Gammons and Backgammons

If you’re just playing with your uncle who taught you, you’re probably playing for the immediate win. But sometimes one of you gets extra lucky and really beats the pulp out of the other. Shouldn’t that count for more? Enter Gammons, where a win is worth 2 points instead of 1. Gammon wins (also widely known as Mars in the Middle East) are heavily featured in the modern Western variant of backgammon that is played in international tournaments, and can dramatically impact the strategy of checker play. 

In a typical game, you win by bearing off all your checkers before your opponent Gary can bear off his. The last roll in such a game would look like this:

You (in blue) just rolled a 61, and you can use the 6 to bear off the checker on the 4-pt and the ace (the 1) to bear off the checker on the ace-pt (the 1-pt) to win. Your opponent had started bearing off their checkers, but couldn’t catch up to you, leaving about 10 checkers on the field. This is a standard single game win. Over 75% of backgammon games end in single wins like this.

Suppose you managed to bear off all of your checkers before Gary even bore off one of his. The board might look something like this:

This counts as a gammon win, and is worth 2 pts. Note that even if those 2 checkers in the outfield (on the 9-pt and 13-pt) were in Gary’s homeboard, say, on the 19-pt, and not borne off either, it would still count as a gammon win.

Things become interesting when you start playing and scoring for multiple games in a session. Depending on the type of match you’re playing or the match score, securing that second point could be crucial. Here’s an example of a position whose play is completely dictated by whether or not you need to win a gammon:

You have trapped Gary’s 2 backcheckers behind a strong prime structure, and rolled a 61. A natural, safe, play would be to bring the spare checker from the midpoint (the 13-pt) onto one of the points made in the homeboard. That is, 61: 13/6. Any other 6 would break your 6-prime, and give your opponent a fighting chance to escape. As expected, the midpoint play does in fact generate the largest win chances, estimated to be over 86%.¹

However, what if you were trailing 6-5 in a match to 7 points? In that scenario, winning a gammon would win the match, whereas winning a single game would just tie the match at 6-6, necessitating a tiebreaker… and who knows how that will turn out! If you’re willing to play aggressively and to break your prime, you can hit both of the blots (white solo checkers) in your homeboard, putting 2 checkers on the bar (8/2*/1*). This play is certainly more risky than the first play, because by breaking your 6-prime you are giving your opponent a tiny chance to escape and win (for example, through the unlikely sequence of rolling 11 and entering and advancing both checkers,  and then rolling 66 to jump the prime). You are also leaving a blot of your own exposed in your homeboard! Therefore, despite still being the favorite, your win chances after making this play are a bit lower, around 84%. However, having 2 checkers on the bar will severely slow your opponent down, dramatically increasing your Gammon chances from 28% to 54%, nearly doubling! This tradeoff is worth it, making it the correct play at this match score. This sort of decision-making is just a taste of what we’ll learn when we get to our lessons on match play.

Though this is a natural place to end our lesson, it does not mark the end of the story. Suppose you were able to bear off all of your checkers, and your Gary still has a checker in your homeboard, as shown below:

This is called winning a backgammon, and is worth 3 points in a match. This happens extremely rarely (in about 1% of games), and at our current level of play, it is unlikely to enter into our strategic considerations. However, it’s worth being aware of them so that we know to rush our checkers out of our opponent’s homeboard when they are finishing their bear off. 

Note that it would still count as a backgammon if your opponent still had a checker on the bar at the moment you won. It would be cool if there was such thing as a superbackgammon worth 4 points, but alas that is not the world we live in today 🙂

Further reading:

• A video of the current backgammon GOAT, Masayuki “Mochy” Mochizuki, losing by a backgammon in what he calls his most unlucky game ever. This video shows that even the best of the best can experience the worst case scenario in backgammon. It also showcases Mochy’s tremendous grace, and his understanding that sometimes the dice will just rob you of any winning chances.

1. We will discuss how these values are computed in a future article. For now just take them at face value. ↩︎

Next lesson: The Doubling Cube