Game #6
Open Division Final
San Mateo, California
16 February 1997
11 Point Match
Rawlin Pullen (X) vs. Jon Vietor (O)
Score: 9 - 5
Analysis by Blake Sorem
I played backgammon long ago with both finalists. Rawlin Pullen used to play in San Francisco at Day's in the late 70s and early 80s. This was when backgammon was at its peak. There were four weekly tournaments in the Bay Area -- one of the two at Day's often drew 100 people in four divisions. I remember seeing Rawlin do well in one of the World Amateur tournaments they used to hold in Las Vegas, drawing 700-1000 entrants.
I know Jon Vietor from my San Diego days, when the club included Jon, Frank Frigo, Neil Kazaross, Mike Fujita, and others. Jon moved to San Francisco about a year ago and finally made it to his first tournament. He is moving back to San Diego, but promises to make more tournaments.
It is important to go into a game with a strategy as the match gets later. Trailing 5-9, Jon needs to be a bit more aggressive in going for gammons. And, if a gammon does appear on the horizon, he needs to be more aggressive with the cube. Rawlin, on the other hand, should play a bit more conservatively with his lead. If he starts a blitz or gammonish type game, it is generally correct at 2 away versus large-away to play for the gammon rather than cubing.
| Play 1a |
+-------------+---+-------------+ | O X | | X O | | O X | | X O | | X | | X O | | X | | O | 167 | X | | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | X | | O | | X | 167 | O | | O X | | X O | | O X | | X O | | O X | +-------------+---+-------------+ |
X to play 21
Candidate Plays Equities 13/11 24/23 +0.007 13/11 6/5 -0.010 13/10 -0.021 24/21 -0.027 24/22 6/5 -0.073 |
||
| The slotting play of 13/11 6/5 was pretty standard until recently. Today, the majority of top players split with 13/11 24/23. This avoids the risk of losing a great many pips in the race if you are hit on the 5 point. It also gives better chances for making an advanced anchor or escaping, and provides more hitting numbers for blots left in the outfield. Nevertheless, the plays remain fairly close. I usually play 24-23 in matches, and this would definitely be the case with a 9-5 lead. This play is less likely to get into a gammonish priming battle and is more likely to establish an advanced anchor. However, if this were O's roll, I would slot the 5 point to increase my gammon chances. |
| 1. | ||||
| Play 1b |
+-------------+---+-------------+ | O X X | | X X O | | O X | | X O | | X | | X O | | X | | O | 164 | | | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | X | 167 | O | | O X | | X O | | O X | | X O | | O X | +-------------+---+-------------+ |
O to play 41
Candidate Plays Equities 24/20* 24/23 +0.103 24/20* 8/7 +0.041 24/20* 6/5 +0.026 |
||
| 1. | ||||
| Play 2a |
+-------------+---+-------------+ | O O X | | X X O | | X | | X O | | X | | X O | | X | | O | 184 | | | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | X | | | O | | X | 162 | O | | O X | | X O | | O X | | X O | | O X | +-------------+---+-------------+ |
X to play 31
Candidate Plays Equities Bar/22 6/5* -0.130 Bar/24 8/5* -0.182 Bar/22 11/10 -0.227 Bar/22 24/23 -0.240 |
||
| So, already down 22 pips. X wants to avoid piling checkers up on the ace point, so coming in on 22 is pretty clear. The best 1 is then to hit on the 5 point. |
| 2. | ||||
| Play 2b |
+-------------+---+-------------+ | O X X | | X X O | | X | | X O | | X | | X O | | | | O | 180 | | O | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | X | 167 | O | | O X | | X O | | O X | | X X O | | O X | +-------------+---+-------------+ |
O to play 61
Candidate Plays Equities Bar/18 -0.090 Bar/24 13/7 -0.105 Bar/24 8/2 -0.179 |
||
| O just about has to come out to the bar here Bar/18. This is, however, going to give X a chance to go on the offensive. If there is a reasonable alternative to coming out to the bar in situations like this, particularly if O's inner board blot is up higher on the 4 or 5 point, it is usually right to make the alternative play. However, this situation is not quite as dangerous because the inner blot is back on the 2 point and because X has three checkers back, making it harder to blitz. Nevertheless, the alternative 13/7 play is not far behind. |
