This is the fifth in a series of posts I am writing about the game of hypergammon. The previous posts are [Hyper 01], [Hyper 02], [Hyper 03], and [Hyper 04].
Luck and Skill
Every game has luck in it. Games that don’t have luck in them are no fun to play.
Even tic-tac-toe has luck in it, at least when you are new to the game. Children will try different moves somewhat at random until they get a sense of what they are doing. Once they figure out a successful strategy, the luck disappears and tic-tac-toe ceases to be fun. You can’t have fun without luck.
This idea applies even to games we think of as “pure skill” games, such as chess or golf. These games have luck (uncertainty) too; it is just that their luck is hidden.
That’s what I like about backgammon. Backgammon has both luck and skill, like any good game, but the luck in backgammon is open for all to see. You can even measure it.
Biggest Joker
A joker is an unusually good roll, the type of roll that can turn a game around. So what is the biggest joker possible in hypergammon?
How about this position:
 | Black rolls 6-6 |
Before black rolled, his position was pretty bleak. He even had a chance of being gammoned and his equity was a lowly −1.24241.
But black rolls sixes. Glorious sixes! In one roll black gets all his checkers off and wins the game. He even wins a gammon. His equity soars from −1.24241 to +2.0, a difference of +3.24241.
That is the biggest equity swing possible for a single roll in cubeless hypergammon.
Biggest Anti-Joker
An anti-joker is the opposite of a joker. It’s an unusually bad roll. So what is the biggest anti-joker in hypergammon?
Look at this position:
 | Black rolls 5-2 |
Before he rolled, black was looking pretty good; he had a triple shot from the bar at white’s three blots. Only 5 rolls out of 36 miss those blots (6-5, 5-5, and 5-2). Black’s equity was +.82902.
Of course black rolls one of his missing numbers, and the worst one at that. Black is forced to enter and bypass white blots. It gives white a good chance of winning a gammon and black’s equity plunges to a disastrous −1.76175.
That’s a difference of 2.59076 and it is the worst roll you can throw in cubeless hypergammon. The dice giveth, and the dice taketh away.
Biggest Checker Play Error
A whopper in backgammon is big error, usually defined as an error 0.1 or more in lost equity. You can’t afford to make too many whoppers and expect to fair well. In cubeless play especially, where equities are not multiplied by the cube, whoppers are quite serious errors. Nevertheless, everybody makes a whopper once in a while, sometimes worse.
What is the biggest error you can make in cubeless backgammon? Bob Koca figured it out. Look at the following position:
 | Black rolls 1-1 |
It takes only a little thought to realize the correct play. Black should use three of his 1’s to hit whites’s blots, 24/23*/22*/21*, then use his final 1 to cover the blot on his three point, 4/3.
 | After the right play |
At this point, black stands a good chance of winning a gammon. His equity is +1.73588.
But what if black instead played 4/1, 3/2?
 | After the wrong play |
That is a seriously bad way to play this roll. It leaves white a triple shot at black’s lone checker on 24 and white stands a good chance of winning a gammon or a backgammon. Black’s equity plunges to −2.06012. Yikes!
The difference is 3.79600 in lost equity — a 38-whopper — the biggest error you can make in cubeless hypergammon.
Gammon Rate
When you win a game in backgammon, sometimes you also win a gammon (a.k.a., a “double game”). The average number of gammons you win divided by the average number of games you win is called your gammon rate.
Each person has a slightly different gammon rate because gammon rate depends on your style of play. If you play aggressively, you will win gammons at a higher rate (and lose them at a higher rate too).
When bots play backgammon against each other, their gammon rate is usually around 27 or 28 percent. That is to say, about 27 or 28 percent of all games played without a cube end in a gammon or a backgammon. Most good players have a gammon rate in this area too.
What do you think the gammon rate is for hypergammon? Do you think it is higher than in backgammon? Lower? Or about the same?