Cal's Currajong: Simplifying Assumptions
Assumptions. Approximations. What's the right word? There are ideas that seem to work for a while but whether that usefulness is illusory, and whether that usefulness will keep happening, are open questions.
One such idea is an old one, the idea of "the move". This notion is falling out favor with me for the moment, but I think I will wait till next week to discuss it.
Two recent concoctions - by yours truly - continue to entertain. Both are built into the chart I discussed last week. The most revolutionary of the two came to me when I was struggling with the five dot flipflop not so long ago. It suddenly occurred to me that I could think of that flipflop - maybe all flipflops, and maybe all traps - as a given number of isolani plus a two dot trap. So, a two dot trap is zero isolani plus a two dot trap. A five dot flipflop is a two isolani plus a two dot trap. A seven dot trap is three isolani plus a two dot trap. And so forth, at least according to my approximation.
It's easy to see how I incorporated this idea into the chart. I accepted the AJS conjecture as true (another assumption!) through 16 dots. Then, any N revealed to be a flipflop or trap became a two dot trap plus a theoretical number of isolani. For instance, AJS has player2 winning 14 dots both in normal and reverse play. That means, by my scheme, that 14 dots is a two dot trap plus an even number of isolani (since the peacemonger needs to not rock the boat).
The other approximation set into the chart is the idea that a trapeze produced single pivot doesn't have any effect. This notion is almost certainly false as a general proposition, but I'm hoping it is almost always true in individual cases. I used this idea to evaluate the results of various trapeze moves. I simply ignored the pivot and used the game values of the remaining groups after a given trapeze move.
ANALYSIS (Find a shrink.) 14+ The chart discourages player1 from looping, but never forget that the chart is built on approximations. All of the loops are worth considering.
1(15)2 But even apart from the chart, this move entices. The two-thirds rule indicates that player2 is struggling to get his even number of isolani.
1(16)1[3,4] Player2 needs to maximize isolani, since two-thirds of fourteen is closer to nine than to ten. Creating a two spot trap is admirably efficient.
Now player1 can take the efficient dot 16 out of the larger mix with 3(17)16, but player2 will be left with a very efficient resource in 2(18)15. I like better 5(17)6, looking for pharisees in all the wrong places.
--Cal Hudson, First World Champion of Sprouts
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