| 2. | ||||
| Play 3a |
+-------------+---+-------------+ | O X X | | O X X O | | X | | X O | | X | | X O | | | | O | 180 | | | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | X | 160 | O | | O X | | X O | | O X | | X X O | | O X | +-------------+---+-------------+ |
X to play 66
Candidate Plays Equities 13/7* 11/5 8/2(2)* +0.554 24/18 13/7(2)* 11/5 +0.443 22/16 13/7(2)* 11/5 +0.435 |
||
| This is a great roll and X has a good chance to make this the final game by blitzing. Hitting on the 7, making the 5, and pointing on the 2 point seem clear. Even with three checkers back, X has an excellent chance to blitz. |
| 3. | ||||
| Play 3b |
+-------------+---+-------------+ | O X X | | X X O | | X X | | X X O | | X | | X O | | | | O | 156 | | O | O | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 167 | O | | O | | O | | O X | | X X O | | X O X | +-------------+---+-------------+ |
O to play 33
Candidate Plays Equities Bar/22 13/10 6/3(2)* -0.303 Bar/22 13/7* 6/3* -0.304 |
||
| I would definitely play Bar/22 13/7 6/3. I am a bit surprised that the play of hitting only one blot but making an additional inner board point is so close according to JellyFish. Logically, I would hit two checkers. However, when I look at the play JellyFish suggests, it "feels" pretty good as well. (OK, backgammon can be as much art and "feel" as it is math and probabilities.) Making the inner board point produces a fan 1 out of 9 times and does not leave the inner blot. However, hitting only one blot does give X a good chance to make the bar point. |
| 3. | ||||
| 4. | ||||
| Play 4b |
+-------------+---+-------------+ | O O X X | | X X O | | X X | | X X O | | X | | X O | | | | O | 157 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 155 | O | | O | | O | | O X | | X O X X O | | O O X | +-------------+---+-------------+ |
O to play 62
Candidate Plays Equities 7/1* 3/1 -0.362 13/7 23/21 -0.380 13/7 3/1* -0.383 13/7 6/4* -0.439 |
||
| Two years ago, experts would have laughed at making the ace point here. However, JellyFish has helped us to see the power of potential blitzes and making inner board points, even if it is the ace point. I would definitely make the ace point here. |
| 4. | ||||
| Play 5a |
+-------------+---+-------------+ | O O X X | | X X O | | X X | | X X O | | X | | X O | | | | | 157 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 147 | O | | O | | O | | O O X | | X O X X O | | O O X | +-------------+---+-------------+ |
X to play 21
Candidate Plays Equities 24/22* 21/20 +0.376 6/4*/3* +0.370 24/22* 22/21 +0.341 24/22* 8/7 +0.307 24/22* 6/5 +0.291 |
||
| 24/22* 21/20 just feels right to me, and I am a bit surprised that 6/4*/3* is so close. The blitz play does have a chance to be successful and end the match. However, with three checkers back, I would prefer making an advanced anchor and sending a third checker back. And, as Kit Woolsey says, a play that does two things is usually better than a play that does only one. (If you are not able to play Kit at our club or on FIBS, you should at least read his books. His lastest, New Ideas in Backgammon, written with Hal Heinrich, is the best book I have ever read on backgammon. Kit and Hal show how JellyFish is helping to change the way in which modern backgammon is played.) |
| 5. | ||||
| 6. | ||||
| Play 6b |
+-------------+---+-------------+ | O X O X X | | X X O | | X X X | | X X O | | | | O | | | | | 148 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 148 | O | | O | | X O | | O O X | | X O X O | | O O X | +-------------+---+-------------+ |
O to play 21
Candidate Plays Equities 23/21 8/7 -0.167 23/21 3/2 -0.185 |
||
| Making the advanced anchor and playing 8/7 seems clear to me. I would not push the blot to the 2 point. |
| 6. | ||||
| Play 7a |
+-------------+---+-------------+ | X O X X | | X X O | | X O X X | | X X O | | | | O | | | | | 148 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 145 | O | | O | | X O | | O O X | | X O X O | | O O X | +-------------+---+-------------+ |
X to play 22
Candidate Plays Equities 24/22*/20 13/11(2) +0.374 24/22* 13/9 13/11 +0.329 24/22*/20 13/9 +0.303 24/22* 13/7 +0.297 24/22* 13/11(2) 8/6 +0.277 |
||
