Mike Maxakuli vs. John Karian
|From Backgammon Times, Volume 2, Number 2, Spring 1982.|
This year's Holiday Tournament in Las Vegas was won by 1981's most successful tournament player, Mike Maxakuli. The editor of Las Vegas Backgammon Magazine, Maxakuli added this victory to his earlier second place finish at Turnberry Isle in January and his win at the Desert Inn Classic in February. Runner-up was John Karian of Los Angeles, who reached the finals for the first time in his tournament career. The semifinalists were David Leibowitz, no stranger to success in Las Vegas, and Todd Vander Pluym, who had beaten Maxakuli in the finals at Turnberry.
Maxakuli had things rather his own way in the final match, winning comfortably by a score of 21–10. I've annotated the last game, which began with Maxakuli leading 17–10.
|Maxakuli (White)||Karian (Black)|
|1.||3-2: 13/10, 13/11|
|2.||4-2: 8/4, 6/4||5-3: 10/5, 8/5|
|Black to play 4-3.|
|3.||. . .||4-3: bar/22, 13/9|
Splitting to the opposing bar-point, with 22/18, is much more dangerous once the opponent has established a second inner point. Nontheless, it seems better than removing the last builder from the midpoint with 13/9. Karian's distribution is already awkward (note the 5 men stacked on the 6-point) and stripping the midpoint makes the job of exerting control on his side of the board even more difficult.
One of Karian's worst rolls. His play looks unconstructive, but the alternatives are no better.
A good roll moves Karian back into contention . . .
. . . but this shot may knock him out. Maxakuli correctly assesses the 5-point as more valuable than the return hit possibilities on his two blots.
One of Maxakuli's great strengths as a tournament player is his ability to continue playing well even when holding a substantial lead. This is not as facile an observation as it might sound. Most players tighten up unreasonably with a large lead, doubling too late and dropping too soon. As a result, their leads tend to dribble away more often than they should. Many players might take an extra roll as Back in this position, hoping for a certain cash next turn. Maxakuli correctly turns the cube now.
Actually this position is just barely a take even given the match score; in a money game White should pass. As a check, I rolled the position out 100 times, with these results:
In 100 money games, White would lose 100 points by dropping, 120 points by taking. Slightly a pass. To determine the correct strategy in a match, the calculations proceed as follows:
His total probability of winning the match if he takes is (.21 × 0) + (.47 × .04) + (3.2 × .18) = 8%. No different from his chances if he drops, so the decision to take or pass should be made based on other factors. I would take because of the latent leverage in the redouble to 4.
Some players might be surprised that Maxakuli's position is as strong as these figures indicate. Normally one man back vs two men back in an otherwise symmetrical position is a reasonable doubling advantage but nowhere close to a pass. Two factors make Maxakuli's position especially powerful:
Karian's position is much worse than it might appear. Since he can't make his own bar-point without a miracle shot, he has no real hope of blocking Maxakuli's back man. Maxakuli, on the other hand, has the pleasant option of either eventually slotting his 8-point or bringing builders into position for making the 3-point. Once Maxakuli makes a 5-prime, the game will be effectively over.
Given these considerations, Karian's last play is not as automatic as it seems. Worth noting is 6/1*, 24/22. By hitting and splitting, he makes consolidation difficult and generates a double-edged position. The resulting complications are in Karian's favor, since Maxakuli has to be somewhat conservative about accepting a recube to 4 in a possible two-way gammon position.
A better play is 13/8, 9/5. A blot on the 8-point is vulnerable to 6-1 and 5-2, but those are both good rolls for Karian on his side of the board (6-1 makes the bar-point, while 5-2 makes the 3-point). After 13/4, the blot on the 9-point is only exposed to 6-2, but 6-2 is a completely useless roll for Karian otherwise. Besides slotting the more useful point, playing 13/8, 9/4 duplicates the opponent's constructive indirect numbers.
Similar to the idea in the note to Karian's last move.
Although this looks dangerous (a 2 could swing the game around) Maxakuli's other choices are not much safer. The pure play of 7/3, 6/3 leaves Karian 8 numbers that hit on the bar-point (6-1, 6-2, 5-1, and 5-2) plus 5 more numbers (1-4, 2-4, 2-2) that hit the blot on the ace-point. The passive play 13/10, 13/9 makes Karian a 3-to-1 favorite to reenter, after which Maxakuli has 3 blots to safeguard. Maxakuli sensibly tries to win by the most direct way possiblea close-out.
Maxakuli has a choice of which point to leave open. Besides his move, he could play 13/1*, 5/1, leaving the 3-point open, or 7/3(2), 5/1*(2), leaving the 5-point open. Although the closeout is easier if a higher point is open (Maxakuli's builders are closer to the target) his play is correct. If Karian does succeed in establishing an anchor, he remains a big underdog if he makes the ace-point, while he is right in the game if he makes the 3-point or 5-point.
