As most experienced players already know, proper use of the doubling cube involves utilizing the concept of market losing sequences. It is not incorrect to roll if there aren't any market losing sequences -sequences after which your opponent will not have a take on your next opportunity to offer the cube. This rule of logic brings about some interesting paradoxes when applied to tournament play Proper Cube Strategy in Post Crawford Game . The most common of these is the proper cube strategy at the 2-away,2-away score. Assuming perfect play, it is an easy exercise to show that it not incorrect to double at the first opportunity - even if no market losing sequences exist. So what's the proper backgammon strategy? Double immediately or wait for at least one market loser? Well, it's not incorrect to do either. (i.e. this problem has more than 1 correct answer). Many players are quick to point out that the assumption of perfect play is not valid in practice, and so they adopt doubling strategies which present their opponents with the opportunity to makeerrors. (Of course, these players risk making errors themselves.) Enough articles have previously been written concerning the 2-away,2-away score that it does not need to be addressed further here. Instead, we are going to look at some lesser discussed situations whichyou wouldn't want to have to face unprepared. Post-Crawford Backgammon Game Consider this situation: Score: Blue leads White, 1-away, 3-away, post-crawford Blue: 4-1: 24/23, 13/9 OK...its post crawford...obviously White, who is trailing in the match,should automatically double. Or should he? Just as with the 2-away,2-away score, if you assume perfect play it is not incorrect to double immediately - and almost all of us have been trained to do this. Since Blue doesn't have a free drop available, the take is trivial. But what about waiting for a market losing sequence? If there aren't any market losers, it is not incorrect to roll. At this score, it doesn't really matter much to White if he wins 1 point or 2, so by rolling he may beable to present Blue with the opportunity to make an error later on.The value of the cube to White is when he scores a gammon to win the match. So, does White have any market losing sequences? Lets say that White likes the idea of suckering his opponent and rolls... White: 4-4: 24/16*, 6/2* (2) Blue: Dances 151 180 White 2 5 point match Blue 4 White: Doubles Who's the fool now? Did White make an incredible error by rolling? Ordoes Blue still have a take and will he be blundering by passing into(essentially) double match point. Let's see.. ACTION SCORE (Blue,WHITE) MATCH EQUITY Blue Drops 1-away, 2-away 50% (ignoring free drop equity) Blue Takes and Wins Blue wins 100% Blue Takes and Loses Single 1-away, 1-away 50% Blue Takes and Loses Gammon White wins 0% 3 Variables to Consider: W, the amount Blue wins L, the amount Blue loses single G, the amount Blue loses a gammon By definition, W + L + G = 1 Blue's match equity if he takes is the amount he wins (W) plus 50% ofthe amount he loses single (L): E-take = W + .5*L = W + .5*(1 - W - G) Blue can take if this equity is greater than the 50% equity he would have by dropping: E-take > .5 W + .5*(1-W-G) > .5 W + .5 - .5*W - .5*G > .5 .5W > .5G W > G So Blue can take if he winsmore than he gets gammoned. Back to the above position...can Blue take?JF level 7 evaluates the position as follows: Blue wins: 33% White wins: 67% (41% single, 26% gammons) Since Blue wins more than he gets gammoned, it's still a clear take. Even with this favorable sequence, White has not lost his market. And many good players would drop this backgammon position, justifying White's earlier decision to roll. Continuing the exercise, consider this situation: Score: Blue leads White, 1-away, 5-away, post-crawford White: 4-2: 8/4, 6/4 Blue: 4-3: 24/20 13/10 White decides to wait and rolls his best... White: 3-3: 8/5*(2), 6/3(2) Blue: Dances 149 165 White 2 7 point match Blue 6 Now White doubles...does Blue have a take? This time I will give JF's level 7 evaluation first: Blue wins: 25% White wins: 75% (40% single, 35% gammons) From the analysis above, we know that this would be a drop for Blue ifthe score was 1-away, 3-away post crawford. What about the current score: ACTION SCORE(Blue,WHITE) MATCH EQUITY Blue Drops 1-away, 4-away 70% (ignoring free drop equity) Blue Takes and Wins Blue wins 100% Blue Takes and Loses Single 1-away, 3-away 70% Blue Takes and Loses Gammon 1-away, 1-away 50% Using the same variables as before, we can calculate Blue's matchequity if he takes: E-take = W + .5*G + .7*L = W + .5*G + .7*(1 - G - W) = .3*W - .2*G + .7 Blue can take if this equity is greater than the 70% equity he wouldhave by dropping: E-take > .7.3*W - .2*G + .7 > .7W > 2/3 * G At this score, Blue can take if he wins at least a FRACTION of theamount he gets gammoned! Plugging in JF's numbers we see that Bluestill has a SLIM take, since his 25% wins is more than the 23% factoredgammons (35% actual gammons * 2/3 = 23% factored gammons). Again, White has not lost his market and gains if Blue drops. The formula above can be generalized: In all odd-away, post crawford positions, the leader can take trailers cube if he wins at least afraction F of the amount he gets gammoned. F is easy to calculate: F = (D - TG) / 100-D, where D is the match equity if leader drops and TG is the match equity if leader takes and gets gammoned. (Example: At 1-away, 5-awaypost-crawford, D=70% and TG=50%, so F = 2/3 ) POST CRAWFORD SCORE GAMMON FRACTION (F) -1, -3 1-1, -5 2/3-1, -7 2/3-1, -9 4/5-1, -11 2/3-1, -13 1/2 Doubling in Post-Crawford - Summary But buyer beware! Remember, the example positions were chosen very carefully. Doubling immediately in these situations is not incorrect.If instead you decide to adopt the post-crawford cube waiting strategy,you really need to be aware of your market losing sequences. Otherwise, the small gains you make from this strategy will quickly be wiped outwhen you roll that joker only to see your opponent dance and thencorrectly Pass your sucker cube.

return to index