Taking Risks 
Kit Woolsey Many readers will remember a television commercial for oil filters a few years ago. The punch line of the commercial was, "You can pay me now, or pay me later," which meant that the consumer had a choice of paying a small amount for an oil filter now, or a large amount for a ruined engine later.
It would not be surprising if the writer of that commercial were a backgammon player. The problem of whether to pay now or pay later — that is, whether to take a chance now or play safe for the roll at the possible cost of taking a greater risk later — recurs constantly in backgammon.
Television Ad
"You can pay me now ...
... or you can pay me later."
In the early stages of the game, when the opponent hasn't built up his board, the cost of being hit is small, so it is usually correct to "pay me now." For example: on an opening 21 roll most experts will slot the five point, since the cost of being hit now is much smaller than the cost of not owning the five point at a later stage of the game.
It is with bearing in positions, when getting hit will cost the game, that the most crucial paymenow or paymelater decisions arise. A player must often decide whether to take a risk on the current roll, with relative safety remaining if he gets away with it, or to play safer for now but leave a more awkward position with the likelihood of leaving later shots. Many good players misevaluate this type of position. They forget that the potential later shot still has to be hit to cost, so they tend to pay now when it is safer to pay later.
If we assume that getting hit loses and escaping wins, we must calculate for a given play the probability of getting hit either now or later. This figure is: probability of being hit on this roll + probability of being missed on this roll × probability of leaving shots(s) on future rolls × probability of future shot(s) being hit.

Example 1. Black to play 54 
Suppose we play safe, playing the number in our inner board. Let us assume we will have, on average, two rolls before the eight point must be cleared (this assumption is on the low side), and during this time we might roll double 2, 3, 4, or 5 for safety. (I realize that 22 and 33 are not completely safe, but I ignore 11, which is helpful as a compensating factor. I'm just trying to get an approximation, so I'm keeping the assumptions simple.)
So for each of the two rolls we have 8/9 probability of not safetying, or 64/81 chance of still being on the midpoint when the eight point is cleared. Once the eight point is cleared we have ten bad rolls and four good rolls, so the probability of leaving a shot is 10/14, and it is a seventeennumber shot, so the probability of being hit is 17/36. Consequently if we "pay me later," the probability of being hit is approximately 64/81 × 10/14 × 17/36 = .267, so this is the safer play. I realize that there are several things I haven't taken into account, but I tried to make my simplifying assumptions equally favorable to both sides to make a rough calculation possible.

Example 2. Black to play 54 

Example 3. Black to play 65. 
I don't think so. Even if we assume that if Magriel doesn't ever get hit he will win, which is clearly not a valid assumption in this position, the safer play (for now) would have to leave a shot and have it hit at least 4/25 more often than Magriel's play to compensate for the immediate danger. This would involve leaving a direct shot almost 40% more often, which seems pretty high to me.
Look at it as a proposition in the following form: Would you take Magriel's play and play it playvs.play twentyfive times each way on the assumption that the initial shot was missed, but spot your opponent four wins? This is essentially what Magriel's play does.
Now, when is it correct to "pay me now"? If your opponent hasn't built up his board, it may be correct in any of the previous positions. If his board is built up it is almost never correct to leave an unnecessary direct shot, unless doing so otherwise improves your winning or gammon chances (i.e., there is more involved than just safety). However, it may be correct to leave a few extra shots for future safety, if playing safer now is likely to lead to later problems.

Example 4. Black to play 62. 

Example 5. Black to play 42. 
The concept may apply to potential shots as well as immediate shots. Here, it is often correct to pay now. Consider Example 6.

Example 6. Black to play 62. 