2away/4away Quiz

This week's lesson of the week is in the form of a quiz.  There are 5 positions, and in all cases, the score is 2away/4away--one of the most interesting and complex (and fun) scores you can have.  I wrote this article a couple of years ago, but I have revised the answers and discussion based on the new Rockwell/Kazaross Match Equity Table.

2-away 4-away Quiz

By Phil Simborg



This score is really one of my favorites.  The take point for BOTH players is somewhere between 18 and 20 percent depending on who you ask, and the cube and checker plays can be very challenging.  Gammons are a major consideration, which complicates matters even more.  (The new Rockwell-Kazaross equities put the leader’s take point at 19.8 and the trailer’s take point at 18.5.)


Let’s see how you do with this quiz—if you find it challenging, you’re in good company, as many really fine players have had difficulty with positions like this at this score.  Right or not, I guarantee you that you will get some insights from the solutions.


Since I give the answers and an explanation right after each problem, try not to look until you’ve made your decision.



Position 1:


Blue leads 7-5 in a match to 9 and is on roll?  Should Blue double?  If Blue doubles, should White take?



Blue should not double, and if Blue doubles, White should take.  As you can see from the GNU evaluation below, White wins this game almost 23 percent of the time.  Blue is better off rolling, and if he rolls well, or simply breaks the 11 point and doesn’t get hit, he will probably be able to double and get a drop and be ahead 8-5 Crawford where he is favored to win the match around 82 percent of the time.  That’s a lot better than the 73% he was favored before the roll.  And what if Blue didn’t double and rolled poorly or if White his the indirect shot?  Then Blue would be very happy he didn’t double. 


As for the take, it’s simple…it’s better to have 22.6 percent match winning chances by playing this game out than it is to have 18 percent if he drops.



Position 2.

Blue leads 7-5 in a match to 9 and is on roll.  Should Blue double?  If Blue doubles, should White take?






Answer:  Blue clearly should double.  Blue wins immediately with 26 out of 36 rolls (anything without a 1, except 1-1).  So it’s clearly a big double and would be a 56% error not to cube. 


Now, what about White?   As stated above, White’s take point at this score is 18.5 percent.  The math and the evaluation tell us that White wins this game 27.8% of the time, so it would seem that this is a take.  27.8 is well above 18.1.  But the evaluation says White should drop!  How can this be?  Can you figure this out for yourself?


 The reason White’s take point is 18.5 percent is that is about his odds of winning the match if he drops.  So if he has a position of greater than 18.5 percent, he should take the cube, redouble immediately, and play that game for the match.  The problem in this position is that he will not have an opportunity to get the cube turned to 4.  If Blue doesn’t clear his checkers, it’s double/pass.  So if White takes the cube, he will either win 2 points or lose 2 points.  In most other positions he would be playing this game for 4 points.  Since there is no chance to play this game out with a 4 cube, if White takes and loses, he loses the entire match, and if he takes and wins, he only gets to a 7-7 tie in the match.  His odds of winning are too small to risk losing the match vs. getting to a tie.  This illustrates the difference between a “dead” cube and a “live” cube.  The 18.5 applies to a “live” cube, or one that can be used again during the same game.  Since this is a dead cube situation, the trailer’s take point is actually 36.5 percent.

 Position 3

Blue leads 7-5 in a match to 9 and is on roll.  Should Blue double?  If Blue doubles, should White take or drop?

Answer:  Blue should not double because he is “too good” to double.  He has a good chance to win a gammon and can win the match without turning the cube.  If things don’t go so well for Blue, he probably can still double at a later point and win a point or possible get White to take a bad cube.  


What should White do if Blue does make the mistake of doubling here?   This is one of those rare positions where it is both too good to double but a take if doubled.  After the cube is turned to 2, and White gives it back immediately to 4, gammons no longer matter.  So the only question is whether or not White wins this game more than 18.5 % of the time.


As you can see from GNU’s evaluation below, white actually wins this game about 19% of the time—so it is slightly better to take than to drop. 



 Position 4 

In the position below, White trails 5-7 in a match to 9 and is on roll.  Should White double?  If White doubles, should Blue take or drop?






Answer:  White should double and Blue should drop.

Take a look at the GNU evaluation below.  It shows that Blue wins 40.7% of these games.  We know that Blue’s take point is 19.8%, so why should he drop?  Do you know why?



If you guessed that it’s because of gammons, you’re right.  Blue gets gammed 23.2 percent of the time, and getting gammoned on a 2-cube would cost Blue the match.  Winning a gammon has the same value as winning a game with the cube turned, or in other words, the “price of gammons” for Blue at this score is 1.  So every gammon is equal to a full win, or a full percentage point.  When you subtract 23.2 from 40.7 you get 17.5.  That’s well below 19.8, so it’s a clear drop.


By the way, if you are the kind of player who cannot look at this position and estimate that there are 23.2 percent gammons and 40.7 percent wins, JOIN THE CLUB!  Even the best players in the world have to guess and approximate these numbers and it would not be surprising at all for top players to get cube decisions like this wrong.  My goal here is to help you understand the theory and show you some very close positions that illustrate the point so that you will at least make the right decision most of the time when the decision is not this close.  The better and more experienced you get, the more often you will get the close ones right too.



 Position 5

In the position below, White trails 5-7 in a match to 9 and is on roll.  Should White double?  If White doubles, should Blue take?




Answer:  White clearly should double here at this score….and there are two major reasons he should double:  1)  he needs to activate gammons—if he rolls really well and either hit’s Blue’s blot on the 14 or makes the bar point, 4-point, or 2-point, he could not only win a lot of games, but also a good number of gammons.  What a shame it would be to win a gammon without the cube turned.  At this score, the player that is trailing must be quick to turn the cube when there are reasonable gammons chances.  2) He has many “market losers.”  Market losers are rolls that are so good that if he waited to double the next roll his opponent would drop the cube.  Just as White would feel terrible if he rolled great and missed the chance to win a gammon on a 2 cube, he would also feel bad if he only won 1 point for a simple win instead of 2.  Your goal, always, is to try to feel really good!  Note that you should not feel bad about making your opponent feel really bad—if he wasn’t a masochist he wouldn’t be playing backgammon in the first place!  So the double is clear.


What about Blue?  Should he take or drop?


As you can see from the evaluation below, he should take.  As we learned from Position 4 above, his price of gammons is 1 and in this game, largely because he has an anchor on White’s 3 point, he only gets gammoned about 17 percent of the time.  Since he loses 43 percent, when you subtract the 17 from 43 that’s 26.  26 percent is well above the 19.8 he needs to take at this score, and that is why it would be a large blunder (28.8%) for Blue to drop this cube. 






So what have we learned?  Have you learned that backgammon can be an extremely complicated game that is very hard to get right over the board?  But I bet you are more likely to remember the take points for both players at this score.  I bet you are more likely to remember the very large value of winnings gammons for the trailer after the cube is turned, and the high value of gammons to the leader before the cube is turned. 


Years ago I also learned that three things happen if take the time to really study the game:  1)  you get better and the game gets easier, and 2) the game becomes more enjoyable as you understand more of the nuances and intricacies and as you see yourself playing at a higher level and winning more, and; 3) the actual process of learning becomes, in itself, and enjoyable pastime. 


Remember the words of Abe Lincoln:  “If I had 8 hours to chop down a tree, I’d spend 6 sharpening my axe.”