| X could make a five point prime here with 13/9(2). However, this is quite awkward with no extra checkers to play with at the prime, and he might find it quite difficult to escape the three back checkers without breaking the prime. When your opponent is able to take the offensive, five point primes are usually not that difficult to escape from. I would simply hit and come up with 24/22*/20, and move two down with 13/11. Slotting the 9 point after hitting just does not feel right to me. |
| 7. | ||||
| Play 7b |
+-------------+---+-------------+ | X O X X | | X X X O | | X O X X | | X X X O | | | | O | | | | | 140 | | O | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 167 | X O | | O | | X O | | O O | | X O | | O O | +-------------+---+-------------+ |
O to play 52
Candidate Plays Equities Bar/23 13/8 -0.436 Bar/23 7/2 -0.480 Bar/23 6/1 -0.499 |
||
| Not much choice. |
| 7. | ||||
| Play 8a |
+-------------+---+-------------+ | O X O X X | | X X X O | | X O X X | | X X X O | | | | | | | | | 140 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 160 | X O | | O O | | X O | | O O | | X O | | O O | +-------------+---+-------------+ |
X to play 41
Candidate Plays Equities 20/15 +0.441 11/6 +0.383 |
||
| X definitely has to come out here with 20/15, to fight for control of the outfield. If he plays 11/6 and O is able to escape the back checker or hit the blot on the 11 point, X could be in big trouble. |
| 8. | ||||
| Play 8b |
+-------------+---+-------------+ | O X O X X | | X X X O | | X O X X | | X X O | | X | | | | | | | 135 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 160 | X O | | O O | | X O | | O O | | X O | | O O | +-------------+---+-------------+ |
O to play 22
Candidate Plays Equities 23/21 13/11(2) 6/4 -0.178 23/21 8/4 6/4 -0.208 23/21 13/11(2) 8/6 -0.234 |
||
| 23/21 has to be right so O can escape the back checker. Although blocking 6s is a bit awkward, leaving very few builders to play with, it seems right. Then slot the 4 point. |
| 8. | ||||
| 9. | ||||
| Play 9b |
+-------------+---+-------------+ | X O X X | | X X X | | X O X X | | X X | | O X | | | | | | | 128 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 152 | O | | O O | | X O | | O O O | | O X O | | O O O X | +-------------+---+-------------+ |
O to play 66
Candidate Plays Equities 21/15(3) 7/1 -0.037 21/15(3) 8/2 -0.046 |
||
| A great roll. 21/15(3) for sure. I would play 8/2 with the final 6. Not sure why JellyFish thinks 7/1 is better. |
| 9. | ||||
| Play 10a |
+-------------+---+-------------+ | X X X | | X X O X | | X X X | | X X O | | X | | O | | | | | 128 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 128 | O | | O | | X O | | O O O | | O O X O | | O O O X | +-------------+---+-------------+ |
X to play 61
Candidate Plays Equities 11/4 -0.077 11/5 7/6 -0.090 11/5 13/12 -0.090 11/5 8/7 -0.096 8/2 13/12 -0.128 |
||
| This is a good play by JellyFish. I might have moved the blot on the 13 point, without thinking, in order to minimize the hits. However, O is probably not going to hit anyway since he has two blots, so X might as well safety the 11 point blot, particularly when it allows him to start the 4 point. |
| 10. | ||||
| Play 10b |
+-------------+---+-------------+ | X X X X | | X X O | | X X X | | X X O | | X | | O | | | | | 121 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 128 | O | | O | | X O | | O O O | | O O X O | | O O O X | +-------------+---+-------------+ |
O to play. Double or roll?
Equity (centered) O 61.3% G 0.5% BG 0.0% X 38.7% G 2.2% BG 0.1% Equity (O): +0.208 Equity (cubeless) O 56.3% G 2.4% BG 0.1% X 43.7% G 3.8% BG 0.1% Equity (O): +0.112 |
||
|
The advantage has now swung to O .
Should he double?
After all,
he is trailing in the match 5-9.
If O loses this game,
his chances of winning the match are very low.
Therefore, doesn't he have almost nothing to lose?
Might as well cube?
The answer is no.
If O loses the game,
he is trailing 5-10.
He can still win almost 11% of time from that score,
so he should be careful about throwing this away.
(Note that this 11% figure comes from the standard match equity table,
which assumes that the two opponents are about equal in skills.
Sometimes this can be a huge assumption.
Applying standard match equities to unequal matches is one
of the most misused techniques in backgammon.
