Yes, a lottery system is used for a particular lot size if after proportionate division, the number of shares comes out to be less than the minimum lot size.

To explain this in more detail, let me take the example of Basis of Allotment for Indigo Paints shared above. There were only 1,167,514 shares reserved for the HNI category. But application for 305,807,610 shares came in the HNI category.

In the 14 lots (140 shares) category, there were 2276 applicants who applied for a combined total of 318,640 shares. This is 0.10% (318,640/305,807,610 *100 = 0.10419623%) of the total shares applied for in the HNI category. Hence, for this category (aka 14 lots), only 0.10% of the total reserved shares (aka 1,167,514) would be allotted. This comes out to be 1216.5 shares (0.10419623% * 1,167,514), which got rounded to 1220 shares as their lot size was 10 shares. Now these 1220 shares need to be proportionate allotted to 2276 applicants. As after trying to proportionate allot these shares, the number of shares per applicant comes out to be less than 10 shares i.e. their minimum lot size (1220 / 2276 = 0.53 shares per applicant), a draw of lots need to happen in this category to allot the 1220 shares in minimum lot size of 10 shares per applicant. That would mean only 122 applicants (1220 / 10) would be eligible to get the shares out of the 2276 applicants.

Similarly, if we check the 235 lots (2350 shares) category, only 10 applicants applied for a total of 23,500 shares. That comes out to be 0.01% (23500 / 305,807,610 * 100 = 0.00768457005%). Hence, for this category (aka 235 lots), only 0.01% of the total reserved shares (aka 1,167,514) would be allotted. This comes out to be 89.7 shares (0.00768457005% * 1,167,514), which got rounded to 90 shares as their lot size was 10 shares. Now these 90 shares need to be proportionate allotted to 10 applicants. As after trying to proportionate allot these shares, the number of shares per applicant comes out to be less than 10 shares i.e. their minimum lot size (90 / 10 = 9 shares per applicant), a draw of lots need to happen in this category to allot the 90 shares in minimum lot size of 10 shares per applicant. That would mean only 9 applicants (90 / 10) would be eligible to get the shares out of the 10 applicants.

But, if we check the 33,557 lots (335,570 shares) category, there were 109 applicants who applied for a total of 36,577,130 shares. That comes out to be 11.97% (36,577,130 / 305,807,610 * 100 = 11.9608305%). Hence, for this category (aka 33,557 lots), only 11.97% of the total reserved shares (aka 1,167,514) would be allotted. This comes out to be 139,738 shares (11.9608305% * 1,167,514 = 139644.3. You will notice that 94 extra shares were added to this category). Now these 139,738 shares need to be proportionate allotted to 109 applicants. That comes out to be 1282 shares ( 139,738 / 109). As you would observed, the allotment to each applicant exceeded the lot size multiple of 10 shares. This is possible because of Point (e) referenced above.

As you would have noticed, after an application of certain number of lots (in the above example, that is 250 lots), each applicant was assured to get the allotment of shares. That is usually around the number of times the category was over-subscribed (in above example, the HNI category was over-subscribed by 261 times, hence people who applied for 250 or more lots got assured allotment). In the case of Shyam Metalics, this number would have been around 340 lots. Any application whose size was above 340 lots would have been assured to have gotten the allotment of shares because even after proportionate division of shares, each person would be getting at least minimum lot size (aka 45 shares). To know the exact chances for getting shares alloted for various lot sizes, we will have to wait for Shyam Metalics Basis of Allotment document. From what I could find, this document isnâ€™t public yet (It would likely be accessible here once its made public).