The proper calculation when using two or more independent events is more complicated. But using converse probability makes things a little easier, as demonstrated in the monster calculation above. Just ask yourself "how likely is this NOT to happen" and then work backwards.

See if you can redo the p4orAbove and p2orAbove calculations above using conditional probability. You should get 75% and 97.2%, respectively. Note: for another stab at describing conditional probability, see "Probability for Game Designers".

Raiding a Land Territory
Roll both dice when attempting a RAID. If you raid a territory that has equal or lower strength then your longship, then you must roll at least 1 axe to succeed. If the territory is higher strength then your longship, then you need at least 2 axes; also, no monsters may be showing.

_{Cymru (Wales) Has a Strength of 4, Mercia has a Strength of 6}

Chance of rolling an Axe, per die:

• pAxe = 2/6 = 33.3%

Chance of rolling a Double Axe, per die:

• pDAxe = 1/6 = 16.7%

Chance of rolling at least one axes' worth, per die:

• pAxeOrBetter = 3/6 = 50.0%

• pNoAxe = 6/6 -- 3/6 = 3/6 = 50.0%

Chance of rolling at least 1 total axe on two dice (use converse probability):

• pNOAXES2DICE = 3/6 * 3/6 = 9/36 = 25%

• p1AXEorMORE = 1 - 25% = 75% < -- Raid success when equal or stronger

Now to the other raid situation (raiding when weaker than the land territory). The chance of rolling at least two Axes on two dice AND no monsters are showing can be calculated different ways:

Method 1 (adding individual probabilities):

pAnswer = chance(exactly 2 axes with no monsters) + chance(exactly 3 axes with no monsters) + chance(exactly 4 axes with no monsters).

The first component is the chance of "exactly 2 axes with no monsters."

• p2AxesNoMonsters = 2/6 * 2/6 + 1/6 * 1/6 + 1/6 * 1/6 = 16.7%

The only combos that satisfy this are when both dice show one Axe, or either die shows a Double Axe but the other die doesn't show Monsters or Axes. So the 2/6*2/6 component is the chance of both dice showing an Axe at the same time; the 1/6*1/6 component is when one die shows a Double Axe and the other die shows the only valid result: a blank (anything else is an axe or a monster, which doesn't count towards p2AxesNoMonsters). This 1/6*1/6 is counted twice because you can have the combo two ways: Double Axe on die 1 and Blank on die 2, or vice-versa.

The other chances are figured similarly:

• p3AxesNoMonsters = 2/6 * 1/6 + 1/6 * 2/6 = 11.1%

• p4Axes = 1/6 * 1/6 = 2.8%

• pAnswer = sum of the above = 30.6%

If none of this method made sense, you're in luck. Brute Force can often overcome what fancy figuring can't.

Method 2 (Brute Force):

Count the actual dice combos and figure probability by doing ratios.

pAnswer = [(number of combos for rolling 2+ axes) - (number of combos of those that has a monster) ]/(number of total combos).

To figure this out, let's go ahead and list all the combos:

Longship Custom Dice Combo Enumeration

• Number of total combos on 2 dice = 36

• Number of combos with 2+ Axes = 15 (shaded green or orange)

• Number of those that has a Monster = 4 (shaded orange)

• pAnswer = (15 - 4) / 36 = 11 / 36 = 30.6%

Casualties while Raiding:
Lose one crew member for every monster rolled during the raid attempt.

_{Blaaargh! (image courtesy Chris Bourassa)}

When Raiding a land territory, you can always lose some crew, regardless of whether you win or lose in the Raid. Every monster you roll results in a crew loss.

We already derived the chance of rolling at least one Monster on two dice earlier. Repeated here for convenience:

• pAtLeastOneMonster = 1 - 4/9 = 5/9 = 55.6%