Occasionally a player in Karian's position will double, with the following rationale: "If I lose, I'm sure to be gammoned, and I'll lose the match anyway. Since I have nothing to lose, I'll double now. That way, I'll be sure of winning 4 points if I eventually win the game."
Plausible, but spurious. A more correct appraisal of the position goes like this:
In short, redoubling can't gain anything and loses some equity in a small percentage of situations.
A slight inaccuracy. This play leaves a blot if Maxakuli's next roll is 4-4. After 8/4, 6/3, no number can blot next turn.
Maxakuli is rolling poorly, but he remains a huge favorite. This play correctly removes his last 5, assuring the preservation of his board as long as possible. Incidentally, this play is much safer than the alternative. It leaves a blot only after a subsequent 3-3. The play 5/4, 5/2 leaves blots after 6 rolls (6-6, 3-3, 6-4, and 5-1).
A great shot. Suddenly Karian is back in the match.
In a money game, this would be a premature double. Although Karian is a favorite, Maxakuli's gammon chances are much greater, and his overall equity is just slightly less than Karian's as a result.
At this score in the match, of course, Maxakuli's gammon chances don't count, since he only needs 4 points to win. As a result, this is an excellent double and a marginal take/pass.
Here are the results of 100 trials of the position:
Combining these figures with match probability charts as before reveals that Maxakuli has about an 82% chance of winning the match whether he takes or passes. I would take in such a position, since Karian's position can easily be misplayed.
A serious mistake. Playing 13/12 creates the possibility of making extra blocking points with a subsequent 6-5 or 4-3. Unfortunately, it risks losing to an immediate 6-3 or 5-4 on Maxakuli's part, an unacceptable risk. Simply 19/16, 19/18 is better.
Crime and punishment.
Karian neglected to play a 2. Maxakuli decided to let the illegal play stand.
Maxakuli is still not home free, since fully 9 rolls leave a shot next turn.
Letter to the EditorBeing a professed tyro at the game, I wonder if you could put this question to your panel of experts. Reference is to Bill Robertie's super analysis of the final Maxakuli/Karian game. My question concerns the 4-4 move (#13).
The actual move, and the two possible alternatives mentioned by Mr. Robertie, all hit on the ace-point. But is there anything fundamentally wrong with not hitting at all, playing instead: 13/9, 10/6, 7/3(2)? As Robertie says, even if Karian makes the ace-point he is still a big underdog; therefore, why risk having another man sent back when the one White man already back has a lot of good numbers to get out and a fair amount of time to do it in?
From the 4-4 move I suggested, I rolled out 100 games, with the following results: Maxakuli wins 26 straight games, 53 gammons, and 10 backgammons. Put another way, he wins the match outright 63% of the time and leads 19–10 26% of the time. He loses a straight game 10% of the time and is gammoned 1% of the time. He still leads 17–12 losing the 10 straight games, and 17–14 the one time he is gammoned. So, unless I am badly mistaken somewhere, my 13/9, 10/6, 7/3(2) seems to me like a good move.
Edward G. Shack
Bill Robertie RepliesMr. Shack's question is a good one and I should have commented on the point in my notes. The reason for hitting on the ace-point is that although White is a big favorite against an ace-point game, he is a much bigger favorite if he can close out three men on the bar. He is therefore justified in trying for a close-out even at the risk of having additional men sent back.
Some general figures: if White closes out three men, and escapes his last checker, he should win a gammon or backgammon about 80 to 85% of the time, win a single game 10 to 15% of the time, and lose about 5% of the time. Against a reasonably timed ace-point game, White could lose anywhere from 15 to 30% of the time, depending on the exact structure of the position. Of the remaining games, White should win about as many gammons as single games. (Remember, against an ace-point game, White is about a 9-to-1 favorite to leave at least one shot!)
In the position from the Karian-Maxaculi game, White can adopt one of two strategies: (1) hit loose and continue to hit loose until he either closes the ace-point or runs out of builders; (2) bring extra builders into position until he either rolls a number to close the ace-point exactly or Black rolls an ace and closes the point himself. If he plans to adopt strategy (1) he should begin immediately; there is no advantage in waiting one turn.
The problem with strategy (2) is that Black is quite likely to establish an ace-point game; I calculate that he is about a 2-to-1 favorite to do so. Since Black's own formation is not yet imposing (and Black does have to enter three men from the bar) White should avail himself of what is almost a free shot at completely eliminating the ace-point game equity.
One general point to mention: a move which makes one a big favorite can still be a serious blunder if there is a move which makes one an even bigger favorite. A good player has to try relentlessly to squeeze the most out of even the most routine positions.