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Way back when I was in high school and college, I was great at math. One of my strongest subjects, right behind English. But that was a long time ago, and know I just plain suck at it. So I need a little bit of help with percentages.
I'm looking to compare two different options for some characters. What I need to know is which of the two options has better returns -
1) Wounding on a number we'll call "X" (doesn't matter the number; all toughnesses apply), or;
2) Wounding on a roll of X+1, but with rerolls.
So basically, one weapon has +1 strength, but the other allows rerolls. Which weapon would be better overall, not taking into account like extremely high toughnesses or extremely low toughnesses. Would the total number of attacks come into play? (Assume four attacks for each weapon)
Option 2 is statistically better, I number crunched this sort of thing a long time ago for BS4 versus BS3 twin-linked.
I won't bamboozle you with figures and numbers, but basically BS3 twin-linked came out as BS4.5 (sort of). It's basically the same principle.
Let's say X is 4.
1) Wounding on 4+. You have a 50% chance of wounding. So, with 4 hits, in theory, 2 will wound.
2) Wounding on a 5+. You have a 33.333332% chance of wounding. So, with 4 hits, in theory, 1 will wound. However, you may re-roll the other failing 66.66667%. So, you are re-rolling 66.66667% with a success estimate of 33.33332%. 66.66667% - 33.33332% = 33.33335%. So re-rolling 3 failed wounds in theory should roll 1 more successful hit.
So, from a mathematical point of view, both will generate the same amount of hits. However, I'd rather have a higher Strength value than having re-rolls, as I am more likely to be able to instant kill some targets.
It's up to you, but I'd choose higher Strength.
You two just confirmed pretty much what I suspected. I was able to figure out four okay, since those are simple fractional numbers to work with, but started getting messed up with the 5's versus 6+/6+ , and so forth. It comes out almost the same, if I did my math right, with the rerolls edging just slightly ahead.
As for the Instant Death thing, the scenario I'm using this for is strength four versus strength five, so not really an issue. If it was strength five versus strength six, I would most likely go for the higher strength.
Sounds like it's not a big enough deal to really change all my characters around for. Thanks guys!
Glad to help!
As you said, there's no point changing your characters around for such a small difference.
Heh, it depends on the value of x...
If x is less than or equal to 4 (ie wounding on 4's or 5's with re-roll), it's better to take the re-roll. If x=5 then the wounding on x is better, if x = 6, then the re-roll is better, since it's either wounding on 6 or wounding on 6 with re-roll.
Simple no?
x-----on x-----------on x+1
1-----4---------------3.888888889
2-----3.33------------3.555555556
3-----2.66666-------3
4-----2---------------2.222222222
5-----1.33333-------1.222222222
6-----0.66666-------1.222222222 (wounding on 6 vs wonding on 6 with re-roll)
This is the average number of wounds you would cause, using the law of large numbers. Not always correct I know, but easiest to understand.
Last edited by dymew; September 25th, 2005 at 20:28.
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