The complete reference for every distance from 1 to 24. Know exactly which dice combinations threaten your blots, how blocked points change the math, and how to turn probability into better decisions at the board.
There are 36 possible dice combinations on any roll (6 × 6). The table below shows, for every distance from 1 to 24, how many of those 36 combinations can reach a blot — assuming no intervening blocked points.
| Distance | Combinations | Probability | Which Rolls Hit |
|---|---|---|---|
| Direct shots (1–6) — single-die range | |||
| 1 | 11 | 30.6% | 1-1, 1-2, 1-3, 1-4, 1-5, 1-6 (and reverses) |
| 2 | 12 | 33.3% | 2-x (any), 1-1 |
| 3 | 14 | 38.9% | 3-x (any), 1-2, 2-1, 1-1 |
| 4 | 15 | 41.7% | 4-x (any), 1-3, 3-1, 2-2 |
| 5 | 15 | 41.7% | 5-x (any), 1-4, 4-1, 2-3, 3-2 |
| 6 | 17 | 47.2% | 6-x (any), 1-5, 5-1, 2-4, 4-2, 3-3, 2-2 |
| Indirect shots (7–12) — require both dice or doubles | |||
| 7 | 6 | 16.7% | 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 |
| 8 | 6 | 16.7% | 2-6, 6-2, 3-5, 5-3, 4-4 |
| 9 | 5 | 13.9% | 3-6, 6-3, 4-5, 5-4, 3-3 |
| 10 | 3 | 8.3% | 4-6, 6-4, 5-5 |
| 11 | 2 | 5.6% | 5-6, 6-5 |
| 12 | 3 | 8.3% | 6-6, 4-4 (via 4+4+4), 3-3 (via 3+3+3+3)… but standard: 6-6 |
| Long-range (13–24) — doubles only | |||
| 15 | 1 | 2.8% | 5-5 |
| 16 | 1 | 2.8% | 4-4 |
| 18 | 1 | 2.8% | 6-6 |
| 20 | 1 | 2.8% | 5-5 |
| 24 | 1 | 2.8% | 6-6 |
There's a massive safety cliff at distance 7. At distance 6, you're hit 47.2% of the time. At distance 7, it drops to 16.7% — less than a third as dangerous. When you must leave a blot, put it beyond the 6-point cliff whenever possible.
A direct shot is any blot within 6 pips of an opponent checker — reachable by a single die. Direct shots are always dangerous, but some distances are worse than others:
Distance 6 is the worst. Every die face contains a 6, so 6-anything hits. Add combinations like 4-2, 5-1, 3-3, and 2-2, and you reach 17 out of 36 combinations — nearly half. Never leave a blot exactly 6 points from an opponent if you can avoid it.
Distance 1 is the safest direct shot (still 30.6%). Only rolls containing a 1 hit. But because 11 of 36 combinations include at least one 1, it's still dangerous — almost 1 in 3.
Distances 4 and 5 are equally dangerous (15/36 = 41.7%). Both benefit from double-2s (reaching 4) and multiple combination rolls, but distance 5 cannot be hit by a single die lower than 5, so it feels safer than it is — the indirect combinations make up the gap.
Play: blot on midpoint after 6-5 lover's leap — how many rolls hit?Beyond distance 6, only combination shots (using both dice together) or doubles can hit. The probability drops dramatically:
Distance 7: 6 combinations (16.7%). These are all the ways to make 7 from two dice: 1-6, 2-5, 3-4 and their reverses. No doubles reach 7, which is why it's the first truly "safe" distance.
Distance 8: Also 6 combinations (16.7%), but includes double-4s. The combinations are 2-6, 3-5, and 4-4.
Distance 9: 5 combinations (13.9%). Includes double-3s (3+3+3). Combinations: 3-6, 4-5, 3-3.
Distance 10: Only 3 combinations (8.3%) — 4-6, 6-4, and 5-5. Very safe.
Distance 11: The safest indirect distance — only 5-6 and 6-5 (5.6%). If you must leave a blot at indirect range, 11 away is ideal.
Distance 12: Slightly more dangerous than 11 because double-6s reach here (8.3%). Never forget double-6s — they're the most common source of surprise hits at long range.
Beyond 12, only doubles can hit, and each double covers specific distances:
Each of these is a 1-in-36 chance (2.8%). Rare, but they happen — and when they do, the positional impact is often devastating because neither player expected the hit. The practical lesson: don't expose a checker 18 or 24 away and assume it's safe. Double-6s exist.
Double-6s reach 6, 12, 18, and 24 pips — the full length of the board. A checker on the 24-point can be hit from the opponent's 1-point by double-6s. It only happens 2.8% of the time, but many games have been decided by exactly this roll.
The chart above assumes an open path — no intervening points blocked by your opponent. In real games, blocked points dramatically reduce indirect shot probabilities.
The rule: if a combination shot must pass through a blocked point (one held by 2+ opponent checkers), that combination is removed from the hit count. You cannot land on a blocked point, so you cannot use it as a stepping stone.
Example: Your blot is 8 points from an opponent checker. Normally, 6 combinations hit (2-6, 6-2, 3-5, 5-3, 4-4). But if the intervening 6-point is blocked, the 6-2 combination is gone — your opponent can't play the 6 first because it lands on a blocked point. This drops the hit count from 6 to 5 (13.9% instead of 16.7%).
A strong prime blocks entire swaths of indirect shots. If you hold points 5, 6, 7, and 8, an opponent checker on your 1-point cannot be hit by any combination using those numbers as intermediate steps. The practical hit probability can drop to near zero behind a well-constructed prime.
Play: six-prime — how many rolls escape?When counting how many rolls hit your blot, mentally walk through each combination and check whether it passes through a blocked point. The advertised probability from the chart is always the maximum — real-game probabilities are often lower because of intervening blocks.
When you leave two or more blots exposed, the risk compounds — but not by simple addition. The probability of at least one blot being hit is:
P(at least one hit) = P(A) + P(B) − P(both hit)
If blot A can be hit by 11 rolls and blot B by 6 rolls, and 2 of those rolls hit both, the chance of at least one hit is: (11 + 6 − 2) / 36 = 15/36 = 41.7%.
The key strategic implication: leaving two blots at the same distance duplicates your opponent's good numbers, keeping compound risk lower. Two blots both 4 away means your opponent needs 4s to hit either one — the same rolls threaten both. But blots at distances 3 and 5 are threatened by different numbers, maximising the total combinations that hit at least one.
Play: two exposed blots — count the dangerThis is the foundation of duplication strategy — deliberately arranging your blots so your opponent's good numbers overlap. Read more in the full strategy guide.
Memorising the chart is useful, but the real skill is applying it in context. Here's the decision framework:
Leaving a blot is worth the risk when the positional gain outweighs the expected cost of being hit. Slotting your 5-point (leaving a blot there) is a classic example: the 5-point is so valuable that making it next turn justifies the ~30% chance of being hit.
If you must leave a blot, prefer distances where: (1) fewer combinations hit, (2) intervening points are blocked, and (3) being hit is least costly — e.g., near your own home board where you can re-enter easily, rather than deep in opponent territory.
Avoid voluntary blots when: you're ahead in the race (no need for contact), your opponent's home board is strong (being hit is very costly), or you're bearing off (any hit sends you back 20+ pips).
Risk is relative to reward. A 47% chance of being hit is perfectly acceptable if making the point wins the game. A 5% chance is too high if you're already winning the race and don't need the contact. Always weigh probability against positional context.