear in advance, and can take up calculation time to uncover.

Never underestimate the power of a free move. Many games have been won by someone being forced to move on a free move square. Don’t give up free moves for free.

On the other hand, don’t underestimate the power of a good major board position, even if securing it gives up a free move. If your opponent has a 3br threat, it is often worth quenching it, even if that gives them a free move somewhere else. A 3br threat, once it exists, will hang over your head for the rest of the game, because it means that any free move square you land on ends the game. Likewise, you want to have a good 3br threat if you can get one. It’s a move that pays you interest.

If you can win or draw on merely three boards – the center, and two opposing corners – that is sufficient to not lose the game, even if your opponent wins every other board. (This is why the outcome of Tic-Tac-Ku is so different from regular ULT.)

Because we can’t see everything, it is often a good idea to ‘hedge your bets’ and not commit to trying to win a certain line of boards (at the expense of the others) too early. A board that seems to have a bad position one turn may turn out to be useful just a few minutes later.

Once boards start being won, it is harder to win others without paying an extra cost. The sheer mass of your opponent’s already-won boards, even if they are not particularly good boards, can make all the difference when you’re both being forced into tight spaces.

Openings

Because the board is symmetrical, there are fewer openings than there are squares:
Center-Center (e5, 55) – “The Main Line”
Center-Corner (d4/51, d6/57, etc.) – “The Corner Attack”
Center-Edge (e4/52, e6/58, etc.)
Corner-Home Corner (a1/11, a9/77, etc.)
Corner-Alternate Corner (a3/17)
Corner-Opposing Corner (c3/19, etc)
Corner-Center (a2/15, etc.)
Corner-Aligned Edge (a2/12)
Corner-Unaligned Edge (b3/18)
… and a plethora of edge board openings too tedious to mention in detail.
UTTT.ai analysis scores are shown after an opening’s name.

Center-Center (e5, 55) – The Center Game – “The Main Line” – +11.81
This is considered the most solid opening. It gives you a decent (though not insurmountable) advantage on the center board, and your opponent’s move will give you the option of playing the first move on a second board, probably a corner board. Strong AIs strongly prefer this move.

Center-Corner (d4/51, d6/57, etc.) – The Corner Game – “The Corner Attack” – +11.07
When it comes to alternate openings (besides e5), this was my initial unstudied preference. This move seems to give a greater edge on the center board than e5 does, because of the lack of a piece to oppose your own. I second-guessed this opening for a while, but computer analysis has revealed that it is, in fact, a top-2 opening, as I originally imagined.

Center-Edge (e4/52, e6/58, etc.) – +8.16
The center-edge opening places an uncontested piece on the center board and gives O the lead move in an edge board. The edge square is weak in the center board, because it has only two lines, one of which runs through the center square – which is also weaker than normal because it allows the opponent to immediately reply. I’d suspect I’m not meeting my potential here, but it is likely playable, since the edge board compensation your opponent gets is slim.

Corner-Home Corner (a1/11, a9/77, etc.) – +6.47
Places a contested piece on a corner board, giving X and O near-equality on this board and allowing them to pick the next board, but keeping the first move on that board. This move is not obviously bad and seems, at first glance, not worse than the following options.

Corner-Alternate Corner (a3/17)
Places an uncontested piece on a corner board, allowing O the lead move in another corner. This move completely ignores the center board, leaving that board’s status the ‘elephant in the room’. This is perhaps one of the purest openings in terms of allowing the player to measure the strength of the first-move advantage, as X and O’s positions at this point seem rather equal otherwise.

Corner-Opposing Corner (c3/19, etc) – +6.12
Places an uncontested piece on a corner board, allowing O the lead move in the opposing corner. This move is similar to the previous one, but has the characteristic of weakening your chances for 3br from your initial board, due to giving compensation to your opponent at the other end of the line. I am unsure of it on those grounds.

Corner-Unaligned Edge (b3/18)
Places an uncontested piece on a corner board, allowing O the first move on an edge board that does not overlap with the corner board’s rows. It seems plausible that X maintains a slight advantage here and that the move is not outright ‘bad’.

