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!


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