The Game of Pent

Puzzles are a big part of my work as a teacher and curriculum developer, as you can see in this article, in the Geometric Puzzles launch page on my website, and in fact throughout my books. (Not to mention my parallel career of sorts as a cryptic crosswords constructor, and how I spend much of my free time.) On the other hand, I have not used games much. Still, I made a directory of games on my website per the request of one regular visitor.

Pent is a strategy game invented by George Mills. When I taught elementary school, I made it available for students to play if they finished their work early or during recess on rainy days. You can now play it on my website. Today’s post was written by George in response to questions about Pent. He ends with his own questions. Play the game, think about it, and share your answers in the comments.

— Henri

Questions about Pent

Why does each player only have eight pieces? A winning path through the center would require nine. Perhaps that center space should be greyed out?

Interesting questions. The simplest answer is that I was playing the game with chess pawns as the pieces, so there were 8. I no longer recall for certain if I considered having 9 or even if I noticed that no winning path with 8 could go through the center. I suspect I did (both), but perhaps not.

In hindsight, a more reasoned answer involves strategy.  I do recall my sense that in general having more pieces makes it easier for player 1 to win.  I would conjecture (today) that it is “easy” for player 1 to win if there are unlimited pieces (which makes moving already played pieces pointless and, I believe, makes draws impossible). With limited pieces, the strategy decision of whether to place a new piece or move an already placed one (so as to keep more unplayed pieces in reserve) is significant.  Whether 8 makes an optimally challenging and enjoyable game may be a matter of taste.  I can say that players found the game quite nuanced and enjoyable with 8 pieces.

As to greying out the center space, I would say that even with 8 pieces the center could play a strategic role when moving already placed pieces to adjacent spaces. It might be on the shortest (unblocked) route from one space to another that you wish to occupy. Or it might be advantageous to occupy the center early so as to be able to later move quickly in any direction. Also, I found that beginners often think the shortest route will go straight across the board, so the center space may be a kind of decoy for the unwary.  All in all I wouldn’t recommend greying it out. I think it adds spice to the game.

For these reasons my choice today would be to stick with how I designed the game in 1971.  But it’s been years since I’ve actually played the game, so it will be interesting to hear what a new generation of players discover about strategy.

Some questions:

  1. Is my conjecture about unlimited pieces true – that draws are impossible and that player 1 would have an “easy” win?
  2. With 8 pieces is there a winning strategy for player 1 (or 2?), or does best play on both sides necessarily lead to a draw (a forced draw being, as in chess, three repetitions of the same board position)?
  3. How would it affect strategy (or enjoyment) if the center field were indeed greyed out?

—George Mills

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