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Critical Notchers
Critical notchers are notchers that represent a critical point in the notcher space. An example is the flying saucer shape, coded 222WW, which is dead. Anything weaker is obviously also dead. Anything stronger, however, is either unsettled or alive. We will derive the critical notchers from the Table of Notchers.
116WW can live. Anything stronger than it can obviously also live. Anything weaker is dead. Black 1 lives. White can start at many places to kill Black, but 1 and A are natural born killers. unkx80: Normally for this type, we say "6 die, 8 live".
116NS is alive, and 11SN is too. Anything stronger than it is also alive. Anything weaker can be killed or killed in ko. DavidPeklak : Could somebody please show how a 116 NW can be killed by white? I just don't get it... Er, you are right. I seem unable to recreate the sequence that convinced me it could. Give me some more time. --Dieter DavidPeklak : I put up a table of critical notchers: Since the status of a notcher is hichly dependent on which color may play the next move, I divided the list into two tables: One informs about life and death of a notcher when black has sente, the other one when white has sente. For that purpose I would like to define the expressions "weaker" and "stronger" precicly. A notcher is defined nkl xx. A notcher is stronger than another notcher where one or more variables out of n, k, l or xx are greater than the corresponding variable of the other notcher. For CC, SS > SN = NS > SW = WS > WN = NW > WW. (I assume NN = SW = WS here? -- KarlKnechtel) For this table, critical notchers are defined as follows: A critical notcher is a notcher that is alive or lives depending on Ko. Every notcher that is stronger than any critical notcher is alive (unless it is in the list of critical notchers itself and marked K or D). All the other notchers are dead. When white has sente, critical notchers are: 116WN K - 116NW D - 115WS K - 116WS K - 115SW D When black has sente, critical notchers are: 116WW L - 115WN L - 113WS L - 125WW L - 123WN K An xyz NN notcher always gives the same result as nkl SW and nkl WS. If the two are different, the result favours black. (Exeption: the 511 xx notcher) ...The correctness of this list depends highly on the correctness of the Table of Notchers ;-) This is a copy of the living page "Critical Notchers" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |