I gave a lecture on match play at the Memorial day tournament in Chicago. One of my main points was that knowing a couple prototype positions, (namely 85 pip race and 54S, 33A, F blitz) at various match scores could help give an idea of how to adjust what one knows about money reference positions to match play without needing to do all the match play math. It was a wide ranging topic to cover in one hour and I knew I would not be able to go in depth for some of the ideas. For more on the basics I suggest Kit Woolsey's book How to Play Tournament Backgammon or Walter Trice's Backgammon Boot Camp.
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What is the cube action for 54S 33A F at money play? Did you obtain your answer by just knowing this position already or comparing to a similar looking position that you already know? Can you estimate the percentage of wins and gammons?
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| XGID=aa-B-BC-A---dE---d-e----B-:0:0:1:D:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 66.42% (G:27.69% B:1.25%) | 66.78% (G:28.54% B:1.26%) |
| Opponent Winning Chances: | 33.58% (G:7.44% B:0.37%) | 33.22% (G:7.51% B:0.38%) |
| Cubeless Equities | +0.540 | +1.109 |
| Cubeful Equities | ||
| No double: | +0.786 (-0.055) | ±0.005 (+0.781..+0.792) |
| Double/Take: | +0.842 | ±0.007 (+0.835..+0.849) |
| Double/Pass: | +1.000 (+0.158) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 20736 Games rolled with Variance Reduction. Dice Seed: 4 Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 6 hours 26 minutes | ||
eXtreme Gammon Version: 2.00.166.beta
If you were just guessing consider learning a few reference positions. A few can go a long way. If you play only money games, then just the equities may be important but paying attention to the win and gammon percentages are important for match play. With that information how can this known result for money play be used if this position comes up at a match score?
A few basic concepts are useful. A market window indicates when a double take could possibly be correct. The lower value indicates what win %age is needed in a last roll position to make a cube correct and the higher value indicates what percentage is needed for the opponent to have a break even decision on the take or drop. For money play if we ignore gammons and recube power the window is 50% - 75%. That gives a 25% value for the take point which can be seen by looking a a gain loss analysis. If you drop you lose 1 point for sure. If you take and lose you've lost one additional point but if you take and win you've swung 3 points, winning 2 instead of losing 1. A 3-1 ratio means you need at least 25% wins compared to 75% losses. A gammon price shows the relative importance of winning a gammon compared to just winning the game. For example suppose you have a safe play that wins a game for sure but could make a risky play that gives some losses but also wins more gammons. In money play each loss swings you from +1 to -1 for a difference of 2.
The following position is a good example of using the gammon price idea. A bold play of bearing off two checkers gives a shot but leaves you even and may save a roll in a close race for the gammon. There are more single wins swung to gammon wins than there are wins swung to losses but not twice as many more. The bold play is incorrect at money but correct at a score of 4a 2a with opponent holding a two cube.
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| XGID=aa-B-BC-A---dE---d-e----B-:0:0:1:D:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 66.42% (G:27.69% B:1.25%) | 66.78% (G:28.54% B:1.26%) |
| Opponent Winning Chances: | 33.58% (G:7.44% B:0.37%) | 33.22% (G:7.51% B:0.38%) |
| Cubeless Equities | +0.540 | +1.109 |
| Cubeful Equities | ||
| No double: | +0.786 (-0.055) | ±0.005 (+0.781..+0.792) |
| Double/Take: | +0.842 | ±0.007 (+0.835..+0.849) |
| Double/Pass: | +1.000 (+0.158) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 20736 Games rolled with Variance Reduction. Dice Seed: 4 Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 6 hours 26 minutes | ||
eXtreme Gammon Version: 2.00.166.beta
Now back to the 54S 33A F position at a score of 3 away 3 away. How does the cube action compare to money? The basic doubling point ignoring gammons is a consideration. Ignoring recube power also the window at score is 50% - 70% compared to 50% - 75% for money play. The taking player has more recube power though. The basic window on a 2 cube is indeed 50-75 like it is for money. Here though there is no rerecube power. The cube level of 4 ends the match. In money play a long race cash is about 78.5%. Taking the recube power into account the cash point for a long race for money is about 78.5% and at 3a 3a it is about 74.5%. This argues for the cube being stronger at score than for money.