Corner-Aligned Edge (a2/12)
Places an uncontested piece on a corner board, allowing O the first move on an edge board that overlaps with the corner board’s rows. My intuitive guess is that this position is a little worse than the previous one, although it is hard to measure or project without an in-depth study.

Corner-Center (a2/15, etc.)
Places an uncontested piece on a corner board and gives O the lead move in the center board, which gives them similar prerogatives to the main openings. This move seems to put O in the driver’s seat, allowing X to defend with a position stronger than what O could have had. Philosophically I doubt that it is as viable an opening as the others, but it might be a good psychological ploy, or a good move for someone who is used to playing as the second player and would like to reuse as much of their knowledge as possible.

Edge Board Openings
There is a wide variety of possible openings here, given that there’s not only a home-square edge, but also corners or edges that do not overlap with the first board’s rows, versus ones that do, but they seem to have one thing in common: they’re all bad. Any move on an edge board is likely to either result in a seemingly equal position (not clearly accomplishing anything for X), or to even give O the advantage. This might be viable for a handicap game or a pie-rule tiebreaker, but it should be ruled out as a serious move between comparable players.

Conclusion

Check back periodically to see if there have been revisions to this, as there likely will be in the future. In the meantime, be on the lookout for a fourth article; there is still more to say about this game, and also about some close variants of it.

 

N-in-a-Row Games, Parts 1 & 2

These are two classic gPress posts, originally uploaded August 28, 2022 and September 2, 2022 respectively, combined into one.

Some years back, I challenged a friend to a long (100-game) series to determine who would be the World Champion Tic-Tac-Toe player. What started as a jest developed into a serious interest into the world of n-in-a-row games. In these posts, I over-analyze simple things, show the depth of the better games, and try to instill an interest in them.

Tic-Tac-Toe, three in a row…

Tic-Tac-Toe is proven to be a draw with perfect play, but it is a good starting point to understand the principles of n-in-a-row games.

As everyone in the western world knows, in a regular game of Tic-Tac-Toe, there are nine squares, in three rows and columns. Each player, X and O, take turns placing one of their pieces on an unoccupied square. If there is three-in-a-row of one piece, that player wins. Otherwise the game is a draw (or “cat” game).

Breaking it down more mathematically, we see that on a three-by-three (3×3) Tic-Tac-Toe board, there are eight possible rows of three: the two diagonals, three horizontal, and three vertical. Because the board layout is symmetrical, each corner and edge square initially have identical value. This also means that there are only three openings: center, corner, and edge. In general, a square that has more possible n-in-a-rows through it is a more powerful square, so the center square, which can be in four possible rows, would seem to be the strongest starting position.

a b c
3
2 X
1

In this situation, O has two options, a corner or an edge. After subtracting the rows that are made unwinnable due to the first player’s move, any corner has two rows that go through it; any edge has only one, so the corner is mathematically and intuitively the stronger square.

(If we play the edge, we find that the edge defense loses; X plays either a corner or an edge diagonal to the edge chosen, forcing O to defend against 3r, then X can immediately set up a 3r threat from both of his previous squares.

Center Game, Edge Blunder, Corner Variation
1. b2 a2
2. a1+ c3
3. c1#

a b c
3 O
2 O X
1 X X

On the other hand, after the corner move, although X is in the stronger position and has the initiative, he is usually unable to win. Most moves he makes will set up a 3r threat, but can also be immediately and directly countered by O.

Center Game, Corner Line
1. b2 a1
2. a3+ c1+
3. b1+ b3
4. c2+ a2~ (draw)

a b c
3 X O
2 O X X
1 O X O

X does have one possible option for a trap:

Center Game, Trap Sprung
1. b2 a1
2. c3 a2+
3. a3#

a b c
3 X X
2 O X
1 O

The proper defense is to play on a corner.

