## Saturday, 2 February 2013

### Probability for wargamers 8 - +1 vs reroll

It's one of the rule-writers' common ways of making weapons in Warhammer-like d6 systems different. Some weapons get +1 to hit, some get a reroll. Which is better though?

Interesting question, and with the amount of stuff we've worked out in previous posts, not that hard.

With a target number of four, for example:

• Your normal odds are 3 in 6, or 50%.
• With a +1, obviously, they become 4 in 6, or 66.7%.
• For the reroll, you have a 50% chance of succeeding on the first attempt, plus odds of (chance to miss * chance to hit a second time), i.e. 50% + (50% of 50%). Which makes 75%. Clearly the reroll's the better bet.

I won't work out the details for other target numbers: here's the table:
 Normal +1 to hit Re-roll misses 3 66.67% 83.33% 88.89% 4 50.00% 66.67% 75.00% 5 33.33% 50.00% 55.56% 6 16.67% 33.33% 30.56%

OK, so it looks like the re-roll's a better bet unless your target is hard to hit.

Another favourite of designers is the '+1 strength' modifier on the wound roll. Let's look at that: typically, for WAB, equal STR means wounding on a 4.
 Hit+Wound (normal) Hit+Wound (norm/+1STR) Hit+Wound (reroll) 3 33.33% 44.44% 44.44% 4 25.00% 33.33% 37.50% 5 16.67% 22.22% 27.78% 6 8.33% 11.11% 15.28%

Again, interesting, The re-roll's still better, but less so.

Moral of the story? Given the choice? Take the weapon that gives the re-roll!