Game #7
Open Division Final
San Mateo, California
16 March 1997
11 Point Match
Ron Karr (Black) vs. Richard McIntosh (White)
Score: 4 - 4
Analysis by Nick Ballard
On Sunday, March 16th, Backgammon by the Bay (directed by Beth Skillman and Joan Clark) held its monthly tournament. Richard McIntosh faced Ron Karr in the final round.
Richard McIntosh started playing backgammon in late 1994, and discovered the r.g.b. newsgroup and FIBS a year later (his handle is "rambeau"). He has played in every BGBB tournament since the second one (March '96), shortly after which he volunteered to develop and maintain this WWW site. Besides the two BGBB Intermediate wins that propelled him into the Open division, he won the recently concluded Zapped #1 on GamesGrid.
Richard is a confirmed UNIX and Macintosh zealot, and an internet user since 1978, back in the dark ages of character-mode FTP and 300 baud modems over what was then called the ARPA-net. In the 70's, he ran marathons, played basketball, packed in the Sierras, and studied statistical methods and computer modeling of voting behavior. In the 80s he gravitated to software development, and in the 90s to customer satisfaction and business metrics.
Earlier in this tournament (round 3, the quarter-finals), I was given the opportunity to be impressed by Richard, with whom I was paired. After a long game he took a 1-0 lead. The next game was a seesaw battle in which he redoubled me, but fortune turned the tides and we reached a bearoff in which he suddenly faced an 8 cube. He had the choice of being down 1-4, or letting the conclusion of this bearoff dictate whether he would trail 1-8 or win the match. His take point was 28%, but his chance of winning this particular position was only 25%.
Richard says he he did not do all the math, but felt that our skill difference made this a straightforward take-and-pray situation. This reasoning is simultaneously flattering and frustrating -- He was clever enough to realize it was not in his interest to go with the theoretical odds only to be ground down. Richard was rewarded with a 6-6 the following roll. He went on to defeat his next opponent, to face Ron in the finals.
Ron Karr played backgammon on and off from 1978 to 1989 (and won the intermediate jackpot in 1986 Nevada State tournmament). He resurfaced when he started playing on FIBS in December 1994 (his handle is "ronkarr"), and later placed 2nd in the Championship Consolation of the November 1996 Las Vegas Open.
Professionally, Ron once made a living as a card-counter at blackjack (1976-1983). He now works at Apple Computer, writing technical documentation for software developers. At one time, he played a lot of duplicate bridge, but more recently his hobbies include piano (jazz, pop), and writing (philosophy).
I should make clear in advance that I have never worked directly with any programs. My knowledge of JellyFish's strengths and weaknesses is based only on having been present at several computer backgammon conversations amongst top players (some Jellyficionados, some not). Incidentally, I'm grateful to Malcolm Davis for having proffered the most guidance to me in this regard, but just to protect the man from ridicule, please understand that my views are not necessarily his.
The following example illustrates what can happen when JellyFish is followed blindly, without applying common sense. This position (also shown in the April/May Chicago Point), was reached in an advanced round of March's Copenhagen tournament (Mike Svobodny was Black, Perry Gartner was White):
| Score: Black needs 3, White needs 2 | ||||
| Play A |
Black to play 2
Candidate Plays Equities 22/20 +1.000 7/5 +0.950 5/3 +0.942 |
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Black, who rolled 3-2, has entered with a 3 and has a 2 to play. The three choices are to move the builder to the 3 point, stack on the 5 point, or come up to the 20 point.
Elliott Winslow did only a short rollout using JF 2.02 (seed 32, 1296 games, settlement 0.550), for respective Black equities of +0.942, +0.950, and +1.000, but apparently there were longer rollouts with similar data. Such data "prove" that Black's best play with the deuce is to come up to the 20 point!
How can this be? Doesn't Black want to pick up a second checker? Easing the gammon pressure on White flies in the face of logic. Can it really be that Black loses so many games cracking his six-prime through awkward sequences (allowing White ace followed by 6)?
Without having watched JF play, I speculate; but I strongly suspect the answer is that it misplays -- it does not maximize gammons by leaving the ace point slotted for Black after hitting there. JF just has Black close White out at the first available opportunity.
If so, JF will lose out on a plethora of gammons, and naturally will support the play that wins a tad more games. Coming up to the 20 point will rate best because Black will never get trapped. Stacking on the 5 point will rank second because it doesn't risk 4-3 and 4-4 cracking when White keeps the bar point.
At the table, Black chose to slide to the 3 point. Perhaps stacking is a hair better, perhaps it isn't. Black risks losing to more nightmare sequences, but hits on the ace point more often, which, with correct play, should lead to an increased gammon percentage.
[It is conceivable that coming up to 20 is correct anyway because the improved 7-5 distribution of the spares is more important for recirculation than staying back on the 22 is valuable in the short term. In this case, JF would luck out, getting the right answer for the wrong reason. In other words, if JF chooses coming up to 20 over not playing the deuce, it would surely be demonstrably wrong.]
The point here is that I do not believe JF's rollouts of the illustrated position can be trusted, and that it would seem reasonable to question JF's rollouts of any position in which a rolling prime is involved.
