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 × 4 rectangle. There is 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 is 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 higher than if the I piece is held throughout the first bag in the Standard PC Opener. It is 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 one places 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 one has 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 is 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.

shapes	setups		#	shapes	mirrored
TTIO	TTIO , TTOI, TITO		3
TTIL	TLTI, TITL, TTLI, TILT, TLIT, TTIL	TITL, TLTI, TTLI, TTIL	6	TTIJ	TJTI, TITJ, TTJI, TIJT, TJIT, TTIJ	TITJ, TJTI, TTJI, TTIJ
TTIS	TTIS, TITS		2	TTIZ	TTIZ, TITZ
TTOL	TTOL, TOTL	TOLT	3	TTOJ	TTOJ, TOTJ	TOJT
TTOS	no setups		0	TTOZ	no setups
TTLJ	TTJL, TTLJ TTJL, TJTL	TLTJ, TTLJ	4
TTSZ	TTSZ	TTZS	2
TTSZ	STTZ	ZTTS	2
TTLS	not with T first		0	TTJZ	not with T first
TTLS	STLT, LSTT		2	TTJZ	ZTJT, JZTT
TTLZ	TLTZ, TTZL, TTLZ TLZT	TZTL, TTZL	5	TTJS	TJTS, TTSJ, TTJS TJST	TSTJ, TTSJ
TIOL	TOLI, TOIL, TIOL		3	TIOJ	TOJI, TOIJ, TIOJ
TIOS	no setups		0	TIOZ	no setups
TILJ	TLIJ, TILJ	TJIL, TIJL	4
TILJ	JTLI, [JTIL]	LTJI, [LTIJ]	2
TISZ	no setups		0
TILS	not with T first		0	TIJZ	not with T first
TILS	STIL, ISTL		2	TIJZ	ZTIJ, IZTJ
TILZ	TZIL, TIZL, TZLI	TZIL, TIZL, TZLI	3	TIJS	TSIJ, TISJ, TSJI	TSIJ, TISJ, TSJI
TOLJ	not with T first		0
TOLJ	JTOL, JTLO	LTOJ, LTJO	4
TOSZ	no setups		0
TOLS	not with T first		0	TOJZ	not with T first
TOLS	SOTL		1	TOJZ	ZOTJ
TOLZ	no setups		0	TOJS	no setups
TLJS	TSLJ, TLSJ		2	TLJZ	TZJL, TJZL
TLSZ	TSLZ, TSZL	TLSZ	3	TJSZ	TZJS, TZSJ	TJZS

Keeping the T piece on hold

The following section lists all beneficial ways how to create a 4 × 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.

See Also

• Perfect Clear Opener: the Standard PC Opener
• PC Opener Success Rates: lists all PCable second bags for Grace System
• Perfect Clear Methods a list of all Perfect Clear methods featured on this Wiki

External links

• a document listing all PCable second bags for Grace System