What about gammons? The gammon price on a 2 cube (for both players since the score is equal) works out to be 0.5 as it is for money. If the cube reaches 4 though gammons no longer matter. Some see this as an argument for the take being easier. Part of the opponent's advantage is from gammons won and that can be taken away by just recubing to 4. You don't really want to do that though until you are winning. And if you are winning it is probably you who are winning more gammons. At some scores the possibility of giving a gammon killing (or reducing) recube is especially important but at 3a 3a score the gammons actually work out to making the cube more strong. There are reasonable ways to try to take all of this into account but they can be difficult. For higher scores even the rerecube power may be important. A rollout indicates that we have a close pass with double/take equity of 1.02. Since the math is hard (and exactly how much recube power to give is especially difficult) what I suggest is using this blitz as a prototype blitz position, knowing its DT equity at many scores, and then adjusting appropriately. For example we have seen that the DT equity is .19 higher at 3a 3a score than for money. Similar positions will also be about .19 higher. Now not all blitzes are equal. If one has the same money equity but wins more gammons with less wins overall then looking at the particular gammon prices may be important. The possibility of a gammon killing or reducing recube may become more important. The technique does give a good starting point though.
The following table gives the 85 pip race cube points, cash points, and 54S 33S F DT equity on a 1 cube for a 5 point match COMMENT: The handout from the lecture had some errors which are corrected here:
The five values after the score are
I) the cubing point on a 1 cube
II) the cash point on a 1 cube
III) the cubgin point on a 2 cube
IV) the cash point on a 2 cube
V) The double take equity for a 1 cube for 54S, 33A, F
All future cube power is already accounted for.
MONEY PLAY 71 78.5 73.5 78.5 0.84
2away 3away 71 75 NA NA 0.26
3away 2away 66 74 NA NA 1.35
2away 4away 79.5 81 NA NA -.45
4away 2away 74.5 80 NA NA 1.72
2away 5away 73.5 77 NA NA -.11
5away 2away 77 83 NA NA 1.23
3away 3away 69 74.5 67 75 1.02
3away 4away 72 75.5 77.5 81 0.62
4away 3away 73 78.5 48 60 1.56
3away 5away 73 78 81.5 84 0.54
5away 3away 73 80.5 56.5 67 1.14
4away 4away 73.5 77.5 61.5 67 1.3
4away 5away 70 75.5 70.5 74 1.15
5away 4away 75 80.5 64 70 1.03
5away 5away 73.5 80 69.5 74.5 0.93
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One interesting aspect is that at the score 4a 5a that the leader has more cube power than the trailer does. If the choices are close for money many would tend to make safer opening plays with a lead but that is not always correct. For example at money it is a close choice how to play an opening 43. Playing 2 down loses more games and more gammons than splitting but makes up for it by winning more gammons and is just barely better. It is close enough that with a match lead often one should play the safer split but at 4a 5a an opening 43 should be played two down taking advantage of the greater cube power. The table also gives the cube and cash points for a race in which the leader has 85 pips. The trailer's pipcount was adjusted until a switch occurred (either from no double to double or from take to pass) and interpolations were done from rollout results to give the win percentage needed . If the race is less than 85 pips and the opponent has some cube power after the cube than the cash point will be lower due to the shorter race having more volatile equity and less efficient cube turns . In a shorter race the cube points will be lower also. The greater volatility gives more of a chance for market loss so the cube will come further from the cash point. One score where this is particularly important is the 4a 3a score. After taking the cube at 2 the window for the 3 away player holding a 2 cube is 30 – 60. With this lower window comes more cube power so there will be a greater difference between the table values (85 pip race) and a shorter race than there would be for other match scores.
One interesting fact from the table is how low the cube power is in a race for a player who is 5 away. Getting to 3 away is not a strong score from a cube power perspective and it shows up in the 5 away cash points.
In conclusion the table can give guidance to a wide range of match score situations. Even if the table is not wished to be memorized looking through it to see where your intuition was in error can improve your match play with a low amount of effort.