Center Game, Trap Avoided
1. b2 a1
2. c3 c1+
3. b1+ b3 … and draw

a b c
3 O X
2 X
1 O X O

This sums up the center game.

Because of the simplicity of the defense against it, the center opening is sometimes eschewed in favor of a corner attack.

a b c
3
2
1 X

Consider the position O is in. A corner is taken, meaning that there are only five out of the eight possible rows that O can still win. The center now has three such paths; each remaining corner has two. The edges orthogonal to the occupied corner have one, but the others still have two.

The corner and edge defenses are fatally flawed in a similar fashion to the edge defense previously discussed.

Corner Game, Opposite Corner Blunder
1. a1 c3
2. c1+ c2
3. a3#

a b c
3 X O
2
1 X O X

Corner Game, Adjacent Corner Blunder
1. a1 c1
2. c3 b2
3. a3#

a b c
3 X X
2 O
1 X O

Corner Game, Opposite Edge Blunder
1. a1 b3
2. a3+ b2
3. c1#

a b c
3 X O
2 O
1 X X

Corner Game, Adjacent Edge Blunder
1. a1 a2
2. b2+ a3
3. c1#

a b c
3 O
2 O X
1 X X

So, O moves in the center.

a b c
3
2 O
1 X

Because of O’s move, X’s square is now worse than it was previously, and is actually worth a little less than O’s. Having the first move advantage means he keeps the momentum, but this is only enough to guarantee a draw. Why, then, does anyone prefer the corner?

If O isn’t careful, she may wander into a trap.

The favorite X response is normally to play the corner opposite to his initial move, which sets up the corner trap: if O moves in one of the other corners, X takes the third corner, blocking 3r and creating two 3r threats of his own, winning the game.

Corner Game, Corner Trap Sprung
1. a1 b2
2. c3 a3+
3. c1#

a b c
3 O X
2 O
1 X X

A more subtle but similar variation is the edge trap. X plays in one of the edges adjacent to the opposite corner. If O plays in the wrong corner (the corner furthest from the other two squares), X can again block her 3r attempt and create two threats of his own.

Center Game, Edge Trap Sprung
1. a1 b2
2. b3 c1+
3. a3#

a b c
3 X X
2 O
1 X O

However, both of these traps require specific wrong moves from O to succeed. With other easily found moves, the game will end with a draw after a series of blocked 3r attempts. Some games may run out of possible rows before they run out of moves.

Corner Game, Corner Trap Avoided
1. a1 b2
2. c3 a2+
3. c2+ c1+
4. a3+ b3+
5. b1 and draw

a b c
3 X O X
2 O O X
1 X X O

Corner Game, Edge Trap Avoided
1. a1 b2
2. b3 a3+
3. c1+ b1 and an easy draw

a b c
3 O X
2 O
1 X O X

Some players have criticized the edge opening and claimed that it loses outright. This is false, but it does require more precise play from X than the other lines. However, because some players are unfamiliar with this system, this may be a way to try for a win.

There are unsound defenses from O that lose by force. These are the adjacent edge and opposing corner.

Edge Game, Adjacent Edge Blunder
1. a2 b3
2. a3+ a1
3. b2#

a b c
3 X O
2 X X
1 O

Edge Game, Opposite Corner Blunder
1. a2 c1
2. a1+ a3+
3. b2#

a b c
3 O
2 X X
1 X O

On the other hand, the center, opposing edge, and adjacent corners are all solid defensive options, with good chances for O if X makes a mistake.

Edge Game, Center Defense
1. a2 b2
2. b3 a3+
3. a1+ a3+
4. c1+ b1 and draw

a b c
3 O X O
2 X O
1 X O X

Edge Game, Symmetrical Defense
1. a2 c2
2. c1 a1 and draw

a b c
3
2 X O
1 O X

Edge Game, Adjacent Corner Defense, Opposite Blunder
1. a2 a1
2. c2+ b2+
3. c3+ c1#

a b c
3 X
2 X O X
1 O O

There are a couple of principles that we can observe in this. The first is that the direct approach seems less successful in an n-r game. The attacks with the best chance of working involve delayed actions that produce multiple threats. Anyone can notice when you have two pieces lined up in a row against him, but it is possible to miss the point of a ‘developing’ move and respond with a play in a bad square.

