Grace System

Grace System is a Perfect Clear Opener where the T piece is held throughout the first bag and the other 6 pieces form a 6 x 4 rectangle. There's a 88.6 % chance to achieve a Perfect Clear with the next 4 pieces.

Comparison to the Standard PC Opener
Placing the first T piece vertically will result in the same stack as in the Standard PC Opener (where the whole first bag was placed on one side).

In this case, there's still a 61.2 % chance to achieve a Perfect Clear using the following ways:

If the T piece is held throughout the first bag in Grace System, then the chance is actually higher than if the I piece is held throughout the first bag in the Standard PC Opener. It's 88.6 % for Grace System compared to 84.6 % for the Standard PC Opener. Additionally, the solutions for Grace System are usually easier to spot. On the other side, the Standard PC Opener is more often applicable (it will always work, if you place all 7 pieces).

The page PC Opener Success Rates lists all second bags for which either setup can end in a Perfect Clear.

Completing the PC with the T piece
The following table lists all beneficial ways to achieve a Perfect Clear with the help of the T piece you have in hold initially. This T piece is colored grey in the following illustrations. Most often, the T piece can be placed immediately. However, there are a few exceptions which are illustrated in grey letters below. For example, for the sequence [T]SOTZ, the pieces must be placed in the order STTZ (there's no solution involving the O piece, and for the piece combination TTSZ only the build with S piece on bottom will work for this sequence). Anyway, for every combination consisting of 4 pieces, there are 6 different orders where the T piece comes first. The higher the black numbers under #, the better the chances that this piece combination can be placed in one of the listed ways. Greyed out solutions will always have a lower chance.

Keeping the T piece on hold
The following section lists all beneficial ways how to create a 4 x 4 square without the use of a T piece (and where each shape occurs only once). This will be only possible for the piece combinations LJIO, LJIS, LJIZ, LJOS and LJOZ. There are 24 orders for each combination. All of these solutions are redundant.


 * LJIO: Here all 24 orders can be placed like in the first picture (I piece row may vary). Other ways may be used to avoid softdrop.


 * LJSI / LJZI: Here 20 out of the 24 orders can be stacked in one of the following 4 ways. First picture always works if L comes before S (I piece row may vary). Last picture is only needed for the order SLJI whereas softdrop must be used.


 * LJOS / LJOZ: Here 5 out of the 24 orders can be stacked in the following 2 ways.