A Graphical Abbreviation

Today while eating lunch I began to think about big numbers. Chess has 64 squares. A popular version of checkers has 100. Go has a whopping 361 vertices upon which to do battle. Might not sprouts eventually evolve some big numbers too? I think it is not only possible but likely, and I would venture to say that it is already true that the most skillful sproutsters in the world need up to 20 or 30 spots to be challenged.

But higher numbers of spots begin to get unwieldy! A game board is ready made and is neatly stable. A sprouts diagram, though, must be drawn by hand and gets more and more complex as the game proceeds. Just drawing 30 or so spots to start a game already is tedious. I am reminded here of one of my childhood whimsies. Setting up the pieces to begin a board game seemed analogous to winding up a mechanical toy. Work was required before the fun could begin. (The laziness which has plagued my adult life was already incipient.)

Thinking these thoughts and thoughts like them while eating lunch today, I suddenly thought of a way to avoid the "windup" necessity in sprouts. A simple abbreviation technique allows us to dispense with original spots altogether! The technique I came up is simply to write the integer representing the cardinality of the original spots, in the appropriate region, rather than draw the spots. Say a game of 50 spots is to be played. The number 50 can be written in the upper left hand corner of the diagram to show how many original spots are in the outer region. Now say Left wishes to play the open move. He replaces the number 50 with the number 48 and then draws the open move (a veteran cannibal connected to two ghosts). If Left had wanted to play a closed move instead, he would have drawn instead an enclosure with two spots on the enclosure and with a number inside the enclosure, and he would have replaced the original number 50 with a lesser number such that that number plus the number inside the enclosure would add up to 49. In general, a player draws the move he wishes to play and adds or adjusts numbers in new or affected regions to keep up with original spots. The numbers just tell how many original spots are contained in each region.

I am thinking that some players might like to use this technique to keep a neater diagram. A subtle merit of this technique is that it is a way to "move" spots. Normally we have to draw our lines so as to go out and get the original spots we need for a given enclosure. With this technique the spots come to us.

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