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Annotated Game |
Bill Robertie vs. Simone Naim
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| From Backgammon Times, Volume 4, Number 1, Spring 1984. |
| When Bill Robertie won the Championship at the Monte Carlo tournament this past summer, he played some of the toughest players in the world. His exciting final match against Israeli Simone Naim appears below—along with Robertie's post-play commentary. |
This year's World Championship match was a long, close, always tense struggle. My opponent, Simone Naim, was an Israeli playing in his first major tournament final. The previous evening he had scored a stunning upset in his semifinal match, rallying from an 18–6 deficit to beat Gabby Horowitz, 23–21. (In the quarterfinals, he had overcome at 12–0 deficit to edge Ferretti.) I had had an easier time against Adrian Swartz, also of Israel, leading comfortably all the way and eventually winning, 23–19. The final match was to 25 points.
In the first third of the match, the edge swung back and forth. Trailing 9–10, Naim won the only gammon of the match to take a 13–10 lead. Playing well, he increased his advantage over the next several games to as much as 21–15. At this point he fell into a trap, a very common one in the last rounds of major events: playing too conservatively to protect a lead. Doubling early, I was able to steal some games and creep within a point at 21–20.
The next game was crucial. I gave an aggressive double, Naim took, and finally swung the game around. Instead of cashing two points, however, he played for a gammon in a position that offered only slight hope. An awkward set of boxes forced him to leave a shot while bearing in, and I was able to hit and close my board for the win and a 22–21 lead. We then traded points to reach 23–22, my favor, the equivalent of 1–0 in a 3-point match.
First, some percentages that every player should know: a 1–0 lead in a 3-point match is equivalent to a 60% chance of winning the match. If the leader wins a single point, his 2–0 lead with the Crawford game in effect makes him a 75% favorite. If the trailer wins 2 points, his 2–1 lead makes him a 70% favorite.
Whether the leader should hold the cube, double, or play on for the gammon is a function of his gammon chances. His doubling window is actually quite narrow at this score, and if his gammon chances rise above 25%, his doubling window actually shrinks to zero. With gammon chances that high (typical of back games, blitzes, and some ace-point games) his position is always either too good or not good enough to double.
The chart below shows the leader's approximate doubling points for small gammon chances. Note: (20-53-27) means a position where the leader has 20% gammon chances, 53% winning chances, and 27% losing chances.
| Probability of Gammon |
Good Enough to Double |
Too Good to Double |
| 0% 10% 20% |
(0-70-30) (10-63-27) (20-56-24) |
— (10-80-10) (20-60-20) |
| Gammon Chances |
Winning Chances To Take with 1–0 Lead to 3 |
Winning Chances To Take For Money |
| 0% 10% 20% 30% 40% |
29% 33% 37% 41% 46% |
25% 30% 35% 40% 45% |
These differences are somewhat more significant than they appear, since winning chances in a money game assume the ability to use the cube to cash positions which would otherwise eventually be lost. In the match situation, the leader owns a dead cube, and consequently must win that percentage of games played out to the finish. In practice, the leader must be 5–8% more conservative than for money.
The trailer's doubling point is naturally earlier than for money. It's also nearly impossible for him to ever correctly play for the gammon. If he ever reaches a position where he is enough of a favorite to do so, he probably missed a good double earlier. The next table summarizes his approximate doubling points.
| Probability of Gammon |
Good Enough to Double |
Too Good to Double |
| 0% 10% 20% 30% |
(0-59-41) (10-46-44) (20-34-46) (30-22-48) |
— (10-82-8) (20-64-16) (30-46-24) |
* * *
| Black to play 6-3. |
| Bill Robertie (Black) | Simone Naim (White) | |
| 1. | 6-3: 24/18, 13/10 | |
Throughout the match I had aimed for the most complex positions possible. A tiny one-point lead was no reason to change this policy. With a comfortable lead I would have played 24/15.
| 1. | . . . | 5-4: 24/15* |
| Black to play 2-1. |
| 2. | 2-1: bar/22 |
Probably correct. I need to make the bar-point to equalize the game, and this move gives me the best chance to do so. The move does incur some risk: White has 16 double-hit numbers, which lead to an early rout. The alternative is bar/24, 13/11.
| Should White double? |
| 2. | . . . | Double |
Slightly incorrect, although not as bad as most observers thought at the time. The commentators in the outer room poo-poohed this as an atrocious cube, with the single exception of Gaby Horowitz, who thought it a marvelous pressure double. I recall thinking it seriously premature, and was delighted to take.
A simulation revealed a slightly different picture. Because Black cannot use the cube and cannot win a gammon, White's double actually has some teeth. My simulation (108 trials) gave these results:
| White wins a gammon | 15% |
| White wins | 37% |
| Black wins | 48% |
As explained earlier, the trailer needs slightly more of an advantage than this to double at the 15% gammon level. White's double also suffers from the fact that no bluff equity is involved: there is no chance that anyone in his right mind would pass from Black's position. In this sense it is the very opposite of a pressure double. Still, although White should wait a turn before doubling, his double is not a very serious blunder at this score.
