In classic Piquet virtually all die rolls are opposed. That is to say that both player's roll a dice and the result is determined by the difference in the dice. In a morale challenge roll, for example, the attacker rolls a dice against the defenders dice and there are four possible outcomes:
- The defender beats the challenge by rolling higher.
- The defender fails the challenge by rolling the same or less (disordered).
- The defender fails the challenge by rolling less and his score is doubled (routed).
- The defender fails the challenge by rolling less and his score is tripled (routed unralliably).
Last night, following the Wednesday war gaming session, I said to the guys as they left "You know there is more chance of rolling higher and tripling than there is of doubling." Both Graham and Peter were unconvinced, in fact I think they thought I'd gone a bit crazy. I thought I'd worked this all out in the past and discovered it to be true but, with these guys being pretty good with maths, I started to doubt myself. Surely, it is easier to double?
When I went to bed I got to work with the Sumerian abacus. Stop tittering. Hold your hand palm up. Stop tittering. Take the thumb of that hand and place it on the first bone of your index finger, that is 1. Moving up the next bone is 2. Moving up each finger and across you can count to twelve on one hand (I've heard this is why the dozen came about). Using the other hand to keep track of dozens you can count to 144, though I work left to right on both hands. It's useful for keeping a track when doing this kind of thing in your head.
Well, lets look at cases. D8 Vs D8.
- There twenty ways to beat the defender without doubling or tripling.
- There are seven ways to double the defender.
- There are nine ways to triple the defender.
This all comes about because of the double / triple quirk on low defender rolls. In the rules, triples always take precedence over doubles, so when the defender rolls a one, there is only one way he can be doubled - the attacker rolls a two - but there are six ways the defender can be tripled on a one - the attacker rolls three, four, five, six, seven, or eight.
Now I haven't worked out all the combinations of opposed dice, but a I'm fairly sure a similar thing happens when any attacking dice is rolled Vs D8. It's quirky.