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2017 Boston Quiz Contest Part 4

So far we’ve looked at Quiz positions 1 through 15 from the quiz contest at February’s Boston Open. In this post you can test yourself on positions 16 through 20.

Good luck!


Problem 16: Black to play 5-1

White – Pips 150

Black – Pips 107
Black to Play 5-1

Black has a perfectly safe play available – 23/22 6/1. But he can’t play it, because he’s 49 pips ahead after he plays his roll. In one or perhaps two rolls he’ll have to run into the outfield anyway, and then White’s game will be much stronger because he’ll have released the spare checkers on Black’s 5-point into the outfield.

With a huge race lead and a deteriorating position, you can’t try to play a holding game. Instead you have to try to run before your opponent’s game gets better and yours gets worse. Hence the five is clear: Black has to make his move with 23/18, then figure out the best ace.

He has two plausible aces: 4/3, giving no extra shots on his side of the board, or 8/7, giving White a 3-shot but preserving his 4-point board. To see which is right, consider these two features of the position.

(1) A lot of hitting is about to happen. Black is trying to run his checkers into the outfield, and White will be hitting pretty much any shot he sees, even if he has to leave shots in return. In a slugfest, you need a good home board, which is a strong argument for keeping the 4-point and playing 8/7.

(2) After Black moves 23/18, White’s best hitting number is a 3. Playing 8/7 duplicates threes. True, White will hit with 20/17* rather than 10/7*, but the duplication reduces the cost of being hit on the 17-point, since White had an acceptably good hit elsewhere.

Put those two ideas together, and it’s clear that 23/18 8/7 is the play.


Position 17: Black to play 3-2
White – Pips 151

Black – Pips 138
Black to Play 3-2

“Points are good.”

“Stacking is bad.”

“Take small risks to improve your position.”

These are all good rules of thumb, which apply in many positions. Here are some others that are also useful:

“Play safely to protect a big racing lead.”

“Your opponent’s inner board strength will tell you how aggressively to play.”

And finally, one more:

“Weight possible gains against possible losses when deciding how much risk to take.”

Now let’s look at Position 17. Black has stacks everywhere, and the only safe play (11/6) creates an even bigger stack. He does however, have a play that unstacks and makes a new point – 13/11 6/3, leaving only 12 shots. (13/11/ 13/10 leaves 18 shots – too many). What’s right?

First, let’s note that Black has one major asset in this position – his racing lead. After he plays his 3-2, he’ll be up 18 pips. Other than that he doesn’t have much, so he’s got a very strong incentive to protect that lead.

Next question: How risky, really, is 11/6? Sure, it’s ugly as sin, but how likely is it to leave a shot next turn? After all, the logic behind 13/11 6/3 is that Black is taking a small risk this turn to build a position that will be safer down the road. Let’s compare 11/6 and 13/11 6/3 in terms of how likely they are to get hit on both the first and second turn, assuming White can hold his position.

On the first turn, 11/6 is obviously totally safe, whereas 6/3 gets hit with 12/36 numbers (33%). A clear safety advantage to 11/6, of course.

Now on to the second turn. After 11/6, Black will leave a shot with a total of 14 numbers (6-5, 6-3, 6-2, 5-4, 5-1, 3-1, and 2-1). Assuming White hits on average about 40% of the time, depending on where Black’s blot ends up, White will get about 5.6 hits in 36 rolls, a bit under 16%.

How much safer is 13/11 6/3 on the second roll (assuming the blot got missed on the first roll)?

After 13/11 6/3, Black will leave a shot next turn (again, assuming White holds his position) with a total of 19 (!) numbers: 6-5, 6-3, 6-2, 5-4, 5-1, 4-3, 4-2, 3-1, 1-1, 2-2, and 6-6.

Oops.

The ‘flexible’ play is not only riskier on the first roll, it’s also riskier on the second roll if White missed the shot on the first roll! That’s not what you might expect, but it makes sense when you think about it. Black has to cover the blot with half his roll, then look around for how to play the other half of his roll. He won’t have a lot of choices there, so it’s not so surprising that he’ll have to leave a lot of shots. (In addition, the existing blot prevents some of his doubles from playing safely, whereas doubles are always safe if you didn’t have any blots to start with.)

Under the circumstances, 11/6 starts to look better and better. It’s actually much safer than it first appears, and that’s enough to make it the right play.


Problem 18: Black to play 6-1
White – Pips 161

Black – Pips 115
Black to Play 6-1

When you have the best possible 5-point board (2-point to 6-point) and your opponent has a blot on your ace-point, you nearly always want to hit unless your opponent has a very strong board or prime. Most players know to hit when they have a cover number or two already in place. In fact, you should hit even if you’re not likely to cover for two or three turns.

In Position 18, for instance, the right play is 7/1* 21/20, not 13/7 21/20. Simply making a prime gives White a direct shot to make an ace-point game. He may make that anyway, but at least you’ve given yourself a better chance at a closeout.

Look at it another way: if you knew White wasn’t going to throw an ace next turn (which he’s 70% not to do) which position would you rather have? Clearly you’d want the position with two men on the bar. So go for it now. Hitting with 7/1* actually wins more gammons and more games.


Problem 19: Black to play 5-4
White – Pips 111

Black – Pips 77
Black to Play 5-4

Most players would make the right play here but for the wrong reason.

The best play is 18/14 9/4, giving White a 5-4 shot to hit (which is not necessarily winning for him because of his weak board). This looks like a sort of ‘pay now or later’ problem, giving one indirect shot now to avoid leaving a direct shot clearing the 9-point later on.

But that’s not what’s happening here. At double match point, for instance, 18/9 is actually correct! (By a tiny bit.) The idea of playing 9/4 now is that Black is playing for the gammon and wants to start his bearoff with plenty of spares on the 6-point and 4-point. Sticking a spare on the 4-point and keeping his two other checkers on different points gives him the best chance to keep those spares on his 4-point and 6-point.

After 18/9, Black’s fours are blocked, so as he tries to clear the 9-point he may have to put spares on his low points. If White enters on the first or second turn, Black may have to move more checkers down to his low points as he waits to clear the 9.

The net effect is that keeping his outfield checkers split boosts Black’s gammon chances by more than 5%, while costing him a little more than 0.5% in losses. So go for the gammon, but be aware that safety isn’t the issue here.


Problem 20: Black to play 2-2
White – Pips 104

Black – Pips 82
Black to Play 2-2

Bearing in can be tricky.

Black can clear his 8-point right now with 8/6(3) 6/4, but that leaves a lot of men (eight) on the 6-point. Combined with the gaps on the 1-point and 3-point, Black might have trouble playing 5s and 3s in the future.

Looking more carefully, 65, 54, and 52 would leave shots, as well as 63, 43, and 32. That’s 12 blot numbers out of 36 rolls. There must be a better play.

Since Black rolled a double, he can look at switching with 5/3(2), then either 6/4(2) or 8/4. By making the 3-point, Black has a landing spot for his 5s and 3s, as well as all his other numbers. So the switch must be for sure, then Black just needs to decide on his last two deuces.

The race is pretty much a lock (Black’s up 30 after the roll), so he has no need to rush a checker in unless it’s actually the safest play. Notice that if Black plays 8/4 with the last two deuces and White rolls a five, Black would leave a direct shot with 61 or 63. He can avoid that sequence by keeping a spare on the 8, so he should play 6/4(2) with his last two deuces and be pretty safe for the next turn. At most White will get an indirect shot.

Some positions are like this — you can’t rely on general principles. You just have to get down in the weeds and see what’s actually happening.

Posted: April 20, 2017 | In Backgammon Quizzes

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