The chance of winning the 3 lines reward of Wondrous Tails is ridiculously low

[axemtitanium]

If you use Second Chance Shuffle to complete any 2 lines, there is a 8.33% to complete the 3rd line. This is because placing your 8th stamp in 6 out of the remaining 9 slots will still build toward a 3rd line. A stamp placed in the remaining 3 slots will not be capable of completing a line. Once this 8th stamp is placed, there is only 1 spot left out of 8 that could possibly finish your 3rd line. Thus, the probability is 6/9 * 1/8 = 1/12 = 8.33%.



You can prove this to yourself by completing any two lines in a stamp card. For example:



Place a stamp in each of the open spots, in sequence. You'll notice that for 6 of those 9 open spots, there is exactly 1 spot that will result in a triple line. The remaining 3 open slots are duds.

I'm still working on the chances of shuffling into a double line formation.

[Raikki]

I'm still working on the chances of shuffling into a double line formation.

I already did the work on this if you're interested. 32/11440 7-seal cards have two lines, so you have a 0.28% chance to shuffle into one. However, of those, only 16 have three ways (8.3% chance) to make the 3rd line. 8 have two ways (5.6% chance), and 8 have one way (2.8% chance). Overall, the average two-line 7-seal card has a 6.25% chance to become a three-line card when the last two seals are added.

[StouterTaru]

If you use Second Chance Shuffle to complete any 2 lines, there is a 8.33% to complete the 3rd line.

...

the probability is 6/9 * 1/8 = 1/12 = 8.33%.

That only applies to one diagonal line and one horizontal/vertical, of which there are 16 combinations.

If you have one horizontal and one vertical line, there is only one diagonal combination that works, so odds are 2/9 * 1/8 = 1/36. There are also 16 of those combinations.

That means a 7 sticker shuffle gives a 1/715 chance of a two line that has a 1/12 chance of triple, and a 1/715 chance of a two line that has a 1/36 chance of a triple. It's worth holding on to if you get it, but not something to keep shuffling until you do.

[Raikki]

That only applies to one diagonal line and one horizontal/vertical, of which there are 16 combinations.

If you have one horizontal and one vertical line, there is only one diagonal combination that works, so odds are 2/9 * 1/8 = 1/36. There are also 16 of those combinations.

You're missing the horizontal+vertical cards where both diagonals work, the ones where one line is at an edge row and the other line is in one of the middle columns, and vice versa.

[StouterTaru]

You're missing the horizontal+vertical cards where both diagonals work, the ones where one line is at an edge row and the other line is in one of the middle columns, and vice versa.

OK see that now, so it's:
3/1430 chance at 1/12
1/1430 chance at 1/36

It's still only 24 double possibilities at 7 stickers, and several times as many combos that are potential triples without two full lines.

[Raikki]

It's still only 24 double possibilities at 7 stickers, and several times as many combos that are potential triples without two full lines.

824/11440 (7.2%) of 7-seal cards have the potential to turn into 3 Line cards. The average probability of obtaining a 3-Line card from one of those is 2.9%.