You have seen an example of what can happen if a prime that only has one pip left to be rolled forward is mishandled. Now back up the prime, and you can imagine how the error could be multiplied. By making lower board points (particularly the ace point), even when wrong, JF avoids reaching a position where it won't misplay again!
Newer versions of JellyFish continue to emerge and improve, yet still need to fully appreciate the value of a rolling prime. When JF hits a shot from a backgame, its containment policy places too great an emphasis on closing inner board points and too little on forming/strengthening a prime. This means that JF is vulnerable to a greater chance of a fluky escape, and it fails to capitalize on the optimal strategy of generating numbers that will force a second blot -- to maximize the number of such opportunities. As a consequence, JF's rollouts evaluate backgames and (to a lesser degree) deep holding games to be weaker than they are in actual play.
This defect has a retrograde effect on checker moves in earlier, undeveloped positions: JF perceives too much upside and not enough downside in making lower board points. The larger the gap between the ace point and the next point made, the more likely the potential strategical resource of a prime has been lost, and the greater the JF misevaluation could potentially be.
To summarize:
- JF's evaluation of a candidate move should be adjusted favorably towards the side who is more likely to end up with multiple checkers back as a result of vulnerability to hits or a hit exchange.
- Candidate moves which make (or even hit or slot) lower board points (particularly when higher points are gapped, and there is still the potential for that side to reach a backgame-ish position) should be evaluated lower than JF indicates. Look for these themes in the notes to the game below.
How much should one dock "safe" plays and ace-point make/hit/slot moves? One must be careful not to get carried away. JF does, after all, play most positions very well, and to reach backgames or deep holding games often requires parlays.
JF worshippers may argue that such adjustments should be relatively small (or even negligible), and in most cases they're probably right. However, at this point, I do not believe even the top JF addicts have enough experience with the creature to authoritatively determine the size of such adjustments. Required are comparison of JF rollouts with very extensive top player rollouts in a variety of positions.
In these notes, candidate moves will be written in shorthand notation, listing only the checkers' destinations. For example, when the opening move "24/18 13/11" appears next to the diagram, I refer to it as "18,11." "JellyFish" is usually abbreviated as "JF."
And now, without further ado, let the game begin.
Ron Karr (Black) vs. Richard McIntosh (White)
Score: 4 - 4
11 Point Match
| Play 1a |
Black to play 62
Candidate Plays Equities 24/18 13/11 +0.012 24/16 -0.005 13/5 -0.014 24/18 24/22 -0.049 13/7 24/22 -0.052 13/7 13/11 -0.054 24/18 8/6 -0.066 |
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|
To reflect actual equity,
JellyFish's numbers for "18,11" (or "18,22" or "18,6")
should be lowered,
because Black may get hit on White's bar point
and hit White back one or more times.
"5", "7,22", and "7,11" should be raised (to less negative numbers),
because White will often send Black back on roll.
So, which move is actually best is uncertain.
Almost everybody plays "18,11" (my choice as well). If it is best, then in my opinion there is no need to try "5" even against a significantly weaker opponent, as "18,11" already does a good job of seeking complications. |
| 1. | ||||
| Play 1b |
White to play 51
Candidate Plays Equities 13/7* -0.054 6/1* 8/7* -0.078 13/8 24/23 -0.137 13/8 6/5 -0.156 |
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|
"7*" shows good restraint here,
smoothing the distribution.
Now 1's (as well as 6's) will make the bar point without giving up the 8 point.
Hitting a second checker does protect the blot on the bar point. And, though otherwise antipositional, hitting on the ace point can generate tempi which lead to a blitz or partial blitz and a sudden tactical advantage. White is just a little short on ammunition to have it pay often enough. Put another way: Hitting with the 5 would be much better than standing pat, but bringing down the 5 to a stripped point takes priority. As for theoretical adjustment of JellyFish's numbers: After "7*", sixteen numbers send back a checker with possibly more to come; after "7*,1*", only eleven numbers hit. Also, "7*,1*" means potentially making the ace point with a large gap. Both reasons argue for "7*" being an even better choice than JF indicates. |
| 1. | ||||
| Play 2a |
Black to play 11
Candidate Plays Equities Bar/24 11/10 6/5(2) +0.161 Bar/23 6/5(2) +0.149 Bar/24 8/7 6/5(2) +0.134 Bar/24 6/5(3) +0.116 |
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|
Black wants to make the most of his sudden advantage, "24,5(2)".
There are three choices with the fourth ace which further improve his position.
"24,7,5(2)" is a useful duplication, and could be the correct idea if somehow the position were a little different and Black were a underdog, seeking complications. As it is, while 5-1, 4-2, 6-2, 6-3, 3-3 are only small gains for White, 6-5 is a medium gain and 6-1, 6-4, 6-6 large gains. Adjust JellyFish's number up slightly for any potential backgames this play might create. "23,5(2)" improves the placement of the back checkers, and looks compelling -- probably the move most players would make. When Black is not attacked, this will add most of 2-1, 3-2, 4-3 and 6-5 (although doubles downgrade) to his list of good numbers. If White's 8 point were stripped, this move would be the correct approach. "24,10,5(2)" is quiet but effective; it adds 3-1, 6-2 and 6-3 to Black's good numbers (though 4-1 makes the 9 instead of 7 point), and likely upgrades 3-2, 4-3 and 1-1. In addition, and what many people underrate, this ace improves the placement of a builder even when not harnessed immediately. "24,10,5(2)" commands an advantage with less murkiness than the other two choices. |
| 2. | ||||
| 3. | ||||
| Play 3b |
White to play 22
Candidate Plays Equities Bar/23 13/11 6/4(2) +0.187 Bar/21 6/4(2) +0.164 Bar/23 24/22 6/4(2) +0.159 Bar/23 6/4(3) +0.070 |
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|
Again,
we're faced with a turnaround in advantage,
and three good choices for the fourth number.