The second is that when it comes to balanced games, you don’t win so much as wait for your opponent to lose. If your adversary intends to draw, and moves with the purpose of blocking you as much as possible, there’s no reason they shouldn’t be able to get what they’re after. They are in danger when they decide to play a tricky game and try to ‘steal’ a victory. Of course, the larger and more complicated the game, the less applicable this is.

On that note, stay tuned for the next part, where we discuss some more advanced n-in-a-row games – Tic-Tac-Toe on larger boards, both balanced and imbalanced games.

* * *

Considering the ubiquity of regular Tic-Tac-Toe, it is curious that few have thought to take their game to the next level. In this article, we will explore the next step in n-in-a-row play, larger boards and larger row requirements.

It is evident after a brief look that an expanded Tic-Tac-Toe game is going to require more than three-in-a-row. For a thought experiment, consider the play of Tic-Tac-Toe+1. This game is exactly like Tic-Tac-Toe, except that an extra square is added onto the edge of the board: next to any of the existing squares, either horizontally or diagonally.

If the new square is anywhere but to the diagonal of a corner square, the game becomes a forced win for X:

New Square at a4, Game 1
1. a3 b2
2. a2#

New Square at a4, Game 2
1. a3 a2
2. b2+ c1
3. b3#

New Square at b4, Game 1
1. b2 c3
2. b3#

New Square at b4, Game 2
1. b2 b3
2. a3+ c3
3. a1#

By the same measure, a greater row requirement can lead to a game that is too easily drawn, even by the standards of a game like Tic-Tac-Toe. A brief playthrough of 4-in-a-row on a 4×4 board should illustrate the point.

A Bad, Boring 4×4 Game
1. a1 c3
2. b1 b3
3. c1+ d1
4. a2 d2
5. a3+ a4+
6. c2 d4+ 7. d3 c4+
8. b4 and a draw

The best size for a board tends to be the largest one that is not proven to be a win for the first player. For 4-in-a-row games, the only suitable symmetrical board is 5×5 [1].

Given a 5×5 board and 4r, what does the opening play look like?

Although X may have motivation to try different options in Tic-Tac-Toe, in this game, there is no reason to play anything but the center. This gives him the most room to expand his attack.

At this point, O must move in a square diagonally adjacent to the center. Anything else is a forced win for X.

Edge Defense Refutation
1. c3 b3
2. b4 d2
3. d4 c4
4. b2#

a b c d e
5
4 X O X
3 O X
2 X O
1

Time and space don’t presently allow an exhaustive listing of X’s options after a corner defense, but the strategy is focused on getting one of the possible combinations which lead to 4r in short order, which include:

  • 1 three-in-a-row, with no pieces blocking either end.

  • 2 simultaneous three-in-a-rows, either or both of which may be blocked on one end.

  • 2 simultaneous two-in-a-rows, with no pieces blocking either end.

A solid strategy for this game is to play the center of the board as a regular game of Tic-Tac-Toe. If you keep this foundation in order, the threats at the edges are easy to prevent. The biggest problem a player is likely to run into is the desire to ‘cheat’ by playing a move oriented towards getting a winning threat when they should be focused on defense.

A Sample 5×5 Game
1. c3 b2
2. b4 d2
3. e2 d4?!
(Complicates the game, but probably for the worse.)
4. d3 c2!
Saves the draw.
5. a2 b3
6. a3 a4
7. d1 e3
8. c4 b5
9. c5 and draw

Another Sample 5×5 Game
1. c3 b2
2. b4 d2
3. e2 c2
4. a2 d3
5. d4 e4
6. b1 a4
7. b3 d5 and draw

It is occasionally useful, at least psychologically, to make a move that blocks only one end of a row, when you have the option to do otherwise. This seems to be halfway between playing a solid defensive move and a ‘cheat’. Whether it will prove to be sound or unsound depends on the details of the position and whether your opponent keeps track of what you’re up to, but I suspect that it is slightly incorrect and this habit can get you punished in similar games on larger boards.