I have seen players memorize the tables to decimal places
and then apply the figures even when the skill levels were very unequal.
It is much more important to have a rough idea
of how score and skill differences
in a match should affect your play and cubing
than it is to memorize a bunch of numbers.)
There are four reasons not to cube here. First of all, O is not favored by much. He has the advantage because X has two checkers back on the 5 point, but the race is close. Second, O has very low gammon prospects. If there were significant gammon chances then a cube here, when behind in a match, puts a lot of pressure on your opponent. The third reason not to cube is that the position is not very volatile, meaning that most rolls will not result in much of a change in winning percentages. This is important because of the fourth reason: X has a very low take point, even with this big lead in the match. Anytime a cube gives the leader just enough to win, such as in this case, the take point is quite low and may even be lower than it is for money. A 2-away score for the leader produces a very low take point when there are no gammons involved. So, it must not be a cube, but let's quickly run through the equities anyway. What is the minimum winning chance that O needs to cube and what is the minimum winning chance that X needs to take? If O does not cube and wins, he is down 6-9 and wins about 25%. With a cube, the score goes to 7-9 and O wins about 31%, for a gain of about 6%. If O loses, he is down 5-10 without a cube -- about 11% wins; with a cube, he loses the match. So O's potential gain by cubing is about 6%, while the loss is about 11%. Therefore, O needs odds of at least 11-to-6 to consider the cube, or 11/17, or about 65%. O is not there yet, so a cube would be premature.
What would be X's take point?
If X drops a cube the score is 9-6 and Black wins about 75%.
If X takes,
a win puts X at 100%,
while a loss puts X at 9-7, or about 69%.
So X stands to gain 25% by taking and winning,
while the loss would be only about 6%.
Therefore,
X only needs odds of about 6-to-25 to take, or 6/31, or about 20%.
So, X has a very low take point.
This means that O would have to get above 80% for X to drop,
which O is not close to.
Even if O was up to the minimum 65% required to cube,
he should still wait,
because X's winning percentage is not likely to change a great deal
over the next few rolls.
In other words,
X still has a take next roll, so wait until next roll.
|
|
| I would not have doubled (level 7 evaluation). |
| 10. | ||||
| Play 10b |
+-------------+---+-------------+ | X X X X | | X X O | | X X X | | X X O | | X | | O | | | | | 121 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 128 | O | | O | | X O | | O O O | | O O X O | | O O O X | +-------------+---+-------------+ |
O to play 64
Candidate Plays Equities 7/1 15/11 +0.059 8/2 8/4 +0.050 |
||
| Well. JellyFish likes 7/1 15/11 and I just do not agree. The advantage of this play is that it keeps a four-point block. However, it leaves 3 inner board blots and a stripped board. I really like 8/2 8/4, making 2 more inner board points. This puts a lot of pressure on the blot on the 12 point. I also think that a strong board is potentially more effective at keeping the two checkers on the 5 point than a fourth block. |
| 10. | ||||
| Play 11a |
+-------------+---+-------------+ | X X X X | | X X O | | X X X | | X X O | | X | | O | | | | | 121 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 118 | O | | O | | O O X O | | O O | | O O X O | | O O X | +-------------+---+-------------+ |
X to play 52
Candidate Plays Equities 13/8 6/4 -0.052 13/6 -0.063 13/8 7/5 -0.074 13/8 4/2 -0.090 13/8 3/1 -0.093 13/8 5/3 -0.108 |
||
| X has to safety the blot with 13/8 and can then make the 4 point with 6/4. With O's three-point board, X cannot risk running out with 20/13. Note, however, that had X followed the last JellyFish play, leaving three inner board blots, the play of 20/13 would be a reasonable one in this close race. |
| 11. | ||||
| Play 12a |
+-------------+---+-------------+ | X X X X | | X X O | | X X X X | | X X O | | | | X | | | | | 114 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | O | 110 | O | | O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
X to play 64
Candidate Plays Equities 8/2 8/4 -0.073 8/2 7/3 -0.080 7/1 8/4 -0.083 8/2 6/2 -0.087 7/1 5/1 -0.089 7/1 7/3 -0.093 8/2 5/1 -0.102 7/1 6/2 -0.109 |
