Water has three common states: If the temperature is sufficiently cold, it freezes and becomes ice. As you raise the temperature, the ice melts and becomes water. And as you raise the temperature some more, the water boils and becomes steam. We run into this every day when we freeze water to make ice cubes or boil water to make tea.
But at low enough pressure, water will go directly from being a solid (ice) to a gas (steam) without becoming a liquid in between. And, at just the right combination of pressure and temperature, water can be in any one of its three states -- solid, liquid, or gas. This is called the "triple point" of water.
It occurs to me that cube actions work the same way. In most match scores (and in money play), the cube does what we are used to: At low winning chances the correct cube action is "not good enough to double." Then, as our chances improve, the cube action goes from "not good enough" to "double/take." Then from "double/take" to "double/pass." And finally (if we have any gammon chances) from "double/pass" to "too good to double."
That's what happens most of the time. But at some scores, and with enough gammons, the correct cube action can go straight from "not good enough" to "too good," without passing through "double/take" and "double/drop."
That got me wondering. Is there a "triple point" of cube actions? A position that is all three states at the same time?
So I went looking, and this is the best I could find. Within the statistical accuracy of the rollout, the following position is: (1) no double, (2) double/take, and (3) double/pass. You don't see that every day!
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| XGID=--BaCBCBB----a------A-cdf-:1:1:1:00:7:3:0:11:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 86.609% (G:21.985% B:0.892%) | 87.577% (G:15.070% B:0.291%) |
| Opponent Winning Chances: | 13.391% (G:1.128% B:0.003%) | 12.423% (G:1.728% B:0.005%) |
| Cubeless Equities | +0.9539 | +1.4632 |
| Cubeful Equities | ||
| No redouble: | +0.9999 (-0.0001) | ±0.0017 (+0.9982..+1.0015) |
 Redouble/Take: | +1.0033 (+0.0033) | ±0.0040 (+0.9993..+1.0073) |
| Redouble/Pass: | +1.0000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 56.5% | |
| Take Decision confidence: | 94.7% | |
| Duration: 4 minutes 18 seconds | ||
eXtreme Gammon Version: 2.03, MET: Kazaross XG2