I would like to clear out that the method when used as a high probability option IS NOT at all something like flipping a coin. In fact the risk can be calculated early enough.

Heres an example from a puzzle already posted in this thread. As you can see after applying basic strategies we are already in VBPN regarding digits 2,5,6 and 9. Like I said in previous messages at this stage those digits are useless.

Digit 4 though is not.. It appears at Block1 at 4,5,6,7,8,9 at Block2 at 4,8 at Block 4 at 8,9 at Block7 at, 1,2,3 and at Block8 at 7,8. It also appears at only 4 solved cells which is comparatively low i.e at positions 3,6,2,4. So unless you can calculate your risk you shouldn’t proceed using this digit. Striking out the solved positions from the unsolved we end up with positions 5,8,9,1 and 7.

This is the ONE and ONLY possibility for digit 4 to eventually be non VBPN. Moreover it is a forced line once 4 is set at Block1 pos 5.

At this stage one can easily check how many the total combinations for digit 4 are. From a quick look I can count 11.(Correct me if I am wrong). So the risk is 1 out of 11 or 9%. Taking up this risk you immediately know that a 4 has to be excluded from Block1 position 5. Doing that in just 2 steps you end up with digit 3 at Block7 position 1 solved.

NB. There are cases when a digit is not in VBPN mode but if you strike out the positions where it was already solved then it proves itself that its going to be in VBPN mode no matter what. That digit is of no use anymore. For example if you check digit 5 at the 4 ½ puzzle of tso you will see that it ends at the following possible BPs: 56,5678,3,35,1345679,57,7,2345,45. After striking out positions 3 and 7 from the unsolved squares you end up with incompatibility so digit 5 will end up in VBPN mode no matter what.

USE OF THE METHOD WITH PROVEN 100% MATHEMATICAL CERTAINTY

I am working on this. For anyone interested to join me in this effort the scope is to prove that a digit is going to end up in VBPN mode. This proof must come from other digits not from the digit iitself. My current line of reasearch is to check what one can do with digits that are already in VBPN mode . Most of them reveal the BPs they left/ or will eventually leave behind.