||
| 8/2 8/4 seems clear to me, even though the numerous alternatives come close in equity. |
| 12. | ||||
| Play 12b |
+-------------+---+-------------+ | X X X X X | | X X O | | X X X X | | X O | | X | | | | | | | 104 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | O | 110 | O | | O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
O to play 54
Candidate Plays Equities 15/6 +0.076 6/1 7/3 +0.065 7/2 15/13 +0.059 11/6 11/7 +0.059 7/2 7/3 +0.046 6/1 15/11 +0.045 |
||
| I would play 15/6, even though this leaves three shots. However, I think slotting two points as an alternative, 6/1 7/3, is close. The slotting play helps in the bear-off and also is the best way to quickly build up your board. Contrary to popular opinion -- or what used to be popular opinion -- it is OK to slot points even when you might get a shot next turn. |
| 12. | ||||
| Play 13a |
+-------------+---+-------------+ | X X X X X | | X X O | | X X X X | | X | | X | | | | | | | 104 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | O | 101 | O | | O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
X to play 65
Candidate Plays Equities 7/1 7/2 -0.131 7/1 8/3 -0.139 8/2 7/2 -0.147 7/1 6/1 -0.159 8/2 6/1 -0.162 20/9 -0.177 |
||
| I like making the 2 point and starting the ace with 7/1 7/2. Even though X might get an indirect shot next roll, it is still usually correct to slot points. Once again, this helps in the bear-off and is the best way to make an even stronger board. The parlay of O leaving a shot, X hitting the shot but leaving the inner blot, and O then hitting the inner blot to win is too small to justify not slotting. |
| 13. | ||||
| Play 13b |
+-------------+---+-------------+ | X X X X X X | | X O | | X X X X X | | | | X | | | | | | | 93 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | O | 101 | O | | O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
O to play 31
Candidate Plays Equities 15/11 +0.088 7/3 +0.029 6/3 4/3 -0.008 15/12 7/6 -0.027 6/2 -0.037 7/4 7/6 -0.042 |
||
| I would safety the blot -- three times out of 36 that blot gets hit. |
| 13. | ||||
| Play 14a |
+-------------+---+-------------+ | X X X X X X | | X | | X X X X X | | | | X | | | | | | | 93 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | O | 97 | O | | O O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
X to play 21
Candidate Plays Equities 4/1 -0.163 8/6 4/3 -0.183 8/5 -0.189 8/6 2/1 -0.190 |
||
| Completing the closed board seems clear. Note that saving a 6 is not the key to this play -- the three plays of bringing the 8 point blot in, but not making a closed board are close behind. Saving 6s is vastly overrated. I hate seeing people destroy their inner boards to save 6s, only to hit a shot and watch the opponent escape easily from the meager board. |
| 14. | ||||
| Play 14b |
+-------------+---+-------------+ | X X X X X X | | X | | X X X X X X | | | | | | | | | | | 90 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | O | 97 | O | | O O | | O O X O | | O O | | O O X O | | O O | +-------------+---+-------------+ |
O to play 54
Candidate Plays Equities 11/6 7/3 +0.188 11/2 +0.161 6/1 7/3 +0.152 7/2 7/3 +0.152 6/1 11/7 +0.127 7/2 6/2 +0.110 |
||
| I would play 11/6 7/3. Note that slotting the 3 point is superior to leaving no blots with 11/2, even though there is a chance that X could run next turn. |
| 14. | ||||
| 15. | ||||
| Play 16a |
+-------------+---+-------------+ | X X X X X X | | X X | | X X X X X X | | X | | | | | | | | | 74 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 81 | O O | | O | | O O O | | O | | O O O O | | O O | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 89.1% G 0.0% BG 0.0% O 10.9% G 0.0% BG 0.0% Equity (X): +0.783 Equity (cubeless) X 75.5% G 0.0% BG 0.0% O 24.5% G 0.0% BG 0.0% Equity (X): +0.510 |
||
|
Well now, the 44 has turned the tide.
Many people would not even consider a cube here,
knowing that it will be thrown back at them at 4 next roll.
While it is true that you need to be very careful with the cube
when you are leading in a match,
this does not mean that you should just consider it a Crawford game.
After all,
how many times have you won a game like this,
afraid to cube,
but then gone on to lose the match?
No one is better at doubling from a match-leading position,
in my opinion, than Neil Kazaross.
So, does X have a cube here?
