Beeswax

Pile-On, Pile Sort, Fifteen Puzzle, Beeswax, etc.

You may know it as Fifteen Puzzle or Pile-On or Pile Sort. Michael Keller calls it Beeswax due to it's similarities with the game Beehive. Millions of people are also familiar with the game from one of numerous apps, many of which don't use playing cards, but rather colored objects like balls, rings, or even liquids. Whatever you call it, it's a great puzzle game, and I wrote a solver to play it.

Not every random deal of this game can be solved, but the odds are fairly good: 99.18%.

This game can also be played with different numbers of ranks, suits, or initially empty fans/columns (as many of the app writers have discovered). I have run tests to determine the win rates for a variety of configurations.

One initially empty fan/column
Suits	Ranks	Deals Played	Games Won	Win Rate %
2	13	1,000,000	132,811	13.3
3	13	1,000,000	7,245	0.72
4	13	1,000,000	118	0.01
5	5	1,000,000	139,560	13.96
5	13	1,000,000	3	0.00
6	5	1,000,000	49,767	4.98
6	6	1,000,000	18,875	1.9
7	7	1,000,000	1,206	0.12
13	4	1,000,000	27,070	2.7

Two initially empty fans/columns
Suits	Ranks	Deals Played	Games Won	Win Rate %
3	13	100,000	99,959	99.96
3	14	100,000	99,906	99.91
4	9	100,000	99,995	99.995
4	10	100,000	99,980	99.98
4	11	100,000	99,912	99.91
4	12	100,000	99,718	99.72
4	13	1,000,000	991,772	99.18
4	14	100,000	98,120	98.1
5	13	100,000	96,444	96.4
5	14	100,000	92,518	92.5
6	13	100,000	92,887	92.9
6	14	100,000	85,338	85.3
7	7	100,000	99,997	99.997
7	13	100,000	89,279	89.3
7	14	100,000	78,872	78.9
8	8	10,000	9,999	99.99
8	13	100,000	86,710	86.7
8	14	100,000	73,985	74.0
9	9	10,000	9,981	99.81
9	12	10,000	9,364	93.6
9	13	10,000	8,531	85.3
9	14	10,000	7,090	70.9
10	10	10,000	9,936	99.36
10	13	10,000	8,392	83.9
10	14	10,000	6,841	68.4
11	13	10,000	8,326	83.3
12	9	10,000	9,988	99.88
12	13	10,000	8,313	83.1
13	8	10,000	9,997	99.97
13	10	10,000	9,935	99.35
13	13	10,000	8,252	82.5

Three initially empty fans/columns
Suits	Ranks	Deals Played	Games Won	Win Rate %
3	13	100,000	100,000	100
4	13	100,000	100,000	100
5	13	100,000	100,000	100
6	13	25,000	25,000	100
7	13	5,000	5,000	100
8	13	1,000	1,000	100
9	13	100	100	100

Any comments are welcome, please send to Mark Masten at:

Last modified September 20, 2021

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