After "23,4(2)",
which deuce offers the biggest improvement?
The 11 point builder controls the 5 point basically risk-free. 6-2 and 6-4 would already be good numbers for Black, covering the bar point and advancing in White's home board. If White does play to the 11 point and gets hit, he will have 26 returns either there or on Black's bar point. Advancing to Black's 4 point or 3 point are thematic, and do rate to gain more than they lose. However, by pounding on the 4 or 3 point, Black can increase volatility (desirable for the underdog) and gain time to advance in White's board. Note that in some such variations, Black will fail but end up with a backgame or deep holding game; therefore "21,4(2)" and "23,22,4(2)" are probably even worse than JellyFish thinks -- making the real comparison wider than the .023 or .028 listed here (or than whatever difference some other JF version might roll out). The concept here is to take into account the downside of generating tactical complications when holding an advantage which does not include a stronger board. On balance, the 11 point deuce offers the best deal; a moderate plus and a tiny minus. |
| 3. | ||||
| 4. | ||||
| Play 4b |
White to play 62
Candidate Plays Equities Bar/23 13/7 -0.010 Bar/23 24/18 -0.065 |
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| After the simple "23,7", it will be about an even game: White has a weaker board (which is why "23,18" would be so rash) and will not be on roll, but will have an equal number of prime points and one fewer checker back. |
| 4. | ||||
| Play 5a |
Black to play 41
Candidate Plays Equities 6/2*/1* -0.027 24/20 24/23 -0.046 24/20 6/5 -0.098 6/2* 24/23 -0.101 |
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Note that up to this diagram,
the players have played well,
neither having made a significant error.
Here, 4-1 gives Black the opportunity to hit twice, maximizing the value of his better board. After "1**", next roll there will be nine numbers to cover the ace point (including 5-2 and 6-1 as possible pick'n'passes). The full blitz does not rate to be successful, but by keeping White off balance, Black has a better chance to anchor on White's 5 point or 3 point. As an aside, note that if the 4 is played to 20, how much stronger 23 (rather than 5) is with the ace, generating a hardier fall-back anchor and more return shots in case White points with 3-1, 3-2, 5-3 or 5-4. |
| 5. | ||||
| Play 5b |
White to play 52
Candidate Plays Equities Bar/23*/18 +0.213 Bar/23* 13/8 +0.212 Bar/23* 7/2* +0.123 |
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Reflexively I give the nod to "23*,18".
The roofing of an enemy checker is a strategic time to split or run.
There are several reasons, however, why bringing the 5 down here is uncharacteristically strong:
Having said all that, it takes an abundance of position-specific reasons to make "23,8" as good as the thematic "23,18". I would still play the latter, as I think it will tend to lead to positions in which my opponent will face more difficult cube decisions. "23,2" is overly aggressive. It will win more gammons, but getting hit to a stronger board costs heavily, and it strips a builder. If the 2 point is made without the three, White will have as many inner points as Black, but he will have made a positional concession: The investment of two checkers without an increase in the strength of his prime. |
| 5. | ||||
| 6. | ||||
| Play 6b |
White to play. Double or roll?
Equity (centered) White 72.0% G 3.5% BG 0.4% Black 28.0% G 0.6% BG 0.0% Equity (White): +0.473 Equity (cubeless) White 56.9% G 30.8% BG 2.9% Black 43.1% G 12.7% BG 0.8% Equity (White): +0.339 |
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I have been exposed only a short time to JellyFish's cube numbers.
Here is what I've gathered:
|
|
| I would not have doubled (level 7 evaluation). |
| 6. | ||||
| Play 6b |
White to play 54
Candidate Plays Equities 8/3* 7/3 +0.222 7/2 7/3* +0.210 23/18 6/2 +0.166 8/3* 6/2 +0.157 13/8 6/2 +0.118 7/2 13/9 +0.013 |
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|
It is hard to muster the courage to make a play like "3*,3",
but observe its flexibility.
The two extra blots are worrisome,
but White is only really hurting if he fans after Black rolls a two
(a 1 in 12 parlay).
The rest of the time White can solidify or keep slashing away,
to try for a big advantage.
Note that if attacking backfires, "3*,3" makes a purer board, and will get more checkers back than will "7/3*,2" or "8/3*,2"; both reasons for which we should adjust upward JF's relative assessment of "3*,3". Now that White's board can be made as strong as Black's, it is the key moment to risk a blitz: "3*,3" (or one of the "3*,2" plays) is indicated. Plays that fail to hit a second checker are too relaxed and garner a cheesy structure. |
| 6. | ||||
| Play 7a |
Black to play 11
Candidate Plays Equities Bar/24 8/5 -0.511 Bar/24 4/2*/1* -0.515 Bar/24 8/6 8/7 -0.552 |
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I admit that I didn't even consider "24,1**";
I need to work on my game.
