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BGonline.org Forums
[Hyper 06] Gammon Rate
Posted By: Tom Keith
Date: Sunday, 15 July 2018, at 2:45 p.m.
This is the sixth in a series of posts I am writing about the game of hypergammon. The previous posts are [Hyper 01], [Hyper 02], [Hyper 03], [Hyper 04], and [Hyper 05].
Opening Equities
Recall that equity is the number of points you expect to win or lose on average in a given position. 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 Single Gammon Backgammon Equity You win game: .52118 + .31021 + .02082 = +0.85221 You lose game: .47882 + .27245 + .01726 = −0.76853 Total: 1.00000 + .58266 + .03808 = +0.08368
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.)
Gammon Rate
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.)
And 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. 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, at about 8.4%.
Almost Gin
You have probably run into this situation: It’s near the end of the game, you’ve got the game all sewn up, and you’re waiting for your opponent to resign so you can get on to the next game. Then, out of nowhere, he gets a freakishly lucky combination of rolls, turns the game around, and goes on to win. You’re left wondering, what just happened?
A “gin position” is a position where you are certain of victory. That leads to the following question: In hypergammon, what is the closest you can be to gin and still not be sure of winning?
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