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Generally speaking, at what point should a player start thinking about thedistribution of his or her checkers, i.e., being sure that big doubles playwell, avoiding gaps,etc.? I find that when I do start planning a smoothdistribution, it's usually too late, and the gaps occur nonetheless.Isthere a general rule?
Kenneth Duryea
There is no general rule -- each position must be analyzed on its ownmerits. Sometimes smoothness has the higher priority, while sometimesimmediate tactical considerations are more important. However, it is nevertoo early to be thinking about a smooth bearin. While you can't determineexactly what the dice rolls will be, following good general principlesand keeping flexible and well-distributed will usually lead to achievingthe optimal goals for any position.
Kit Woolsey
Could you please explain how you derived 60% for the match equity table entry (-2,-3). When I make the calculation without taking the cube into account I get 63%. When I adjust for the slightly higher cube equity that the trailer has I get 62.6%.
Secondly, as these are just estimates, and as Mr. Kleinman hasdemonstrated, an error of .49999% (rounding) can cause a miscalculation of several percent how much value do you think using a match equity table really bestows upon someone who is adept at both the assessment of the position and the match equity calculation?
Craig T. Campbell
I don't know that one can calculate the value of the cube equity whichthe trailer has, but it is far higher than most people think. To giveyou an idea, over a data base of several hundred games where the leaderhad 2 points to go and the trailer had 6 or more points to go, the averageresult for the game was +.30 for the trailer -- almost 1/3 of a pointadvantage. Maybe it shouldn't be this way in theory (or maybe it shouldbe even higher!), but this is what the results showed. The 60% figureI use in the match equity table is largely derived from the results ofseveral hundred matches. It could be wrong, but I believe it to beaccurate in practice even if it is wrong in theory.
Even if the match equity tables are off by a little bit, they are still veryvaluable. They give the player a good target number to shoot for, and willavoid the danger of some huge cube blunder because the player has the wrongequities for his various actions. Even if a rounding error in the equitytables causes one to be off a couple of percent on a take point estimate,that is not so terrible. The real problem usually isn't in calculating theequities -- it is in evaluating the position properly in the first place.How many complex positions are there where even the best players in the worldcan confidently estimate their winning chances to within a couple of percent?Thus, just getting in the ball park on the match equities is quite sufficient.Evaluating the position is the true challenge.
Kit Woolsey
As a confirmed INTERMEDIATE player, but one with 20 years experience, I'venoticed one omission in your discussions on doubling strategy. The rulesare different among skill levels! Watching expert players at varioustournaments I am always astounded at their willingness to take veryunfavorable positions when doubled. My guess is they're right, I'm wrong.But as a practical matter, most intermediate players quickly drop thesepositions, even including positions which are takes in my humble opinion.The lesson is, you can bully a lesser player a much greater part of thetime. In playing on GamesGrid, usually for 7 pt matches, I routinely doublewhen any advantage appears. Much, maybe most of the time, the opponentdrops. These 'stolen' points add up quickly. When I play top players(rarely, but every now and then), I can't get away with this. Clearly I'vemade off with many more free points from bad drops than have lost from tooaggressive doubling. The psychology appears to be "don't let one badgame/gammon lose the match", and this can be taken advantage of. Pleasedon't let anyone who plays me see this letter.
Your experience has been different from mine. I have seen the best playersin the world drop what I think are trivial takes. This error is not atall limited to weak players. I have also seen hopeless takes from bothgood and bad players. It all depends upon the player, and his evaluationof the position. My general philosophy unless I am very sure about aparticular player's tendencies is to treat the cube the same regardless ofthe player. If I think it is a double I double, and then it is their problem.Players of all levels will get it wrong some of the time if you give themthe problem in the first place.
Kit Woolsey