I recognize the value of deflection
(so that Black can more likely make forward anchors),
but giving up the 4 point is an enormous sacrifice.
I am disappointed with JellyFish
for having rolled out and assessed this board-breaking play
as essentially equal to "24,5".
As far as adjusting JF's rollouts, putting a checker on the ace point means we downgrade "24,1**", but the immediate possibility of getting more checkers back would seem to offset that adjustment. Perhaps JF is misplaying the pure ("24,5") position for Black. A strong board like 6/5/4 combined with ace-3 or ace-3-5 (or 3-5 plus potential ace) anchors can go forward or backward; it could cost to fail to aggressively slot one's bar point and 3 point, to strengthen the prime or recirculate (depending on opponent's dice), and to fail to repeat the procedure every time one sends a checker back. (The idea is once failing forward, to break the 5 point when finally forced and play from the ace-3). The alternative position, after "24,1**", leads to more positions where the ace point is made, after which JF should play the position relatively error-free. Even if my speculation is valid, there's a question of how big a difference inaccurate play in the pure position would really make. I'd like to hear opinions from more experts who have watched JF play. Meanwhile: I challenge JF (or any person) to a high-stakes prop, and will spot ten times the difference listed here, which is 0.040 (four points in 100 games), to play "24,1**" while I play "24,5". |
| 7. | ||||
| Play 7b |
White to play. Double or roll?
Equity (centered) White 77.5% G 8.3% BG 1.6% Black 22.5% G 0.5% BG 0.1% Equity (White): +0.643 Equity (cubeless) White 61.8% G 34.6% BG 4.5% Black 38.2% G 10.1% BG 0.7% Equity (White): +0.520 |
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This position appears to contain a much more interesting cube decision.
Since one should be slightly more aggressive at this match score
(only seven points apiece remain)
than for money,
a double here is worthy of consideration.
White may hit with every number. There are fourteen single hits (eight outside, six inside), thirteen double hits (though six leave two blots in the board), six pointing numbers, and two double-pointing numbers. If Black fans, White has lost his market by a lot. If Black enters on the 24 or 22, but White is able to make four-in-a-row (4 point through 7 point), that will probably be a market-losing sequence as well. A backgame is a distinct possibility, and in any case a long game is guaranteed. So, the correct doubling point is probably around 0.450. JellyFish's cubeless evaluation is 0.520, indicating a powerful double. I have to disagree, and venture to suggest it is misplaying Black's side.
I estimate this position to be right on the doubling borderline.
I would double
if I guessed there was at least a 5-10% chance my opponent would drop.
Otherwise I would wait for a position
in which my opponent is more likely to err
(i.e., drop a take or take a drop).
|
|
| I would have doubled (level 7 evaluation). |
| 7. | ||||
| Play 8a |
Black to play. Accept or pass?
Equity (centered) White 77.5% G 8.3% BG 1.6% Black 22.5% G 0.5% BG 0.1% Equity (White): +0.643 Equity (Black owns cube) White 51.1% G 32.2% BG 4.4% Black 48.9% G 1.0% BG 0.1% Equity (Black): -0.378 Equity (cubeless) White 61.8% G 34.6% BG 4.5% Black 38.2% G 10.1% BG 0.7% Equity (White): +0.520 |
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As you've probably guessed from the previous note,
I believe this to be a monster take.
Black has his three best board points;
all he has to do is hit back somewhere,
or make the 20 point,
to cause White to regret having doubled.
|
|
| I would have accepted (level 7 evaluation). |
| 8. | ||||
| Play 8b |
White to play 21
Candidate Plays Equities 8/5* +0.242 24/22 23/22 +0.239 8/6 23/22 +0.218 7/5* 7/6 +0.200 8/6 24/23 +0.179 |
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Tough decision.
After "5*":
nine opponent rolls (fans) yield to White an enormous advantage,
eight rolls (enters not hitting the 20 point) a solid to strong advantage,
and nineteen rolls a slight disadvantage --
overall,
a small advantage.
After "22(2)":
White has a holding position with inferior structure,
but with tactical superiority,
and he's well ahead in the race --
overall,
a small advantage.
I'm sure I would have hit at the table (more complicated), but without being confident of theoretical correctness. "5" leads to more backgames and deep holding games; "22(2)" to mutual holding games, simpler positions. I do sometimes allow myself to be influenced by JellyFish. Seeing the closeness of the data points listed here, I'd recommend "22(2)" against a superior player, "5*" against an inferior player. |
| 8. | ||||
| Play 9a |
Black to play 64
Candidate Plays Equities 22/16 24/20 -0.228 8/2 24/20 -0.243 22/16 20/16 -0.306 |
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"2,20" is the conservative approach,
which ... "Hurts ma aahs, ma boy",
to quote Malcolm Davis
(though different things hurt his eyes than hurt mine).
After this "safe" play,
White can hop into the outfield with little concern;
Black has to roll well to clean up the subsequent position.
