Doubles tumble from the dice cup.  Why are they so difficult to play?

Short answer: most dice doubles are an example of leverage situations in backgammon. 

A leverage situation is a board position where key differences in winning equity hide in sensible checker plays or vague cube decisions. 

Since doubles on the dice can happen early in the opening, they are worthy of study early in any backgammon career.  They recur.

What are the features of dice doubles in backgammon?  The casino game of craps rolls two fair dice.  Each die has a flat probability density (that is, equally likely numbers) and their sum creates a symmetric triangle probability density (peaked at seven).  But backgammon is not at all like that.  First, each die is used separately but may be added if the checker is not blocked.  Next, some ancient genius chose to give dice doubles twice the weighting: treys are played as four threes, for example.  This innovation demands a new understanding of chance in backgammon.  For example, the average roll advances the checkers a shade more than eight pips (49/6), not seven as in craps.  Perhaps the same genius disallowed the play of dice doubles on the opening toss.  Any guesses as to the average opening roll? – it reverts to seven.  The fifteen opening tosses for either Black or White average to seven pips.  The initial response (first roll by the other player) allows the six dice doubles; they as a subgroup thus average twice seven.  With disallowed doubles on the opening toss, for every two initial checker plays that sum to an even number, there are three plays that sum to an odd number – and none of them make a home board point.  Thus the opening structure is tilted to counteract the opening roll advantage in subtle ways.

Why are dice doubles so difficult to play? 

The pips propel the race, jacked up with rocket fuel.  Suddenly a running game plan may be meaningful.  When one game plan sharpens for a player, then often a different game plan for the other player sharpens too.  Plan B.  Each player reviews the strategy demanded by the tossed dice doubles – and from the vantage of both players. 

The toss of non-doubles can sometimes accomplish two things at once – hit and split, or hit twice – but mostly only one asset or action is available.  Dice doubles often permit more than one asset to be gained.  Lady Luck has given a gift.  The shear number of sensible choices grows, and time thinking should perhaps be tripled.  Squeeze every last drop of equity from the Lady’s gift, before Madam Luck turns fickle, then cruel.  The idea is dice doubles are designed into the game to act as turning points, as moments of new potential, as leverage situations.  The wise backgammon player must focus, list all sensible options, weigh them strategically then tactically, and make the best play – before the chance evaporates.  Laziness is not a plan. 

Leverage situation: big differences in equity hidden in sensible checker (or cube) plays

Dice doubles are not the only example of leverage situations.  But they are a good place to start.