If the roll is 4, 6, 1, 2, then your “base options” are 10&3, 5&8, and 6&7. If you already have three white chits on columns, then numbers which are not those

If the roll is 4, 6, 1, 2, then your “base options” are 10&3, 5&8, and 6&7. If you already have three white chits on columns, then numbers which are not those three are removed. So for example if you have chits on 3, 6, and 7, your options will be 3 and 6&7. Similarly, if you have two white chits, combinations that would result in 4 columns having chits are removed, possibly by splitting a pair into two options. If a column is captured, options are further limited.