Recall that equity is the number of points you expect to win or lose on average if a given position is played out to the end of the game. In cubeless hypergammon, your equity is always between −3 (when you lose a triple game) and +3 (when you win a triple game).
As you might expect, the winner of the opening roll in hypergammon has positive equity. The average equity of the opening roll winner is +0.0836795444708631. That means if you are playing for $100 a point, and your opponent offers to “sell” you the opening roll, a fair price for you to pay is $8.37.
Suppose you win the opening roll. Then your cubeless equity breaks down as follows:
|Type of Win or Loss|
|You win game:||.52118||+||.31021||+||.02082||=||+0.85221|
|You lose game:||.47882||+||.27245||+||.01726||=||−0.76853|
The first thing this chart tells you is that the winner of the the opening roll goes on to win the game 52.1% of the time. (And lose the game 47.9% of the time.)
There is something else the chart tells you. The winner of the opening roll wins a gammon 31% of the time. (More than half of his wins are gammons.)
The winner of the opening roll loses a gammon 27.2% of the time. (Again, more than half of his losses are gammons.). Adding these numbers together, 31% + 27.2%, gives 58.3%.
That’s the gammon rate for hypergammon, about 58.3%. It is more than twice as high as in backgammon. This is something to keep in mind when you play hypergammon. Later when we look at cubeful hypergammon, we will see how the hypergammon’s high gammon rate affects cube decisions.
The backgammon rate in hypergammon is also much higher than in backgammon, about 8.4%.
You have probably run into this situation: It’s near the end of the game. You’ve got the game all sewn up. You’re waiting for your opponent to resign so you can get on with the next game. Then out of nowhere, he gets a freakishly lucky combination of rolls that turns the game around, and your opponent goes on to win. You’re left wondering, what just happened?
A “gin position” is a position where you are certain of victory. Hitting gin is the only time you can truly relax and enjoy your win. But what about situations such as the one above, where you are tantilizingly close to gin but not quite there?
That suggests the following question: In hypergammon, what is the closest you can be to gin and still not be sure of winning?