Here's a close up of the box:
- It is a Solitaire game that can be played in turns and scores compared (but no strategies arise due to interactions of players).
- The aim is to "shut" as many tiles (each being one of the digits from 1 to 9) as possible.
- On any given go, a player rolls two dice and/or has a choice of rolling one dice if the tiles 7,8,9 are "shut".
- The sum total of the dice roll indicates the sum total of tiles that must be "shut". If I roll 11, I could put down [2,9],[3,8],[1,2,8] etc...
- The game ends when a player can't "shut" tiles corresponding to the dice roll (including the case when all tiles are "shut").
- Random (Just randomly pick any potential tile combination)
- Shortest (Choose the tile combination that has shortest length: i.e.  instead of [1,2] ~ in case of a tie pick randomly)
- Longest (Choose the tile combination that has longest length: i.e. [1,2] instead of  ~ in case of a tie pick randomly)
- Greedy. This chooses the tile combination that ensures the best possible chance of the game not ending on the next go. This is calculated by summing the probabilities of obtaining a dice roll that could be obtained.
Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
1st Qu.: 6.00 1st Qu.:14.00 1st Qu.:18.00 1st Qu.: 7.00
Median :11.00 Median :21.00 Median :24.00 Median :11.00
Mean :11.42 Mean :20.45 Mean :24.16 Mean :12.06
3rd Qu.:16.00 3rd Qu.:27.00 3rd Qu.:30.00 3rd Qu.:17.00
Max. :43.00 Max. :43.00 Max. :43.00 Max. :43.00
Shortest and Greedy seem to do a fair bit better then the other two. If we take a look at the distribution of the scores that is confirmed:
Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.00
1st Qu.:4.000 1st Qu.:3.000 1st Qu.:2.00 1st Qu.:4.00
Median :5.000 Median :3.000 Median :3.00 Median :5.00
Mean :4.897 Mean :3.414 Mean :2.86 Mean :4.82
3rd Qu.:6.000 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:6.00
Max. :9.000 Max. :9.000 Max. :8.00 Max. :9.00
Df Sum Sq Mean Sq F value P
stbaov$Method 1 11337 11337 196.3 2e-16Residuals 127169 7345725 58
(On a technical note some of the pre analysis is done using python and the actual graphs seen here are done using R)