Matt's Take It Easy Stuff

Take It Easy is a multiplayer solitaire game, and good for starting out an evening of gaming when people are still filtering in and no one wants to start a long game yet. Here's its Board Game Geek page.

High Score

I believe that 307 is the highest possible score. Try to construct it! Want a hint, or just want the answer?

Because I am not good at this sort of puzzle, I solved it using a program that creates many random boards, then breeds them using a simple genetic algorithm. Thus I cannot be sure that 307 is really the highest score, but my program finds it in a few minutes, then fails to find any higher score. And this guy also claims it is.

Statistics

If you play at random, the most common score is zero, which you get 50.95% of the time. Scores of 1 and 2 are impossible. Maybe surprisingly, the next most common score is 24, with runners up 12 and 27. It is quite unlikely to score 7 by accident. The mean score is 11.19. For scores above 60 or so, the probability of a given score decreases slightly worse than exponentially:

   9.70│⠁                                                            
       │                                                             
   8.94┤                                                             
   8.64┤⢀⢀⢀⠠⢀⢀⠠⠐⠠                                                    
   8.34┤           ⢀                                                 
   8.03┤     ⡀⡀ ⢀⠠⡠ ⡀                                                
   7.73┤ ⠁⠈          ⠂⠁⠄⠄                                            
l  7.43┤        ⡀⢀ ⡀⠐ ⡀  ⡀                                           
o  7.12┤   ⠄  ⠄⡂⠂⠂⠐⠐⠄⠑⠠⠁⣐⢀⢁⠁⡀                                        
g  6.82┤ ⠐ ⢀⡀⡀         ⠐ ⠐ ⢀ ⠄⡀⡀                                     
1  6.52┤                  ⠈⠐⠉⠊⠠ ⠄                                    
0  6.21┤    ⠄                 ⠁⠢⠔⢤                                   
   5.91┤  ⠂                       ⠜⣠                                 
t  5.61┤                            ⠑⢄                               
r  5.30┤                              ⠋⠦                             
i  5.00┤                                ⠱⢢                           
a  4.70┤                                  ⠱⢄                         
l  4.39┤                                    ⠣⡄                       
s  4.09┤                                     ⠈⠣⡀                     
   3.79┤                                       ⠉⢆                    
   3.48┤                                         ⠑⢄                  
   3.18┤                                           ⠲⡀                
   2.88┤                                            ⠉⢆⡀              
   2.57┤                                              ⠑⠄             
   2.27┤                                               ⠈⢥⡀           
   1.97┤                                                 ⠰⣀          
   1.66┤                                                  ⠐⠤         
   1.36┤                                                   ⠈⠓⠄       
   1.06┤                                                     ⠐⢂⠂     
   0.75┤                                                      ⠁⠒⢁⢀   
   0.45┤                                                        ⢁⢀⡀⠁⡈
       │                                                         ⡀⢀⢀ 
      0┼──────────────────────────────────────────────────────────────╱
       0                                                            189

The probability of scoring 100 or higher is 1 in 8400, and of scoring 150 or higher is 1 in 7 million. The highest score my program generated in 10 billion trials was 189, which it managed 3 times.

Larger Boards

There is a sequel game called Take it to the Limit which uses the numbers 1–12, giving 64 tiles instead of 27 in Take it Easy. It has two boards. One is a straight-forward extension of Take it Easy: a hexagon with diameter 7. The other uses three linked 3-hexagons. Some additional complications are also added.

For the purposes of this page, let's ignore the complications and focus on simple hexagonal boards of various sizes. Now, the number of tiles on a board of radius r is 1 − 3r + 3r2. ("Radius" means the number of tiles from the center to the edge along a row of tiles, counting the center tile.) The smallest set of tiles needed to play on a board is the smallest cubic number equal to or greater than this. Thus:

RadiusBoard tilesTotal tilesRemark
000The only losing move is not to play
111Score is always 6…
278Still a real game! (We playtested it.)
31927Standard Take it Easy
43764Take it to the Limit
56164
691125
7127216
8169216
etc.

As usual, the amount of fun goes to zero as the adjustable parameter goes either to zero or infinity. Based on Board Game Geek rankings, it has a plateau at 3–4 (i.e. Take it Easy and Take it to the Limit have about the same ranking).

I suspect that no radius over 4 is playable, given that extra bonuses were deemed necessary to make 4 a marketable game. Certainly I would think that a radius 5 game (61 spaces on the board) would be very frustrating if the minimum 64 tiles were used, whereas if 125 tiles were used, maybe it wouldn't be totally awful. But it certainly would be a long game. I suspect that one would have to pick a few safe rows and focus on them or else risk a high probability of scoring zero. If so, it's a bad game.

Exercises Left to the Reader

Repeat all the above exercises for Take it Easy for at least board sizes 2 and 4, and maybe 5 and maybe make some general statements about size N.