If X wins, he moves from 89% (10-5) to 100% (11-5) with a cube, for a gain of 11%. If he loses, he moves from 75% (9-6) to 50% (9-9) since O will recube to 4. Thus, X has a potential gain of 11% weighed against a potential loss of 25%. So, X needs odds of at least 25 to 11 to cube, or 25/36, or about 69%. He has 75.5% now. (Although X is only up seven pips out of 74 pips to go, or just under 10%, he has one fewer crossovers and a better board distribution.) But what does O need to take? If O drops, he wins about 11% (5-10). If he takes, recubes to 4, and wins, he wins 50% (9-9), for a gain of 39%. If he takes and loses, O loses the match, for a loss of 11%. So, O needs odds of about 11 to 39 to take, or 11/50, or about 22%. Since he has 24.5% right now, O has a take.
So, should X turn the cube?
I think it is close either way.
First of all,
even if you are capable of doing match equity calculations at the table,
the above computations are just rough estimates.
The tables are inexact,
dependent on estimated gammons in future games, for example.
More importantly,
the tables assume equal skill levels.
So, whether this is a proper cube or not
(or whether it is even a proper take or not)
depends on the relative skills of the two players,
which is not something I have much knowledge of.
If X believes he is a better player,
then it might very well be to his advantage to roll.
On the other hand,
if O believes that he is the better player,
and will thus win more than the 11% at a 5-10 score,
then he might even have a drop.
Personally,
I would roll against almost everyone,
but I would cube Kit Woolsey.
|
|
| I would have doubled (level 7 evaluation). |
| 16. | ||||
| Play 16b |
+-------------+---+-------------+ | X X X X X X | | X X | | X X X X X X | | | | X | | | | | | | 69 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 81 | O O | | O | | O O O | | O | | O O O O | | O O | +-------------+---+-------------+ |
O to play 51
Candidate Plays Equities 11/5 -0.496 11/6 2/1 -0.505 7/1 -0.506 11/6 4/3 -0.522 6/1 4/3 -0.538 |
||
| Ideally, you would like to distribute your checkers on the 4, 5, and 6 points in the bear-in. 11-5 looks good to me. Note that bringing two checkers in to the 6 point is not even on the list. You want to avoid piling up checkers on the 6 point (unless, of course, you are trying to save a gammon). |
| 16. | ||||
| Play 17a |
+-------------+---+-------------+ | X X X X X X | | X X | | X X X X X X | | | | X | | | | | | | 69 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 75 | O O | | O | | O O O O | | O | | O O O O | | O | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 88.1% G 0.0% BG 0.0% O 11.9% G 0.0% BG 0.0% Equity (X): +0.762 Equity (cubeless) X 74.5% G 0.0% BG 0.0% O 25.5% G 0.0% BG 0.0% Equity (X): +0.490 |
||
|
X has lost one pip,
but is still up six pips out of 69, almost 9%,
has a much better board distribution, has one fewer crossovers, and is on roll.
Nevertheless,
I see no problem with rolling here,
particularly taking into account all the estimates
that go into an equity calculation.
O would have a pretty easy take and recube.
|
|
| I would have doubled (level 7 evaluation). |
| 17. | ||||
| Play 17a |
+-------------+---+-------------+ | X X X X X X | | X X | | X X X X X X | | | | X | | | | | | | 69 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 75 | O O | | O | | O O O O | | O | | O O O O | | O | +-------------+---+-------------+ |
X to play 42
Candidate Plays Equities 12/6 +0.414 9/5 12/10 +0.413 9/5 6/4 +0.399 9/3 +0.376 12/8 9/7 +0.370 |
||
| I would play 9/5 12/10. |
| 17. | ||||
| Play 17b |
+-------------+---+-------------+ | X X X X X X | | X | | X X X X X X | | | | X X | | | | | | | 63 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | O | | | | O | | | 75 | O O | | O | | O O O O | | O | | O O O O | | O | +-------------+---+-------------+ |
O to play 41
Candidate Plays Equities 7/3 7/6 -0.538 7/3 6/5 -0.551 7/3 2/1 -0.555 7/3 5/4 -0.577 7/3 4/3 -0.579 |
||
| I think I would move two in here. This slots the 3 point, but does add another to the pile on the 6 point. The 7/3 is clear. I think the two other 1s are close -- unpiling the 6 point with 6/5 and slotting the ace with 2/1. |
| 17. | ||||
| Play 18a |
+-------------+---+-------------+ | X X X X X X | | X | | X X X X X X | | | | X X | | | | | | | 63 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | O | | | +---+ | O | | | | O | | | 70 | O O | | | | O O O O | | | | O O O O O | | O | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 89.7% G 0.0% BG 0.0% O 10.3% G 0.0% BG 0.0% Equity (X): +0.793 Equity (cubeless) X 77.0% G 0.0% BG 0.0% O 23.0% G 0.0% BG 0.0% Equity (X): +0.539 |
||
|
X is now up seven pips out of 63, or 11%.
