Can't Stop? Try The Rule of 28
Copyright 1998 by Michael Keller; original version published 1986 in WGR 6
Can't Stop is a progressive scoring dice game invented by
Sid Sackson and published in 1980 by Parker Brothers. The board consists of eleven
columns, numbered from 2 to 12. Each column has a certain number of spaces (see the table
below). Each player on his turn rolls four dice, splitting them into two groups of
two and marking the two totals on the board. The player may roll again, placing new
markers (up to a total of three) or advancing markers already placed, according to the two
totals selected. Once three markers are placed, a player must throw at least one of the
three totals each turn, or forfeit the entire turn's progress. A player may stop after
marking any roll, and place colored markers to represent permanent progress. The object of
the game is to reach the top in three columns before any opponent.
A major part of the strategy of Can't Stop is when to stop rolling. The point at which one should stop depends on the three numbers marked and the amount of progress already made in the current turn (measured in fractions of the total distance needed to win a column). The ideal stopping point can be calculated from the probability of a successful roll, and the average progress value of a successful roll. The ideal strategy would consist of a table of 165 entries, one for each combination of three numbers, each entry showing the level of progress at which to stop for that combination.
Such a table would, of course, be impractical to use in an actual game. What we really need is a rule of thumb that is simple to use and reasonably accurate. The following rule, called the Rule of 28, should prove helpful. Add the following values for each number marked or advanced in each column during the current turn (note that each column counts double when a marker is placed) :
|Value when marked||12||10||8||6||4||2||4||6||8||10||12|
|Value when advanced||6||5||4||3||2||1||2||3||4||5||6|
Note that each column counts double when a
marker is placed. Add two points if all three columns marked are odd; subtract two points
if all three columns are even. Add four points if all three columns are less than eight,
or if all three are greater than six. When the total for the current turn reaches 28 or
more, stop rolling (but do not stop before all three markers are placed).
A few turns of a sample game:
(1) 1-1-3-4 Mark 2 and 7. Neither has been marked this turn, so count 12 plus 2, or 14.
1-1-4-6 Advance marker 2, mark column 10. Add 6 and 8 for a total count of 28. This is the total at which to stop.
(2) 1-2-5-6 Mark and advance 7. Count 2 plus 1 for a total of 3.
1-1-3-6 Mark 2 and 9. Add 12 plus 6 for a total of 21. Continue.
1-5-5-6 Advance 7. The total is now 22. Continue.
1-2-4-5 Advance 9. The total is now 25. Continue.
1-3-3-5 Miss. Bad luck!
(3) 2-2-3-3 Mark and advance 5. Count 6 plus 3 for 9.
1-2-2-4 Mark 3 and 6. Add 10 plus 4 for 23, plus 4 (because 3, 5, and 6 are all less than 7) for 27. Roll once more.
2-4-6-6 Advance 6. Add 2 for a total of 29, and stop.
The Rule of 28 will tell you within one roll the correct point at which to stop in 75 percent of all cases (and within two rolls in 92 percent of all cases). This is a fairly good result for a simple, practical rule. However, since you are playing against opponents, do not follow the rule slavishly. Use your judgment as to where you stand in the game when making decisions on when to stop. In particular, when you are behind in the game, or are close to winning a closely contested battle for a column, it is a good idea to take extra chances (thus you would continue to roll even when your turn total exceeds 28).
I would like to thank Robert Abbott for introducing me to this excellent game, and for calculating the table of success probabilities which led to this study.
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