Simple games to play in mind
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Sometimes on the bus, etc. we want to play some games only in mind.

So there are some simple games.

Rules:
- game with "perfect information"
- possible games board positions are less then 50 milions


Why 50 milions? Because some number had to be fixed, and I estimated this.
Better measure of complexity would be number of edges in the game graph, but this would be hard to calculate and hard to explain.

If anyone wants to add a game and does not know how many states it has, please send me a message - I will calculate

ps. srry bout my eanglish
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<252 states
(10 choose 5)
(probably 216)
 
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574 states
Each dice have 6 sites with 4 directions.
6*4*6*4=574
(but to play game without dices you should remember dice, what is not easy...)
 
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<630
Easy to calculate: (9 choose 4)*(5 choose 4)
 
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Only 672 states
I calculated this on a sheet.
 
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5. Board Game: Babylon [Average Rating:5.53 Overall Rank:13228]
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846 states
Source:
http://www.thegamesjournal.com/letters/Nov2004.shtml
 
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6. Board Game: King [Average Rating:0.00 Unranked]
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1680 states
(9 choose 3) * (6 choose 3)
 
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7. Board Game: Clou [Average Rating:5.09 Unranked]
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<5,040 states
position of reds: (9 choose 3)
position of blue: (6 choose 3)
position of hole: (3 choose 1)
(9 choose 3)*(6 choose 3)*(3 choose 1)=5040
 
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8. Board Game: L-Game [Average Rating:5.03 Overall Rank:15274]
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18,368 states (from wiki, x8 mirrors)
 
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9. Board Game: Alak [Average Rating:4.97 Unranked]
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<19,683
Easy to calculate: 3 posibility (black, white, empty) on 9 spot = 3^9
Probably much less.
 
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10. Board Game: Tic-Tac-Toe [Average Rating:2.61 Overall Rank:16322]
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26,830 states (from wiki)
 
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11. Board Game: Chung Toi [Average Rating:5.28 Unranked]
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<107,520
couse:
arrangement of reds: (9 choose 3)
arrangement of whites: (6 choose 3)
rotation of all: 2^6
 
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12. Board Game: X-Ceter-O [Average Rating:5.47 Unranked]
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151,200 states
"1" can be on 10 positions (9+ outside board), "2" 9, etc
10*9*8*7*6*5=151,200
 
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13. Board Game: Mojo [Average Rating:6.50 Unranked]
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362,880 states
 
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14. Board Game: Dao [Average Rating:5.32 Overall Rank:15196]
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900,900 states
(16 choose 4)*(12 choose 4)
 
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15. Board Game: Neutreeko [Average Rating:6.06 Overall Rank:11418]
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* Perfect information
* (25 choose 3)*(22 choose 3) = 3,542,000 positions (allowing symmetric repetitions, way less in practice)
 
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16. Board Game: Nana Shogi [Average Rating:6.50 Unranked]
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3,870,720

1st king: (9 choose 1)
2nd kind: (8 choose 1)
1st player pawns: (7 choose 2)
2nd player pawns: (5 choose 2)
rotation of 4 pawns: 4^4
 
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17. Board Game: Quadtria [Average Rating:5.58 Overall Rank:13861]
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5,717,712
=(17 choose 6)(11 choose 6)
 
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18. Board Game: Fano330-R-Morris [Average Rating:6.76 Unranked]
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<5,511,240
Placement:
On every place can be 2 pieces, one or empty.
3^7
(less beceuse for example this counts where every place is full = 14 pieces, and there is only 8)
In 8 occupied places (it's important whether it's up or down):
white tringles in Binomial(8,2)
white circles in Binomial (6,2)
black tringles in Binomial(4,2)
black circles in Binomial (2,2)
Sum 2520
(3^7)*2520=5511240
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19. Board Game: Pan [Average Rating:3.67 Unranked]
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11,390,625

It is not obvious anymore
- this is not a perfect information game.
But it is for 2 player
-cards are mixed
But we can deal the cards at the beginning of the 2 of every kind, and the better player will win anyway.
-normaly posiibly states are 3^24 = much more, but we can forget about colors
 
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20. Board Game: Nim [Average Rating:3.84 Overall Rank:15882]
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~ 50 milions

If we limit game, for example to 3 piles and 368 stones on a pile
the number of possible states are 368^3 < 50 mln

ps. very easy to play in mind, and it is non trivial game.
 
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21. Board Game: Four Field Kono [Average Rating:4.45 Unranked]
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<43,046,721 states
Every filed have 3 states: black, white or empty, so 3^16=43,046,721
Probably much less.
 
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22. Board Game: Chomp [Average Rating:3.88 Unranked]
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43,046,721 states for 9*8 chocolade
(for smaller much less)

on every row 8 posiibility
9^8= 43046721
 
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23. Board Game: Shove Off [Average Rating:5.67 Unranked]
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<43,046,721 states
Every filed have 3 states: black, white or empty, so 3^16=43,046,721
Probably much less.
 
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24. Board Game: 3D Tic Tac Toe [Average Rating:3.99 Overall Rank:15971]
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I dont know
But the game ends almost immediately, so I think less than 50 million
 
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