This is a good opportunity for Black to launch a challenge. After "16,20", a hit on the 9 point is no big deal; there are numerous return hits, enter/covers, and enter/lifts. A hit on the 8 point hurts, but on the non-hits, Black is gaining control of the outfield, with a mounting strategical advantage. Then again, backgammon is basically a stack-and-race game. Even plays which, upon sight, cause the lily-pure checker-petter to go into a long frenzied diatribe -- even these plays often give away little or nothing (or even gain). Here, JellyFish claims "2,20" to give away only 0.015 (although I would estimate it to be more). |
| 9. | ||||
| Play 10a |
Black to play 42
Candidate Plays Equities 13/9 24/22 -0.304 24/20 22/20 -0.399 22/16 -0.402 24/20 13/11 -0.404 5/1 24/22 -0.425 24/20 5/3* -0.434 13/9 5/3* -0.441 |
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| Forty pips down, Black must play aggressively, though hitting on the 3 point is a bit too precipitous; grabbing the second anchor must take priority. "16" would garner more merit if it wasn't so difficult to contain White's checker; Black's blot on the 2 point remains a thorn in his side. |
| 10. | ||||
| 11. | ||||
| Play 11b |
White to play 64
Candidate Plays Equities 16/6 +0.493 16/7 !? +0.477 16/10 8/4 +0.441 13/7 8/4 +0.420 16/10 13/9 +0.403 |
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| Playing to the 6 point is safe, and is the strongest place to have a builder. |
| 11. | ||||
| Play 12a |
Black to play 53
Candidate Plays Equities Bar/20 5/2 -0.448 Bar/20 13/10 -0.509 Bar/22 13/8 -0.549 |
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| With massive timing, entering on the 22 point would be correct: In case of a hit, having three checkers on the back point and one on the front is better defensively (than the reverse); after a hit, keeping the back point is guaranteed, and both points can be kept/remade more often. Obviously no such timing exists here, however; therefore, Black should enter on the 20 point and use it as a spare checker with which to run. |
| 12. | ||||
| Play 13a |
Black to play 32
Candidate Plays Equities 13/10 13/11 -0.468 13/8 -0.490 13/10 5/3 -0.534 6/3 13/11 -0.553 6/3 6/4 -0.583 |
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|
Whatever Black does,
he must keep the integrity of his board.
Let's say,
for example,
Black plays "4,3",
and White simply chooses to break the midpoint.
Now,
even if Black rolls one of the eighteen hits,
he will need to take numerous risks to win --
the gammon chances are too high.
Black would like to have run from the 20 point this roll, keeping the midpoint, but rolled too small. If Black is to leave a blot, he would much prefer it to be on the 16, 15 or 14 point, for the possibility of return shots or sharpening his defense by switching to an outer anchor. But that is not an option either. The idea behind "8" is to keep White at bay on half the rolls (6-4, 6-3, 6-2, 5-4, 5-3, 5-2, 4-3, 4-2, 3-2) -- White would otherwise like to be able to break the midpoint (relieving the tension at the cost of only seven shots). Next roll, Black might remake the midpoint with a 7, or to come out with a 4, 5 or 6 and upgrade his blot. However, the combined chances of White spoiling that dream by hitting are too high, allowing him not only to escape the seven-number shot, but with good gammon chances. "10,11" doesn't look very inspired, but it is sensible. Black must hope to hit the indirect on the midpoint, or that White will roll 2-1 or 3-1, allowing Black to oppose him with a well-placed blot next roll. |
| 13. | ||||
| Play 13b |
White to play 52
Candidate Plays Equities 13/6 +0.488 7/2 8/6 +0.462 8/1 +0.416 |
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|
"6" allows Black to hit with 7 numbers.
Against that White must weigh the problem
of getting off the midpoint in the future.
The possibility of 6-5 and doubles (eight numbers) next roll are a point in favor of temporary safety ("2,6"). Points against are that White's position will be less flexible (both in positions where he's later hit and those where he's not), and that Black will be better positioned to contain a hit checker (bar point slotted and/or direct covers to the 3 point). It is difficult to design a hard-and-fast rule for deciding to pay now or pay later. One good approach is to memorize specific positions as benchmarks and mentally interpolate. Here, paying now looks right. If Black were at critical mass (on the verge of breaking his board or an anchor), or a hit for Black guaranteed a win, playing safe would have far more plausibility. |
| 13. | ||||
| Play 14a |
Black to play 61
Candidate Plays Equities 20/14 10/9 -0.561 10/3 -0.573 20/14 11/10 -0.576 11/5 10/9 -0.582 11/5 4/3 -0.586 20/13 -0.587 11/4 -0.591 20/14 4/3 -0.592 20/14 5/4 -0.607 |
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|
Let's look at the hit sequences if Black "stands pat"
(i.e. plays 6-1 on his own side of board):
3-1, 2-1, or 1-1 gets White hit with seven numbers,
or 4-4 with eight numbers. That's 43/1296.