One footnote: In a money game, a beaver on Black's part would be a major error.
| 3. | Take | 4-3: 15/8 |
His worst number. He has no more constructive play than to the 8-point.
| Black to play 6-2. |
| 4. | 6-2: 24/18, 13/11 |
Making the 16-point (22/16, 18/16) gives better board coverage, but the checker on the 11-point is very useful in restraining White's last man.
| White to play 6-1. |
| 4. | . . . | 6-1: 8/1 |
8/2 is forced [?], but what's the proper ace? I prefer 24/23, which doubles the shots at the blot on the 14-point, and also gives to direct cover numbers for the 2-point. These advantages seem to more than compensate for the reduction in numbers that escape to the midpoint.
| Black to play 6-2. |
| 5. | 6-2: 13/11, 22/16 |
This surrenders all coverage of White's inner board in return for nailing an iron grip on the outfield.
| White to play 3-2. |
| 5. | . . . | 3-2: 6/1 |
White fails to recognize the danger. He should play 24/21, 6/4, which gives him a few numbers to hop to safety before Black's blockade gets too menacing. There's nothing intrinsically wrong with making the ace-point in this position, since he obviously won't be playing a priming game under any circumstances. Escaping, however, is now top priority, given his 15-pip lead in the race.
| Black to play 3-3. |
| 6. | 3-3: 8/5(2), 6/3(2) |
A great shot. Making two inner points is much stronger than picking up the blots. Notice how well all Black's rolls play next turn.
| White to play 6-6. |
| 6. | . . . | 6-6: 8/2(3), 24/18 |
Disaster. White loses his 8-point and will have difficulty making up his board.
| Black to play 2-1. |
| 7. | 2-1: 8/7*/5 |
This might be right—I'm not sure. The checker is still a useful builder on the 5-point, and 6-1, 5-2, and 4-3 are much less strong for White.
| 7. | . . . | 6-1: bar/18 |
| 8. | 3-3: 13/7* | 4-3: bar/21, 6/3 |
| Black to play 4-1. |
| 9. | 4-1: 5/4*, 11/7 |
The hit is mandatory, especially since half of White's 14 hits do not pick up or cover the blot on the 3-point.
| White to play 2-1. |
| 9. | . . . | 2-1: bar/23, 3/2 |
Another tough play. My inclination would be to play 2/1 with the ace, hoping to eventually cover the blot on the 3-point. That's a long shot, though, without any points in the outfield, and this play just might be correct.
| Black to play 5-1. |
| 10. | 5-1: 16/11, 6/5 |
Black needs the 4-point for a big edge, so he leaves it slotted and consolidates in the outfield. Beginners, even those who correctly hit on the previous move, have more difficulty with positions like this, often picking up their blot with 4/3. The principle, however, is the same. Black will leave the 4-point slotted until either he makes it or White hits it.
| 10. | . . . | 6-5: 23/12 |
| Black to play 5-4. |
| 11. | 5-4: 18/13*/9 |
With this hit, Black takes the lead in the race for the first time. Now White must hit back immediately to be in the game.
| 11. | . . . | —o— |
The decisive swing. Black's winning chances now rise to over 85%.
| 12. | 5-1: 5/4, 18/13 | 5-2: bar/23, 13/8 |
| Black to play 6-4. |
| 13. | 6-4: 13/7, 9/5 |
With a 20-pip lead in the race, Black will take no unnecessary chances from now on.
| 13. | . . . | 3-2: 13/10, 13/11 |
| Black to play 4-1. |
| 14. | 4-1: 7/3, 7/6 |
7/2* is way too dangerous. Black can afford to sit and wait for a gin number.
| 14. | . . . | 3-1: 8/5, 6/5 |
| Black to play 6-2. |
| 15. | 6-2: 11/5, 11/9 |
11/5, 6/4 is clearly wrong since both 6-5 and 6-6 leave shots next turn. Both 11/3 and 11/5, 11/9 pay off to one immediate indirect and leave not direct shots next turn. If the race were close, 11/3 would be correct since Black would have a direct shot if White escaped with 6-1 or 6-2. Here, however, it would actually be a mistake to hit if White runs with 6-1 or 6-2. Black's chances in a straight race are about 95%, whereas hitting makes him only about a 90% favorite. (He has considerable difficulty filling in the ace and deuce points without leaving a shot.) The correct play of the deuce is therefore 11/9.
| White to play 6-3. |
| 15. | . . . | 6-3: 23/14 |
Rewarded! As mentioned above, running is a slight mistake. White should stick around and pray for contact. While it's hard to feel sanguine staring at a mobile 5-prime, this race is much worse than the simple pip-count difference indicates.
| 16. | 5-1: 9/4, 7/6 | 5-3: 14/6 |
| 17. | 4-4: 7/3, 4/off(3) | 4-3: 13/6 |
| 18. | 4-3: 6/2, 3/off Black wins |
| More articles by Bill Robertie |
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