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BGonline.org Forums
Simple bear off redouble
Posted By: Rick Janowski In Response To: Simple bear off redouble (Dmitriy Obukhov)
Date: Tuesday, 17 April 2012, at 9:20 p.m.
The match score and cube level/position at this match score may not significantly modify take-points away from the money norm. However, doubling points will tend to deviate significantly from money norms because redoubling does not give the taker any of the normal benefits of cube ownership. The general effect can be investigated by considering and comparing two theoretical money cases:
The normal cube situation where there could be several subsequent redoubles. For gammonless games the redouble point probability may be approximated by the expression, RD(x.x) = (1+x)/(2+0.5x), where x is the cube efficiency coefficient (a value between 0 and 1, typically about 2/3).
The peculiar cube situation where there can only be one redouble in the remainder of the game (this assumes the maximum cube level has been capped to the level after the redouble) . For gammonless games the redouble point probability may be approximated by the expression, RD(x.0) = 1/(2+0.667x), again where x is the cube efficiency coefficient (a value between 0 and 1, typically about 2/3).
Assuming for the sake of simplicity that the x values are the same for both situations, ie, ignoring the possible effect of doubling window width, then the difference in the redouble points, RD(x,x) and RD(x,0) can be estimated by simple subtraction. Fortunately, the typical value is fairly constant at 7% over a range of x from 0.5 to 0.8, peaking at 7.1% at x=2/3. As a general rule for gammonless games where doubles are capped to a finite number, the minimum redouble point (on the last redouble) is about 7% earlier than for normal money cubes where there is no capping. So where in the normal case, a redouble point would typically be about 70%, in the cube capped case the value would be about 63%.
In the particular match score, where the take point of 23% is close to typical money takes, and the doubling window (50% to 77%) isn’t markedly different from the normal money window (50% to 80%), the 7% early redouble generalisation would appear to be a reasonable adjustment. Adjusting for the slightly smaller window size might have the effect of reducing the doubling point by about 1% but this is probably offset by the fact that the smaller window size would tend to reduce the x value slightly, thereby slightly increasing the difference.
With the 7% early cube adjustment, the actual position would appear to be borderline redouble.
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