Entering from the barExpert
When a checker is on the bar, nothing else can move until it enters. How often it enters is not a feel or a guess, it is a short calculation, and knowing the numbers changes how you evaluate every attacking position.
How entering works
A checker on the bar re-enters on the point matching either die, counting from the far end of your opponent's home board. If both numbers land on points your opponent has made, the roll is dead and you lose the entire turn.
The arithmetic
You fail to enter only when both dice land on blocked points. With n of the six home board points made, the chance of missing is (n/6) squared. That single formula produces the whole table below, and it is worth committing to memory because the jumps between rows are not intuitive.
Where the cliff is
Notice the shape. Going from two made points to three costs the player on the bar relatively little. Going from four to five is brutal. This is why attacking positions are so often decided by whether you can make that fifth point: the marginal value of each home board point rises steeply, it does not rise evenly.
What it means in play
Against a two point board, hitting is cheap and the risk of a return hit is high, so attacking loosely is usually fine. Against a four or five point board, being hit is close to catastrophic, which makes the same loose attack an enormous gamble for your opponent and a strong play for you.
The numbers, computed
Every figure below is enumerated over all 36 ordered outcomes of two dice, not quoted from a table. Shot counts assume the intervening points are open.
| Situation | Rolls that work | Chance |
|---|---|---|
| Entering from the bar against 1 made point | 35 of 36 | 97.2% |
| Entering from the bar against 2 made points | 32 of 36 | 88.9% |
| Entering from the bar against 3 made points | 27 of 36 | 75.0% |
| Entering from the bar against 4 made points | 20 of 36 | 55.6% |
| Entering from the bar against 5 made points | 11 of 36 | 30.6% |
| Entering from the bar against 6 made points | 0 of 36 | 0.0% |
Entering from the bar against 1 made point: Both dice get a chance to enter, which is why the odds stay high early.
Entering from the bar against 2 made points: Both dice get a chance to enter, which is why the odds stay high early.
Entering from the bar against 3 made points: Both dice get a chance to enter, which is why the odds stay high early.
Entering from the bar against 4 made points: Both dice get a chance to enter, which is why the odds stay high early.
Entering from the bar against 5 made points: This is why a five-point board ends games.
Entering from the bar against 6 made points: This is why a five-point board ends games.
What most players get wrong
A bigger home board is better in a straight line, so each point I make helps about the same amount.
The value curve is steep, not straight. Going from one made point to two costs your opponent about 8 percentage points of entry chance. Going from four to five costs them 25. Players who treat home board points as equally valuable consistently under-invest in exactly the point that would have mattered most.
Play a rated game and every decision gets reviewed afterwards against the best move available. The dice are committed before you roll and checkable after, so the number you end up with is a measure of you, not of luck.
Play a rated game freeFrequently asked questions
What is the chance of entering from the bar?
It depends only on how many home board points your opponent has made. With n points made, you fail to enter with probability (n/6) squared, so a three point board lets you in 75 percent of the time and a five point board only 30.6 percent.
Can I move other checkers while I am on the bar?
No. A checker on the bar must enter before any other checker can move. If you cannot enter, you forfeit the entire turn.
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