The 81-card deck
Threezy normally plays with 27 cards and three features. The 81-card mode adds a fourth feature, the number of symbols on a card, which gives you the full deck from the classic tabletop game. Same rule, three times the cards, and a lot fewer sets to find.
Four features instead of three
- Number: one, two or three symbols
- Shape: triangle, circle or square
- Colour: three colours (swappable for colour-blind palettes in settings)
- Fill: solid, striped or empty
The rule does not change: three cards are a set when every feature is either all the same or all different across the three. With four features there is simply one more thing that can break it. Two triangles and a circle is never a set, whatever the other three features are doing.
Why it is so much harder
Pick any two cards and exactly one card in the deck completes the set. In the 27-card deck that third card is one of 25 remaining cards; in the 81-card deck it is one of 79. So a random triple is a set 1 time in 25 with three features, but only 1 time in 79 with four.
On a board of nine cards there are 84 possible triples. That works out to about 3.4 sets on an average 27-card board, and about 1 on an average 81-card board. You are no longer choosing between several sets; you are hunting for the one that exists.
It shows in the scores. Players who play both versions find about 46% as many sets in two minutes on the 81-card deck as they do on the 27-card deck, and the ratio is surprisingly stable across skill levels.
How to approach it
- Work from pairs. Choose two cards, work out the one card that would complete them, and look for it. With about one set per board, checking pairs systematically beats waiting for a set to jump out.
- Use number as a filter. Number is the easiest feature to read at a glance. If two cards both show two symbols, the third must show two as well; if they differ, the third shows the remaining count.
- Expect the long search. A board with one set can take ten seconds or more even for strong players. That is the game, not a sign you are doing badly.
Questions
How many cards are in the deck?
81. Every combination of four features with three options each: 3 × 3 × 3 × 3 = 81, and every card is different.
How many different sets are there?
1,080 in the 81-card deck, against 117 in the 27-card deck. Any two cards decide exactly one third card, so the count is 81 × 80 / 6.
Is there always a set on the board?
In Threezy, yes. The board is re-dealt until at least one set exists, so you never stare at an impossible board. Often there is exactly one.
Does the 81-card mode count toward my rating?
Yes, at a quarter of the weight of a 2-minute game, and on its own scale so a lower 81 score is not read as a bad game. It has its own leaderboard tab.
More from Threezy
- How to play: the rule in one minute, with worked examples
- Today's daily puzzle: one shared board for everyone
- Practice: untimed play, sprints and benchmarks
- Games like SET: other pattern and logic games worth a try
- Daily archive: past boards and winners
Threezy is an independent puzzle and is not affiliated with, endorsed by, or connected to Set Enterprises, Inc. or PlayMonster. SET is a trademark of its respective owner and is mentioned only to describe the style of puzzle.