As most of us know, backgammon is primarily a race. The first one to get their checkers off is the winner. Sometimes the backgammon game ends because one player doubles and the other drops, but the reason for the drop is always because of the low odds of winning that race.
The race is very difficult to assess when there is contact…when some of one player’s checkers are behind the other player’s checkers. In those situations there is either the possibility of leaving a shot that could get hit, or the possibility that it will become difficult to get into a race because a player’s moves may be blocked. But even in those complicated situations, the race, or pip count, is usually a major factor to consider in both checker play and cube decisions.
For all levels of players, it is important to first completely understand the backgammon race and pip counts in non-contact situations, for two reasons. First, that situation comes up often and needs to be completely understood in order to play properly, and second, unless you understand this element of the game, it would be very difficult to adjust your mind to calculate the race when there is contact. So in this article, I want to give you what I consider to be the “basics” of understanding the race, along with my best advice to simplify the process.
For the sake of simplicity, let us assume that every game is a backgammon money game. The reason that is simpler is that in a money game the take point is always around 22 to 25 percent and gammons always cost the player double. Fortunately, this same ratio applies fairly closely to many match scores, but at various match scores this gets changed significantly as the take points can change and there are times where gammons are very important and others where they don’t matter at all.
Let’s talk about that take point for a moment. Most of us understand that the take point in a money game is around 25 percent. If you play a given position 100 times and you win 25 percent of the games, you break even whether you take or drop the cube. Just to give you a simple example, let’s take a look at position 1 below.
White is on roll, and he doubles. You are Black. Should you take or drop?
Let’s do the math. If you take, White wins this game every time unless he rolls a 1, except for 1-1. As we know, there are 36 possible rolls, and there are 10 rolls where he will not get both checkers off. So if you played this game 36 times and dropped every time, you would lose 36 points. But if you took every time, 26 out of 36 games you would lose 2 points, or a total of 52 points. But 10 times you would win, and that’s 20 points, so your net loss would be 32. So even though it’s a losing battle, you LOSE LESS by taking, in the long run, than by dropping.
So if 25% is the break-even for money games, why did I say the take point could be as low as 22%? The reason is “recube potential.” In the position above, there is no recube potential…you either win or lose on one roll. If your opponent rolls a 1 (other than 1-1) the game is over…if you redouble, he would simply drop.
But in more complex situations, where there is time for you to catch up and get ahead, you might well have a recube and a chance to win 4 points if he takes. For example, take a look at figure 2 below.
In this situation, White doubles. He is ahead 95 pips to 107 pips. According to Snowie’s evaluation (Figure 3 below), Black only wins this game 21.5 percent of the time, but it’s still a take. The reason is that there are many rolls left, and some of the time Black will be in a position to redouble White and win that way, and some of the time White will be forced to take the cube (because it’s over 25 percent) and Black will often win 4 points when that happens.
So that is the basic theory of the cube as applied to the race. Now let’s talk about the race itself. How do you know, when you are playing, whether to take or drop when the pip count is 107-95, or 88-77, or 55-48?
There are many, many theories and formula to apply, and every one must take distribution into account as well as the pip count. So before we get into pure pip count differences, let’s talk about distribution for a minute.
Take a look at figures 4 and 5 below.
In both positions the pip count is 42-42. With White on roll, in Position 4, Snowie will tell you that it is not a double. White does win about 65 percent of the time, but that is not enough to double in this situation…he gets redoubled and loses far too often.
But in Position 5 White wins 73 percent of the time and it is a double (and a take). Clearly, the open 4 point will cost Black some games, in this case, about 8 percent, because he will miss if he rolls one or more 4’s in the first few rolls.
Now take a look at positions 6 below.