Now the hit sequences if Black plays the 6 out to the 14 point: 3-1 gets White hit with fifteen numbers, 2-1 or 1-1 with five numbers, or 4-4 with 24 numbers. That's 69/1296. So, with running out Black gets 26 more hits. Say he wins half (?) of those games -- that's about 1%. Ignoring timing and prime-hurdling issues, the major question is whether playing to the 14 point will get gammoned as much as twice (about 2%) as often as standing pat. First, White has to hit (any deuce but 2-6) and not get hit back (284/1296). From these we take the subset of games where Black never hits White (55%?), and from these the subset where the 11+ pips lost will make the difference in getting a checker off (10%?). The net result comes to 284/1296 x .55 x .1 = 1.2%. That's less than 2%, so using 55% and 10% (my guesses) means coming out to the 14 point and risking the gammon appears to be correct. |
| 14. | ||||
| Play 15a |
Black to play 43
Candidate Plays Equities 20/16 11/8 -0.618 20/16 6/3 -0.618 20/13 -0.620 |
|||
| White will not leave a shot this roll, so it makes little difference which move is made, as long as hurdling the prime (with the 4) is part of it. "16,8" is thematic. "16,3" is cute, creating a temporarily weaker board but two extra cover numbers (6-4). |
| 15. | ||||
| Play 15b |
White to play 42
Candidate Plays Equities 8/2 +0.604 8/4 6/4 +0.594 6/2 6/4 +0.517 |
|||
| Moving a checker from the 8 point is standard strategy, preparing to break the furthest point from home. "2" is slightly better than "4(2)" in order to leave more playable 4's -- the largest number blocked from the tallest outside point. (Imagine 4-4, or 4-3, or 5-4 twice.) |
| 15. | ||||
| Play 16a |
Black to play 21
Candidate Plays Equities 16/13 -0.597 16/14 8/7 -0.598 8/6 16/15 -0.599 5/3 16/15 -0.604 8/5 -0.605 16/14 4/3 -0.605 5/3 8/7 -0.606 8/6 4/3 -0.610 3/1 8/7 -0.686 3/1 16/15 -0.687 |
|||
| Either "13" or "14,7" sets up seventeen covers to the 3 point. "13" will keep the bar point better eyed in a hair more roll sequences. |
| 16. | ||||
| Play 17a |
Black to play 41
Candidate Plays Equities 8/3 -0.500 13/9 8/7 -0.519 13/9 4/3 -0.539 8/4 13/12 -0.546 13/8 -0.556 13/9 5/4 -0.572 |
|||
| Black's shot potential is high enough to warrant the squandering of gammon-saving pips to make the board. If this were just a 22 point holding game, then "9,7" would be a good compromise. |
| 17. | ||||
| Play 17b |
White to play 21
Candidate Plays Equities 8/7 8/6 +0.690 4/2 7/6 +0.522 |
|||
| Good roll: Clears the 8 pt, and the extra checker on the 6 helps with the four squeeze. |
| 17. | ||||
| Play 18a |
Black to play 41
Candidate Plays Equities 13/8 -0.683 20/15 -0.705 20/16 13/12 -0.707 13/9 2/1 -0.734 13/9 6/5 -0.734 13/9 5/4 -0.735 13/9 4/3 -0.739 13/9 3/2 -0.751 5/1 13/12 -0.778 |
|||
| No need for a fancy play here. Coming out protects Black against a board-compromising 2-2 next roll, but grants White four immediate pointing numbers. |
| 18. | ||||
| Play 18b |
White to play 63
Candidate Plays Equities 7/1 7/4 +0.739 7/1 4/1 +0.628 |
|||
| Making the ace point is safer for the next roll (only 6-3 leaves a shot as opposed to the 6-2 and 6-4 that "1,4" allows), and creates a stronger board on the eve of Black's departure. However, it creates even more problems: A hazardous distribution, double jeopardy, and a slower bearoff -- a higher probability White will get hit with few checkers off. Overall, "1,4" is the safer play. |
| 18. | ||||
| 19. | ||||
| Play 19b |
White to play 52
Candidate Plays Equities 6/1 4/2 +0.643 6/1 6/4 +0.640 |
|||
| Two plays here, either of which produce a position in which eight numbers leave shots next roll. All else being equal, the play which clears the 6 point faster would seem slightly superior. However, not all else is equal; 6-4 leaves two blots. Also, Black is out of time; if he runs off the 5 point with one checker, White's builder on the 6 point can be used profitably with 2-1 and 4-1. "1,2" is an alert play. |
| 19. | ||||
| Play 20a |
Black to play 43
Candidate Plays Equities 20/13 -0.624 20/16 20/17 -0.624 20/16 5/2 -0.689 5/1 20/17 -0.704 5/1 4/1 -0.757 |
|||
|
It is more often right to run with both checkers than widely believed.
It avoids getting pointed on or pick'n'passed,
which can often minimize net shots and increase gammon chances
for the aggressor.
