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!