November 9, 2010

In recent tournaments, which have all been played by email, I have depended heavily upon Jeff Peltier’s charts to help me get a grasp. But if my dream of in-the-flesh match or tournament play ever reaches fruition, what then? We certainly would follow the custom of such games as chess and go and disallow resort to notes or other external aids. This consideration has led me to begin a search for mnemonic devices to aid memorization of the charts. I have only been at this for a couple of days, so my findings are preliminary and error prone.

The pivot chart is doable, if I have not blundered in my analysis. There seems to be a simple pattern with only a few exceptions. For positions with an even (odd) number of cannibals, I am calling any evaluation of 0/0 “deep even” (“deep odd”), an evaluation of 1/1 “deep odd” (“deep even”), an evaluation of 0/1 “shallow even” (“shallow odd”), and an evaluation of 1/0 “shallow odd” (“shallow even”). By “deep” (“shallow”) I intend a position that will (will not) ultimately resolve to a UT. By “even” (“odd”), I mean with an even (odd) parity of switchmen. I am also labeling the starting positions from n = 0 up as a, b, c, a, b, c, a, b, c, and so forth. For example the starting position of four original spots is a type b.

In my system, any starting position of type a is a shallow even (SE). Any starting position of type c is a deep even (DE). All starting positions of type b are deep odd (DO), except for the littoral positions n=1 and n=4, which are shallow odd (SO).So, moving up from n=0, the starting positions are SE, SO, DE, SE, SO, DE, SE, DO, DE, SE, DO, DE, SE, DO, DE, SE, DO, DE, and so forth, at least through the latest n computer-confirmed to follow the AJS pattern.

Cal Hudson gave a simple rule-of-thumb for positions of the sort treated by the pivot chart: simply ignore the pivot and evaluate the position as two separate biospheres. This is actually a pretty good rule. It works with few exceptions for positions of type aPc, bPb, bPc, and cPc. Consider type aPc, where the Hudson rule gives SE + DE = DE. And indeed, all of the charted aPc positions are DE except where a=2 or c=2, when the position loses its depth and becomes SE. Oh, one other exception is 0P5, again SE, but I think that covers it. (I’m lumping 1/4+ with 1/1 for the purposes of this mnemonic, by the way. There are only 2 of these to remember, 3P5 and 5P9, both type aPc, and I think both usefully can be thought of as DE, as given by my system.)

Hudson’s rule predicts pelagic positions of type bPb to be DE (DO + DO = DE). This is true for all of the charted bPb positions except the littoral positions 1P1, 1P4 and 4P4, positions that again lose their depth to become SE, but here fully in accordance with Hudsonian arithmetic (SO + SO = SE).

Hudson’s expectations in regards to type bPc are perfectly confirmed. All charted positions of type bPc are DO (DO + DE = DO). He was nearly as perfect in regards to the charted positions of type cPc, which are all DE (DE + DE = DE) except for 2P2 (SO).

Positions of type aPa and aPb, however, are nonHudsonian. The Hudson rule-of-thumb predicts the standard aPa to be SE (SE + SE). In fact, aPa positions are all DO, except 0P0, which is SO. The Hudson general expectation for aPb is DO (SE + DO) but all charted positions of this type are actually SO.

Let me summarize. All positions of type aPa are DO, except 0P0, which is SO. All positions of type aPb are SO. For positions of type aPc, bPb, bPc, and cPc, the Hudsonian arithmetic works perfectly, with the exceptions that 2Pc, aP2, and 0P5 are all SE, and with the exception that 2P2 is SO.

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