I liked running one checker here as well. In the next roll exchange, running with both checkers generates only 96 shots, whereas running with one yields 174 shots (includes the 28 volunteers from 2-4, 2-3, 2-1, so need not be counted again in the paragraph below), a difference of 78/1296. Running with one also often gives the option, of staying in a 22point/20point posture next roll, when White is stripped. Intuitively, against this option, I would weigh the negative of White's immediate hits (2-4, 2-3, 1-4, 1-3, 1-2 when not hit back, plus sometimes 2-4, 2-3, 2-1 next roll) as bar point clearers, and call White's added danger and safety a wash. One must also consider the gammon danger from these ten rolls, plus 6-2, 2-2 and 1-1, which is fourteen rolls altogether. Assuming Black always wins when he hits, the additional shots listed above translate to 78/1296 = 6% extra wins; so there has to more than 12% added gammon danger for the play that leaves one checker, to make it wrong. This means that there has to be 12 x 36/14 = 30+% more gammons in the subset of the only fourteen hit rolls which slow Black down. Since, unhindered, Black needs 55+ pips (about seven rolls) to get off, getting hit and fanning (costs five pips, plus a roll for every fan) could easily be critical. I wouldn't have thought getting hit would cost 30+% more gammons on average, but I suppose it's possible. If my analysis is correct, and JellyFish's numbers listed here can be trusted (showing "17,16" and "13" to be equally good moves), then such appears to be the case. I would like to inject an observation here: Going through this type of thought process does not guarantee selection of the proper move at the table. That depends upon how often the given depth of analysis makes the answer obvious, the honing of one's knowledge/intuition and concentration, and how much time one is able/willing to sit at the table and delve further. Personally, I believe it is extremely rude to one's opponent and to the tournament staff to think as long as many players do, so I do not wish to encourage it. I recommend study at home, and from that source allow most of the reward to be reaped. When at the table, think a bit only on the tough moves and then be ready to wing it. If by that time the best move doesn't seem obvious, then in my view either you have not yet earned the right to know the answer through enough experience or study, and/or the answer is close, which means there is little equity to give away. Time to make a move. |
| 20. | ||||
| 21. | ||||
| 22. | ||||
| Play 23a |
Black to play 54
Candidate Plays Equities Bar/20 13/9 -0.941 Bar/16 -0.981 Bar/20 5/1 -1.036 |
|||
| No-brain-er: "20,9". Staying back on the 20 point breaks even or gains on all White rolls save 1-1. |
| 23. | ||||
| Play 24a |
Black to play 65
Candidate Plays Equities 20/9 -1.008 20/14 9/4 -1.047 20/14 22/17 -1.054 22/16 20/15 -1.051 9/3 20/15 -1.078 22/11 -1.081 |
|||
| Running from the 22 point is better only for the gammon-off distribution. Because White's rolls of 3-3, 3-2, 3-1, 1-6, 1-5 and 1-1 would otherwise cost, stacking on the 9 point is required. |
| 24. | ||||
| Play 25a |
Black to play 11
Candidate Plays Equities 22/21*/20 9/7 +0.615 22/21* 9/7 9/8 +0.603 22/21* 9/7 5/4 +0.599 22/21*/19 9/8 +0.571 22/21* 22/20 9/8 +0.562 22/21* 9/6 +0.545 22/21*/18 +0.536 22/21*/20 9/8 5/4 +0.534 22/21*/20 9/8(2) +0.491 22/21* 9/8(2) 5/4 +0.486 |
|||
|
A delightful last ditch hit.
Now,
should Black slot the bar point (say "21*,20,7"),
or not ("21*,19,8")?
If this game is played to the end, certainly. An excellent rule is that slotting the back of a prime, risking a onetime x-6, is the surest road to victory. It seems to always be true, in fact, unless one can guarantee a cash without slotting. One cannot guarantee that here. If White enters, Black's position is so much less potent than having slotted, in fact, that suddenly it is the redouble comes into question, not the take. It seemed unlikely that the risk from 1-6 would overturn this difference, but just to make sure, I asked Richard to run some cubeless rollouts: ("Slot" = "21*,20,7", "Non-slot" = "21*,19,8". "Fan" = White fans, "Enter" = White rolls 1-5, 1-4, 1-3, 1-2 or 1-1, "1-6" = White rolls 1-6).
White --> Fan Enter 1-6
Black Slot Big 0.607 0.054
Black Non-slot 0.638 0.462 0.359
As can be seen in the above cross-table:
If White fans,
he will have to pass --
it makes no difference if Black slots.
If White enters (nine numbers),
Black gains (0.607 - 0.462) = 0.145 by having slotted.
If White rolls a gammon-threatening 1-6,
Black loses (0.359 - 0.054) = 0.305 by having slotted.
To sum up: nine times Black gains 0.145, and only two times loses 0.305. As suspected, the tradeoff is distinctly in favor of slotting. So, hit ("21*"), slot ("7"), and then where is the last ace? Playing "20" yields sixteen prime/board-making numbers (2's, 1-1, 5-5, 6-4, 4-4), and the other twenty numbers hit (in case White enters). Playing "4" yields sixteen primes and sixteen hits. Playing "8" yields fourteen primes and nineteen hits. So, "20" is the best fourth ace. "21*,20,7" is the indicated play. |
| 25. | ||||
| Play 26a |
Black to play. Double or roll?
Equity (Black owns cube) Black 96.6% G 0.0% BG 0.0% White 3.4% G 2.2% BG 0.0% Equity (Black): +0.909 Equity (cubeless) Black 81.9% G 0.0% BG 0.0% White 18.1% G 3.0% BG 0.0% Equity (Black): +0.607 |
|||
|
As a rough estimate,
with White closed out,
call each checker worth about 4+% winning chances
(after five off, it increases).
With three off,
White has 13%.
Sixteen numbers close White out (or six-prime).
The other twenty numbers hit.
A closeout is a big market-loser,
and so is a Black hit followed a White fan
(the threat of a closeout,
reducing White to 13%,
is too strong).
16/36
+
20x25/1296 = 83% market-losers,
over half of them big losers.