He also has better distribution,
which should put O close to a drop for money.
Trailing 5-9,
O still has a take and recube.
I would now tend to cube this,
although it would still depend on who my opponent was.
If I were a big favorite,
I would roll.
|
|
| I would have doubled (level 7 evaluation). |
| 18. | ||||
| Play 19a |
+-------------+---+-------------+ | X X X X X X | | | | X X X X X X | | | | X | | | | X | | | 54 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | O | | | +---+ | O | | | | O | | | 63 | O O | | | | O O O O | | | | O O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 95.5% G 0.0% BG 0.0% O 4.5% G 0.0% BG 0.0% Equity (X): +0.909 Equity (cubeless) X 82.0% G 0.0% BG 0.0% O 18.0% G 0.0% BG 0.0% Equity (X): +0.640 |
||
|
X is now up nine pips out of 54, or 17%.
This is a cube.
O probably has a pass.
(Once again, however, this assumes roughly equal opponents.
If X believes he is a much stronger player,
he might be right to roll.)
|
|
| I would have doubled (level 7 evaluation). |
| 19. | ||||
| Play 20a |
+-------------+---+-------------+ | X X X X X X | | | | X X X X | | | | X | | | | X | | | 48 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | O | | | +---+ | O | | | | O | | | 57 | O | | | | O O O | | | | O O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 95.3% G 0.0% BG 0.0% O 4.7% G 0.0% BG 0.0% Equity (X): +0.906 Equity (cubeless) X 82.7% G 0.0% BG 0.0% O 17.3% G 0.0% BG 0.0% Equity (X): +0.653 |
||
|
Once again, cube and pass according to JellyFish.
Once again, if X is the stronger player,
might be a cube/take or even a no-cube.
(Note that if O is the stronger player,
then the cube/pass becomes that much more important.)
|
|
| I would have doubled (level 7 evaluation). |
| 20. | ||||
| Play 20b |
+-------------+---+-------------+ | X X X X X | | | | X X X | | | | X | | | | X | | | 45 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | O | | | +---+ | O | | | | O | | | 57 | O | | | | O O O | | | | O O O O O | | | +-------------+---+-------------+ |
O to play 32
Candidate Plays Equities 3/Off 2/Off -0.607 6/3 2/Off -0.622 6/3 6/4 -0.645 |
||
| Two off is clear. There are very few exceptions to taking checkers off when you can. Or in FIBS language, "toggle greedy." |
| 20. | ||||
| Play 21a |
+-------------+---+-------------+ | X X X X X | | | | X X X | | | | X | | | | X | | | 45 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | O | | | 52 | O | | | | O O O O O | | | | O O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 93.8% G 0.0% BG 0.0% O 6.2% G 0.0% BG 0.0% Equity (X): +0.875 Equity (cubeless) X 82.2% G 0.0% BG 0.0% O 17.8% G 0.0% BG 0.0% Equity (X): +0.644 |
||
|
So,
if O is at least as strong as X, this is a cube/pass.
The better that X is, the closer to a take it gets,
and eventually even a non-cube.
Jake Jacobs and Walter Trice have recently published
equity tables for unequal opponents,
in Can a Fish Taste Twice as Good?
Suppose that X is rated 200 points better than O .
Using their equity tables for a 200 point ratings difference,
I calculate X's minimum cube to be 85%!
Thus, if X considers himself that much of a favorite,
it still would not be a cube.
This type of equity calculation would be very difficult to do at the table
and the unequal opponent equity tables rely on a great many estimates.
Nevertheless,
it is important to have a rough idea
as to how skill differences affect cube play.
|
|
| I would have doubled (level 7 evaluation). |
| 21. | ||||
| Play 22a |
+-------------+---+-------------+ | X X X X | | | | X X X | | | | X | | | | | | | 34 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 32 | | | | | O O O O O | | | | O O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 80.9% G 0.0% BG 0.0% O 19.1% G 0.0% BG 0.0% Equity (X): +0.618 Equity (cubeless) X 73.7% G 0.0% BG 0.0% O 26.3% G 0.0% BG 0.0% Equity (X): +0.475 |
||
|
A good roll by O,
and now a cube is a huge take.