A game like 5r Tic-Tac-Toe is known and appreciated around the world. It has a variety of names but is best known as the Japanese “Gomoku”.

At sufficiently large board sizes, without or sometimes even with artificial restrictions, Gomoku is known to be a forced win for the first mover; this is true on boards as small as 15×15. [2] It appears to be unknown at present what the largest size is that is proven to be a draw.

I’ve played 5r games at 7×7 and 9×9 sizes. My expectation is that the latter is drawn, but this hasn’t yet been proven. Play allows no room for error.

I’ve never focused my attention on this game in the way that I might have, for two reasons.

Firstly, the fact that it already has many expert and professional players has a chilling factor on my level of interest. I admit being opportunistic in this respect. I would rather try to break ground in a new land and be first-rate at something than to be second or third-rate in a sprawling metropolis. At any rate, I’m not sure how much value I can offer writing about a game that has already been discussed and solved and revised and re-solved multiple times (the previous content in these articles notwithstanding).

Secondly, I discovered Ultimate Tic-Tac-Toe shortly after my first 5r series, and my enthusiasm for that game further dampened my interest in doing an in-depth study of this one. It is therefore appropriate that Ultimate (or, as we’ve taken to calling it, ULT) should be the subject of the next article in this series.

[1] There are larger boards which are said to lead to interesting games. The key phrase here is “symmetrical board”. This vintage site is informative about that, and such variants generally: “Generalized Tic-tac-toe”, by Wei Ji Ma
[2] The proof text is Searching for Solutions in Games and Artificial Intelligence, a 1994 thesis by Louis Victor Allis.

 

Where Honor is Due

This is a classic gPress post, originally uploaded November 3, 2022.

Is President Biden worse than Nero?

Anyone acquainted with history might think this question is ludicrous, but it is a point of confusion in Christendom today. Many feel it is acceptable to indulge in hearing and spreading rumors about someone, or to deride them, or otherwise rail against them, provided that it is a political leader they disagree with.

Far from defending this practice, the Bible shows reasons why we should treat President Biden with respect, most of which are also true for other elected officials.

1) He is a ruler of our country.
Although there seems to be a trend not to recognize anyone you have not voted for, the Biblical perspective is that if someone has authority, they have been ‘set up’ in that position by God. This setting up is not limited to means that we personally approve of; whether the president was ‘duly elected’ seems moot when we recall that several Biblical rulers who were acknowledged as legitimate came to power through conquest or assassination!

1 Peter 2 says to ‘honor the king’. This was likely written in reference to the Roman emperor. It is unqualified, and in context, the statement to respect someone who tradition tells us was responsible for leading a great persecution and executing Peter himself removes from us any kind of excuse. If we find this difficult to practice, it is more difficult to argue that the president is responsible for more evil-doing than either the Roman emperors generally or Nero in particular, and that his rule is an extenuating circumstance.

If nothing else, the Biblical mandate to pray for our rulers, and the spirit of that mandate, opposes the attitude behind this manner of speech.

2) He is aged.
Many use this as a jumping-off point for further dishonoring the president. However, the Bible states in Leviticus 19 that the elderly are due respect, without qualification:

“Thou shalt rise up before the hoary head, and honour the face of the old man, and fear thy God: I am the LORD.”

3) He is a person.
One of the best reasons to refrain from these kinds of comments about the president is that it is wrong to habitually talk about anyone in this manner, whatever their status in life.

It is one thing to criticize the administration’s policies, or to note when the president has done something wrong in his office as a political leader, whether it is immoral or merely imprudent. Even in this case, I would err on the side of silence, in the sense that dwelling on someone’s faults is not expedient, but I acknowledge there is an occasional need for discussion of the conduct of our government.