A redouble is mandatory.
|
|
| I would have doubled (level 7 evaluation). | |
|
And should White take?
Sixteen numbers close/prime,
leaving White with 13% (as mentioned above).
The other twenty numbers hit:
On those,
White hits back 11/36.
If he fans (25/36),
Black will have an average of 24 covers,
and so will fail to cover the ace point 12/36,
White will hit 11/36.
If both fail (12x25/1296),
Black will miss again 8/36,
White will hit 11/36.
Thus White's hitting chances are 11/36 + (25/36 x 12x11/1296) + (300/1296 x 88/1296) = 39%.
(Most of this is in the 11/36 = 30+%.
There are short cuts for estimating curveoffs --
in this case the additional 7% and 1+% --
of if-no-cover-no-hit scenarios
that do not involve such brute force calculation.)
Even if White is able to slime all the way around the board (now or after being hit later) and win, say, a third of these games (gammon-adjusted), that's only about 39%/3 = 13%. Adding this 13% slime vig to the fact that in the remaining 87% of the time White wins 13% after closeout (13% x 87% = 11.3%), yields 24.3% White winning chances (on the subset of the twenty Black hit numbers). So, the 13% from the sixteen primer/closers, and 24% from the twenty hits combine to yield (13% x 16/36) + (24+% x 20/36) = 19.3%. I do not believe White can quite squeeze out a take. |
| 26. | ||||
| Play 26a |
Black to play 33
Candidate Plays Equities 22/19 9/6 7/1* +0.571 20/17 9/6 7/1* +0.566 9/3 7/1* +0.544 22/19 20/17 7/1* +0.543 22/16 7/1* +0.538 20/14 7/1* +0.533 9/6 7/1* 5/2 +0.523 20/17 7/1* 5/2 +0.510 22/19 7/1* 5/2 +0.501 |
|||
|
Since Black cannot close the prime,
he must strike so that White's parlay includes rolling an ace
before escaping with a 6;
therefore,
two of the 3's must hit loose on the ace point ("1*").
Maximal covers is usually the next consideration. Certainly, "6" is indicated. For the final checker play, "19" introduces 6-6 as a 27th cover number. If the game is to played to conclusion, this is the correct play. However, the game will probably not be played to conclusion. If White fans, Black can cash either way, so the long distance cover will gain nothing. Thus, we need only inspect the variations in which White hits. If White rolls ace-6, 6-6 already hits back, so from the standpoint of return shots, the two plays are equal: "19" offers 4-4, "17" 5-5. In addition, Black's checker distribution creates more hitting opportunities on the next roll with "17" (in range of small numbers, with the checker on the 22 point back for final hope). If White rolls an ace without a 6, a struggle will ensue for the ace point. In general, the closer the next outside checker is, the better. This also argues for "17" over "19". Small difference, but I support JellyFish's second listed play. |
| 26. | ||||
| Play 27a |
Black to play. Double or roll?
Equity (Black owns cube) Black 98.4% G 0.0% BG 0.0% White 1.6% G 0.5% BG 0.0% Equity (Black): +0.963 Equity (cubeless) Black 84.8% G 0.0% BG 0.0% White 15.2% G 0.8% BG 0.0% Equity (Black): +0.689 |
|||
|
Black has even more numbers (26) to close/prime;
this redouble is overwhelming.
|
|
| I would have doubled (level 7 evaluation). |
| 27. | ||||
| Play 27b |
White to play. Accept or pass?
Equity (Black owns cube) Black 98.4% G 0.0% BG 0.0% White 1.6% G 0.5% BG 0.0% Equity (Black): +0.963 Equity (White owns cube) Black 83.1% G 0.0% BG 0.0% White 16.9% G 0.5% BG 0.0% Equity (White): -0.658 Equity (cubeless) Black 84.8% G 0.0% BG 0.0% White 15.2% G 0.8% BG 0.0% Equity (Black): +0.689 |
|||
|
This calculation is similar to the last one,
except Black gets the first roll,
and has 26 covers (instead of 24):
Black will fail to cover the ace point 10/36, White will hit 11/36. If both fail (10x25/1296), Black will miss again 8/36, White will hit 11/36. Thus, White's hitting chances are 110/1296 + (250/1296 x 88/1296) = 10%. If White wins a third of these games, that's 3%.
Adding the 3% slime vig to his 13% if closed out gives White only 16%,
which is far short of the take point.
|
|
| I would not have accepted (level 7 evaluation). |
| 27. | ||||
|
An exciting game. Black went on to win the match 11-6. |
The game was recorded on tape and transcribed by Richard McIntosh.
Rollouts were made by Richard McIntosh, using JellyFish Analyzer 2.02. Rollout results show equities for the player on move. Candidate plays were better than or within 0.100 equity of the actual plays, evaluated at level 7. The following plays were judged by the annotator not to warrant separate diagrams:
- Play 12b: 8/2 0.070 weaker than 13/7
- Play 14b: 13/8 6/4 0.057 weaker than 13/6
Parameter values for rollouts on moves were:
- level 5
- 7776 games (36x216)
- horizon 7
- seed 316
Standard deviations of equity estimates were between 0.003 and 0.011.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 316
- settlement limit 0.550
Copyright © 1996-2005 BackGammon By the Bay
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