KEIRIN
Anki Toner, 2006
This is a one-player non-strategy game. You just watch the race. Or maybe it's a betting game, who knows. Is it fun? You tell me!
KEIRINIntroduction:
Unlike the conventional track sprint discipline where riders seek to "draft" or "slipstream" each other, in the first few laps of the Keirin, cyclists are paced by a motorised vehicle called a derny, who leaves the track a few laps before the end, at a speed of about 50 km/h. The first cyclist to finish the high-speed (sometimes at 70 km/h) race is the winner.
This game starts at the precise moment when the derny leaves the track.
Material:
Six cyclists in six different colors, a derny (just because it is nice to have it, not really needed), 21 dice in six colors. 1 die matches the color of rider 1, 2 dice match the color of rider 2... and 6 dice match the color of rider 6.
The track is 60 squares long. (The squares themselves should bee quite short, so that each rider occupies three squares: this gives the game more realism, in my opinion, but it is not really necessary).
Preparation:
The riders start on squares 0,3,6,9,12 and15, forming a line. The derny starts at square 18, in front of the pack.
Movement of the riders:
The rider who starts ahead (let's call him rider 1) throws 1 die all through the race. The rider who starts second (you guessed, we'll call him rider 2) throws 2 dice all through the race. And so on. Rider 6 throws 6 dice all through the race.
All dice are thrown at the same time, to speed up the game and add some ambiance.
For all purposes, 1s and 2s on the dice are assimilated to 3s (the dice can be regarded as D6 numbered 333456)
Only the highest number on each throw is taken into account. Exception, if the throw has more than one 6, each additional six counts as an extra pip.
Example:
Rider 1 throws 2. He advances 3 squares.
Rider 2 throws 15. He advances 5 squares.
Rider 3 throws 366. He advances 7 squares.
Rider 4 throws 1112. He advances 3 squares.
Rider 5 throws 45556. He advances 6 squares.
Rider 6 throws 111233. He advances 3 squares.The highest possible throw, of course, is 6 sixes by rider 6. He would advance eleven squares.
Exception:
Only in the first throw, add two squares to the movement of rider one (as he is draft by the -virtual- derny acceleration).
Winner of the race:
The race is won by the rider who goes further past the finishing line in the throw when the first rider(s) cross the line. (The turn is completed). In the case of a tie, the dice are thrown again between the tied riders for a "photo-finish"..
Note:
In case there are not enough dice available, the dice can be thrown consecutively (the game could even be played with just one die, but it will be excruciatingly slower and unexciting).
I will add an example race one of these days...
Probability (In case you feel like it)
R1 advances an average of 4.000 squares per turn
(3+3+3+4+5+6) / 6 = 4R2 advances an average of 4.638 squares per turn
(9*3 + 7*4 + +9*5 + 10*6 + 1*7) / 36 =4.638R3 advances an average of 5.079 squares per turn
(27*3 + 37*4 + 61*5 + 75*6 + 15*7 +1*8) / 216 = 5.079R4 advances an average of 5.407 squares per turn
(81*3 + 175*4 * 369*5 + 500*6 + 150*7 + 20*8 + 1*9) / 1296 = 5.407R5 advances an average of 5.670 squares per turn
(243*3 + 781*4 + 2101*5 + 3125*6 + 1250*7 + 250*8 - 25*9 + 1*10) / 7776 = 5.670R6 advances an average of 5.897 squares per turn
(729*3 + 3367*4 + 11529*5 + 18750*6 + 9375*7 + 2500*8 + 375*9 + 30*10 + 1*11) / 46656 = 5.897If we call "0" the square where R1 starts we have the following table (square where each rider finds himself at any given turn, rounded at the first decimal, which does not mean anything)
In pink, the theoretical leader after n turns.
Turn
R1 (4.000)
R2 (4.638)
R3 (5.079)
R4 (5.407)
R5 (5.670)
R6 (5.897)
0
0
-3
-6
-9
-12
-15
1
6
1.6
-0.9
2
10
6.3
4.2
3
14
10.9
9.2
4
18
15.6
14.3
5
22
20.2
19.4
18.0
16.2
14.5
6
26
24.8
24.5
23.4
22.0
20.4
7
30
28.5
29.6
28.8
27.7
26.3
8
34
34.1
34.6
34.3
33.6
32.2
9
38
38.7
39.7
39.7
39.1
38.1
10
42
43.4
44.8
45.1
44.7
44.0
11
46
48.0
49.9
50.5
50.4
49.9
12
50
52.7
54.9
55.9
56.0
55.8
13
54
57.5
60.0
60.3
61.7
61.7
14
58
62.0
65.1
65.7
67.4
67.6
15
62
66.6
70.2
72.1
73.0
73.5
18
74
80.5
85.4
88.3
90.1
91.1
20
82
89.8
95.6
99.1
101.4
102.9
Variant: Use one extra die (of a different color) for the derny. Use the derny too.
The derny remains in front of the pack as long as rider 1 follows him by remaining exactly three squares behind him, and no other rider is ahead of rider 1. When this is not the case anymore, the derny is removed from the track.
While the derny is in front of the pack a die is thrown for the derny. If the throw of rider one is not nhigher than the derny's, rider 1 follows the derny (discarding his own throw) and the derny remains in the track for the following turn.
If rider 1 follows the derny, then rider two follow rider one and discard his own throw in case it is not higher than the derny's throw. As long as one rider is following the rider in front of him (or the derny, in case of rider 1), the following rider follow him too. When a rider does not to follow the rider in front of him, his throw being higher than the derny's throw, he and all the riders behind lose the aspiration for the rest of the race.
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