However, most conversation about political leaders consists of emotionally charged rhetoric, abusive language, and personal attacks. If you would not put up with hearing someone speak this way about you – or your family member, or your friend, or acquaintance – why should a stranger be any different, whatever their position? They are all humans made in God’s image.

I’m reluctant to write it out, but this point must be made. I’ve heard someone in the past thoughtlessly say that they wished for the president’s death. I wonder how many times we have entertained such ideas without understanding what is meant by it. If you say this, what you mean (intentionally or not) is that your disapproval of the president is so great that you, believing him to be a sinner, prefer him to immediately face the consequences of those sins, rather than repent. I hardly believe that Christians want this when they speak about someone, but if they don’t, they should pick a new manner of speaking.

Ultimately the president is a man like any other man. If we claim to be concerned about the salvation of the lost, the president and other political leaders are in as much a need of it as anyone else. We should not harshly reject and condemn someone whom God has not.

4) The speech is un-Christian in any case.
“Oh, so you’re a Christian? I never would have guessed.”
It is an understatement to note that someone who seems habitually angry is not modeling Christ. Reviling is no better than profanity or obscenities; the three often go together. Moreover, people judge you not only by how you treat them, but by how you treat others.

Although love, grace and peace are misunderstood nowadays, people can recognize that something is amiss when someone claims to possess these traits and yet is constantly offensive (in both senses of the word). If you can persuade a stranger that you hate a third person, you are well on your way to convincing them that you can’t love them either.

In conclusion, according to Scripture, the president of our country is due our respect, as are other public officials. You do not have to agree with or support someone’s decisions to extend them Christian love, much less the common courtesies that are ordinarily extended between strangers.

While the media wants to make us feel we are ‘familiar’ with these people we have never met, we cannot in good conscience let that supposed familiarity breed bitterness and contempt. If we do, we will have to account for it someday.

Choosing a Popular OS

This is a classic gPress post, originally uploaded April 30, 2022.

There are three mainstream families of operating systems (“OSes”) for regular users in modern computing: macOS, Windows, and Linux (which includes Google’s Chrome OS).

Each platform has pros and cons. I hope to inform less experienced users’ decisions. If you build software from source, this post is not addressed to you.

Table of Contents
macOS
Windows
The Linux family
• Chrome OS
• Debian
Conclusion

macOS

Your choice regarding macOS is made when you buy your computer. It runs on and is designed and licensed for Apple hardware, and since the chief advantage of a Mac is the operating system, it makes little sense to buy one and then run another OS full-time.

Macs are marketed as being easier to use than their alternatives. An influential IBM study found that Mac corporate users were more productive, more satisfied, and saved money compared to Windows users. Apple’s customer loyalty is recognized in the computing world. Modern Macs offer the advantage of being part of the so-called ‘Apple ecosystem’, offering superior synchronization with iPhones and other iDevices.

There are two downsides to the Mac as a platform. The first is that Apple has control over your system. I don’t mean this in the Orwellian sense, but in that your ability to customize or upgrade your machine is limited. If you don’t like the way it comes out of the box, or if something gets changed in an update, you’re stuck with it. If you have a problem, you’re left to Apple’s mercies to fix it. If it works fine, then sooner or later Apple will drop support for it, with the expectation that you will immediately replace it with a newer model.

Macs also tend to have a hefty up-front price, although the least expensive Mac you can get directly from Apple as of this writing (6/15/2025) is $509 [1], not including shipping. Used Macs retain their value quite well. You can save money in the long run, but the entry cost may be prohibitive.

Windows

Windows has been the market share leader in desktop operating systems since the mid-90s, and has usually been ‘good enough’ for most people.

Microsoft has a record of being concerned about legacy applications [2]. You can still run some early-90s programs on modern Windows PCs, which stands in stark contrast to Apple’s regular forced abandonment of old software.

If it is not the most customizable system, it is still very much so. If it is not the most stable operating system, it is more stable than it is given credit for, and harder for users to mess up than a system that assumes competence. If it is not the most intuitive system, it’s intuitive enough; the chances are that after 25 years, you already know your way around it.