I would roll.
Although there are some market losers for X,
most of them do not lose it by too much.
(Cubing just to avoid losing your market can get you into big trouble.
Often, there is nothing wrong with losing your market,
particularly when it is just by a little bit.)
|
|
| I would not have doubled (level 7 evaluation). |
| 22. | ||||
| Play 23a |
+-------------+---+-------------+ | X X X X X | | | | X X | | | | | | | | | | | 30 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 24 | O | | | | O O O | | | | O O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 77.9% G 0.0% BG 0.0% O 22.1% G 0.0% BG 0.0% Equity (X): +0.558 Equity (cubeless) X 72.1% G 0.0% BG 0.0% O 27.9% G 0.0% BG 0.0% Equity (X): +0.442 |
||
|
If a very weak player were playing an expert,
this would be a strong cube,
giving the weak player a good chance to win the match right here.
I would roll.
|
|
| I would not have doubled (level 7 evaluation). |
| 23. | ||||
| Play 24a |
+-------------+---+-------------+ | X X X X | | | | X | | | | | | | | | | | 21 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 19 | O | | | | O O | | | | O O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 93.2% G 0.0% BG 0.0% O 6.8% G 0.0% BG 0.0% Equity (X): +0.864 Equity (cubeless) X 84.6% G 0.0% BG 0.0% O 15.4% G 0.0% BG 0.0% Equity (X): +0.692 |
||
|
This has now become a huge cube and drop.
X is on roll with only five checkers left.
O still has seven.
Don't forget to cube when you have large leads in the match.
If you do not cube,
you still will probably win the match,
so it probably will not make any difference.
It is just that 11% of the time,
when you lose the match after a 10-5 lead,
you will regret not cubing.
|
|
| I would have doubled (level 7 evaluation). |
| 24. | ||||
| Play 25a |
+-------------+---+-------------+ | X X X X | | | | | | | | | | | | | | | 14 | | | | | | | | +---+ | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | +---+ | | | | | | | | 13 | O | | | | O | | | | O O O | | | +-------------+---+-------------+ |
X to play. Double or roll?
Equity (centered) X 93.9% G 0.0% BG 0.0% O 6.1% G 0.0% BG 0.0% Equity (X): +0.879 Equity (cubeless) X 86.7% G 0.0% BG 0.0% O 13.3% G 0.0% BG 0.0% Equity (X): +0.734 |
||
|
Big cube.
|
|
| I would have doubled (level 7 evaluation). |
| 25. | ||||
| Play 25b |
+-------------+---+-------------+ | X X X X | | | | | | | | | | | | | | | 14 | | | | | | | | | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | | | | | | | 13 | O | | | | O | | | +---+ | O O O | | | | 2 | +-------------+---+-------------+ +---+ |
O to play. Accept or drop?
Equity (centered) X 93.9% G 0.0% BG 0.0% O 6.1% G 0.0% BG 0.0% Equity (X): +0.879 Equity (O owns 2 cube) X 86.7% G 0.0% BG 0.0% O 13.3% G 0.0% BG 0.0% Equity (O): -0.733 Equity (cubeless) X 86.7% G 0.0% BG 0.0% O 13.3% G 0.0% BG 0.0% Equity (X): +0.734 |
||
|
O is not close to the 22% that he needs to take,
nor is he close to being the huge underdog
that he would need to be in terms of skills to make this a take.
10-5 is not a hopeless situation.
Just be aggressive and play for gammons,
particularly that first game.
Don't panic here and take the cube.
|
|
| I would not have accepted (level 7 evaluation). |
| O | ||||
| 25. | ||||
| Play 25b |
+-------------+---+-------------+ | X X X X | | | | | | | | | | | | | | | 14 | | | | | | | | | 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | | | | | | | | | | | 13 | O | | | | O | | | +---+ | O O O | | | | 2 | +-------------+---+-------------+ +---+ |
|||
|
X won the next game for match, 11-5. |
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.
Parameter values for rollouts on moves were:
- level 5
- 7776 games (36x216)
- horizon 7
- seed 216
Standard deviations of equity estimates were between 0.003 and 0.008.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 216
- settlement limit 0.550
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