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. Strictly speaking, there are many critical notchers. Some are more interesting than others, such as notchers which are critical in many directions. The directions include the length of the notch, the length of the legs and the weakness of the corners.

Critical one-space notchers

• 113WS notcher or NN or SW: Unsettled. Anything weaker is dead.
• 115WN notcher: Unsettled. Anything weaker is dead.
• 116NW notcher: Alive. Anything weaker is unsettled.
• 122WS notcher or NN: Unsettled. Anything weaker is dead.
• 124WS notcher: Alive. Anything weaker is unsettled.
• 133WS notcher or NN: Alive. Anything weaker is unsettled.

Critical two-space notchers

• 213WN notcher: Unsettled. Anything weaker is dead.
• 214NN notcher: Alive. Anything weaker is unsettled.
• 222WN notcher: Unsettled. Anything weaker is dead.
• 223WN notcher: Alive. Anything weaker is unsettled.

Critical three-space notchers

• 311NS notcher: Unsettled. Anything weaker is dead.
• 322WW notcher: Unsettled. Anything weaker is dead.
• 313WN notcher: Unsettled. Anything weaker is unsettled.

A table of critical notchers: Since the status of a notcher is highly dependent on which color may play the next move, the list is divided 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 the expressions "weaker" and "stronger" must be defined precisely. 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

116SW D - 125WN K - 125NW L - 124WS L - 134WN L

133NS L - 215WN D - 215NW L - 215WS D - 214SW L

215SW L - 223WN L - 322WW L - 313WN L - 411NS L

511 SW D - 511 NN L

When Black has sente, critical notchers are:

116WW L - 115WN L - 113WS L - 125WW L - 123WN K

123NW K - 133WW K - 214WW L - 213WN L - 223WW L

222WN L - 312WW K - 312WN K - 312WS K - 311NS L

411WN L

An xyz NN notcher always gives the same result as nklSW and nklWS. 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