There is something to be said for being consistently no less than second or third-best, but Windows is also first-rate in several areas. Windows has the largest community and support base of any desktop operating system. It is the #1 platform for computer gamers, with a catalog larger, better-supported, and better-performant than the alternatives. “Quantity has a quality of its own”, but with ready access to cutting-edge graphics hardware, you don’t have to choose between the two. Driver support is as good as it can get on the PC’s ‘open architecture’. Generally, for any third-party software that you can name, Windows receives top development priority. These are all perks.

The problem with Windows is Microsoft. Their monopolistic practices have survived to this present day, and they have an atrocious reputation for user privacy and security, underscored by their recent introduction of action-tracking AI onto users’ computers. They also have picked up the habit of spontaneously making changes that no users asked for, sometimes to benefit themselves, other times apparently for no reason but to see things change.

The Linux family

There are dozens of operating systems, but Linux distributions are the only ones that regular users would find easy to take full advantage of. I’m going to select and recommend two of them here, a corporate distribution and a free one.

Chrome OS

Chrome OS is a simple and lightweight Gentoo Linux-based rival to macOS and Windows. Chromebooks have conquered the educational market, which used to be key Macintosh territory, because they are both easy to use and inexpensive. In addition to the standard ‘web applications’ most people are used to, new Chrome OS devices offer passable support for standard Linux programs and Android apps.

There are minor problems with Chrome OS, but its ultimate issue is that it is from Google. It emphasizes cloud storage because Google is a cloud storage provider. You cannot expect privacy because Google is an advertising and search company. Whenever your personal interests and Google’s interests diverge, you have no reason to doubt that theirs will win out. Google seems more competent than Microsoft in their implementation of software, but that is not reassuring if you believe that they have nefarious intent.

Although true Chrome OS installations are built into the eponymous ‘Chromebooks’ (or Chromeboxes/Chromebases), you can deploy a Chrome-like operating system to your own Mac or PC via Chrome OS Flex. Some hardware is better-supported than others; check their list to see if your machine is certified.

Debian

In the past, I wouldn’t have peddled Debian to new users. But after applying my listed standards to recommendations, I’m short on alternatives. Besides, my continuing experience with modern Debian suggests that it has become accessible, when you are willing to learn, or can get help.

As the upstream source for most of the Linux world, Debian has an established community and has stood the test of time. It comes with little inherent bloat, is both configurable and well-supported, and should be reliable for the foreseeable future.

Depending on your machine, you might find hiccups with driver support during initial setup. For example, older Macs are known for requiring wifi drivers that need to be installed separately. Check in advance to see if your hardware has any special needs. If your machine does have trouble, someone has likely already walked someone else through a similar difficulty on a discussion forum somewhere.

Conclusion

Now that I’ve evaluated the traits of each of these platforms, I will give synopses of why you might use them.

If you have money, and either 1) own an iPhone, 2) don’t play many video games, and/or 3) view your computer as an appliance, get a Mac.

If software compatibility is important to you, including but not limited to gaming, you might go with Windows.

If you have a low budget, don’t have extensive processing needs, and/or don’t despise Google, try a Chrome device. (If you have an Android phone, you don’t despise Google.)

If you value customization, and freedom from ‘big tech’ and artificial end-of-life dates, decide for Debian.

If you have questions or comments to make about this list, feel free to drop a message by my address!

[1] This price was for a refurbished M4 Mac Mini. In Sept 2023, a M1 Mac Mini was $469, and a new low-end M2 was $599. In 2022 they were $589/$699 respectively.

[2] Windows 11 breaks some things and makes computers obsolete, but I suspect it is still better than alternatives.

The Second-Person Plural Pronoun

This is a classic gPress post, originally uploaded April 4, 2022.

The shame of modern English’s lack of a second-person plural is that the damage is self-inflicted.

