(a summary of play-tester feedback; rules still available here)
This was a somewhat divisive game for y’all.
On a scale from “No!” to “Yes!”, your most common answers to “Did you like it?” were “Yes,” “No,” and “Meh,” in that order.
Some folks enjoyed the tactile, sliding feel. Others appreciated the moment when you leave the blank spot in the corner, leaving your opponent with only one legal move. Others liked the unusual win condition, where symmetry spells victory. (Or perhaps I should say, “symmetry spells victoryrotciv”.)
But there were some valid complaints, too. Some noted that it’s hard to develop a sense of strategy; the game is dominated by short-term tactical responses. Others got caught in loops, or stalemates that felt like they’d never end.
That impression isn’t wrong.
Andy Juell ran the numbers, and delivered this report:
Out of the 138,600 possible coin setups the pie-slicer can choose, 15,488 leave one player with symmetric coins, and are thus instant losses.
There are also 936 degenerate positions where both players’ positions are symmetric….
With perfect play the majority of the remaining setups (87,144) can’t be forced to a conclusion… The first-move advantage is never enough to overbalance being given the weaker starting position, so these draws are the best the slicer can hope for.
Andy’s results in fuller detail:
| (False Start) | 936 |
| Drawn | 87144 |
| Loss in 38 | 40 |
| Loss in 37 | 0 |
| Loss in 36 | 96 |
| Loss in 35 | 0 |
| Loss in 34 | 96 |
| Loss in 33 | 0 |
| Loss in 32 | 112 |
| Loss in 31 | 0 |
| Loss in 30 | 96 |
| Loss in 29 | 0 |
| Loss in 28 | 144 |
| Loss in 27 | 0 |
| Loss in 26 | 96 |
| Loss in 25 | 0 |
| Loss in 24 | 48 |
| Loss in 23 | 0 |
| Loss in 22 | 104 |
| Loss in 21 | 0 |
| Loss in 20 | 176 |
| Loss in 19 | 128 |
| Loss in 18 | 168 |
| Loss in 17 | 128 |
| Loss in 16 | 112 |
| Loss in 15 | 264 |
| Loss in 14 | 224 |
| Loss in 13 | 200 |
| Loss in 12 | 160 |
| Loss in 11 | 200 |
| Loss in 10 | 160 |
| Loss in 9 | 560 |
| Loss in 8 | 896 |
| Loss in 7 | 1544 |
| Loss in 6 | 1480 |
| Loss in 5 | 3488 |
| Loss in 4 | 1984 |
| Loss in 3 | 5392 |
| Loss in 2 | 3272 |
| Loss in 1 | 13664 |
| Loss in 0 | 15488 |
In other words: the game really is a draw, most of the time.
The game, by the way, is my own riff on “Change, Change,” from Sid Sackson’s classic book Gamut of Games. (That’s the one-player version I gave in the document.) My very early play-testers hadn’t loved “Change, Change,” which prompted me to devise “Mirror, Mirror.” But it drew a relatively warm response from you folks, so perhaps that’ll be the version I feature in the book.
(By the way, Andy Juell also conducted an exhaustive analysis of “Change, Change” and found that, with perfect play, it requires just over 11 moves on average, and 19 moves at the most.)
By the way, one way to escape the stalemate trap in “Mirror Mirror” is with a new path to victory: Calling Your Shot.
Under this rule, you need not achieve symmetry. Instead, you can win by being several steps closer to symmetry than your opponent is.
At the start of your turn, you call, “I’m N moves from symmetry.” (N can be 2, 3, or 4.) Then, show the moves. (Assume that your opponent cannot interfere; you make all the moves.)
Then, restore the board to its prior state. Now, your opponent is allowed N + 3 moves to achieve victory, without any interference from you. If they can do so, they win. If not, you do.
Play-testers made some other nice suggestions, too. One was to allow vertical as well as horizontal lines of symmetry as a way of achieving victory. I plan to investigate that variant myself and see if it improves the game.
Anyway, I leave you with a few numbers on the Fifteen Puzzle that inspired the game.