Basic pronouns, modern English

Singular Plural
First I/me/my/mine We/us/our/ours
Second You/you/your/yours N/A
Third He/she, him/her, his/her, his/hers They/them/their/theirs

You can address or refer to anyone using the pronouns on the above table, unless you are directly addressing a group. In that case, you are forced to either:

1) Say only “you” and hope people infer that you meant the whole group
2) Use a lengthy combination of words: “you all”, “all of you people”, “you guys”, “ladies and gentlemen”, “to the group of human beings I am addressing”
3) Invent a new word: “y’all”, “youse”, “yinz”, “youins”

There’s an ongoing debate about which of these solutions is best. What is little-known is that we have had a solution to this all along, and the cause of our problem is cultural niceties.

Before discussing that, I feel it is helpful and educational to bring up the basic system of Spanish pronouns. This is what helped me to understand the history and development of our English language, by the parallel to another well-known language. The list will not be complete, but it will be enough to give a brief overview.

Basic pronoun forms, modern Spanish

Singular Plural
First Yo Nosotros
Second Tú, usted Vosotros (in Spain only), ustedes
Third Él/ella Los/las

At a glance, you can see that Spanish has all of the major fields covered, and then some. Why the extra ‘usted’ form, though?

The short answer is, words have connotations beyond their grammatical usage. These forms are either ‘familiar’ or ‘formal’. ‘Usted’ is the form you use when addressing someone who is socially superior, or perhaps someone else you don’t want to risk offending. (The corresponding English practice these days is to generously sprinkle ‘sir’, ‘ma’am’, or ‘miss’ through your sentences.)

The problem with having ‘formal’ and ‘familiar’ forms is the duality; if ‘formal’ language indicates respect and an acknowledgement of social standing, what does using the ‘familiar’ form imply?

Back when social statuses were clearly delineated, this wasn’t a problem, but as the world became democratized, using usted/ustedes became the practice in most of the Spanish-speaking world. Only Spain still uses the ‘vosotros’ form, and this distinction, speaking “el español del rey”, would cause you to stand out in a Latino crowd.

With this foundation laid, let’s have another look at English, or rather, English as it was.

Basic pronouns, Elizabethan English

Singular Plural
First I/me/my/mine We/us/our/ours
Second Thou/thee/thy/thine Ye/you/your/yours
Third He/she, him/her, his/her, his/hers They/them/their/theirs

These should be familiar to anyone who has read either the King James Version Bible or Shakespeare. Because those sources are also likely to be the only place they are seen, they are misunderstood, to the point that ‘thees and thous’ have become a byword for things which are considered complicated, archaic, and ‘unnecessary’.

People know the ‘thou’ form because it is a pronoun used to address God in the KJV, but they don’t know why it is used. The reason is shown in the above chart: it is the second-person singular pronoun, and God is a single person, so when someone is directly addressing God, correct Elizabethan grammar demands that form. Meanwhile, the ye form is like the modern-day ‘y’all’.

We lost this system for the same reason that the Spanish language was transformed: the forms acquired connotations of respect or disrespect, and people switched to using the ‘formal’ form all the time. English doesn’t have a dedicated formal form, so ‘you’ was made to do double-duty, as either the second-person plural or the formal second-person singular. I suspect the logic behind that choice was like that of the ‘royal we’.

Incidentally, the King James’ English is said to have been archaic even for its time. When the translators were putting together the work, the thees and thous were on their way out; they chose to stick with those words on the grounds that it was the most direct translation of the original pronouns (which it was, and still is). This choice was said to get criticism from readers who felt that the use of the familiar ‘thee’ and ‘thou’ disrespected God.

At any rate, people forgot over time that ‘you’ was supposed to be a second-person plural, which meant that we ceased to have one. But there are inevitably cases where that form of grammar is helpful, which has since become obvious. Thus, we now have a plethora of conjunctions designed to address this need, as alluded to at the beginning of this post.

The trouble is that they all have the same problem as what got ‘thou’ canned in the first place: they’re perceived to be informal!

The more things change, the more they stay the same…