So I love running predator with HLC, as it gives me a great chance to get 4 hits...but how great is it really?
From playing experience, I'd guess around 80-85% chance of getting all 4 hits (with the 1 reroll version). I'd also be curious to know what it is with a 2 reroll predator, as well as if I had a full target lock and focus combo.
I don't have the numbers handy and I don't have time to run them anew right now, but here's the short version...
With just a focus token and no rerolls, the distribution of successes (that is, hits+crits) on HLC looks like this:
0 hits - 0% (not actually 0, but very small)
1 hit - 5%
2 hits - 21%
3 hits - 42%
4 hits - 32%
With one reroll from Predator, you convert one blank to a hit 75% of the time. That distribution looks like this:
0 hits - 0%
1 hit - 1%
2 hits - 9%
3 hits - 26%
4 hits - 63%
That's compared to full TL and focus, which does this:
0 hits - 0%
1 hit - 0%
2 hits - 2%
3 hits - 21%
4 hits - 77%
(Two rerolls is in between, obviously, but the math is a hair more complex and I'm on a deadline right now.)
Edited by Vorpal SwordI'm also curious how to figure this out using averages. It's a bit odd since you are only re-rolling 1 die out of X.
A single attack die has a 4/8 of hitting, so it averages 0.5 damage. Multiply that by the number of attack dice to get your average number of hits.
A single attack die with a re-roll averages 0.75 hits, because you multiply the chance of triggering the re-roll by not getting a natural hit (0.50) by the chance of getting a hit on the re-roll (0.50) and add the result to the chance of getting a hit naturally (0.50 + 0.25 = 0.75). If you add a focus to that, then change 4/8 with 6/8, so 0.75 + (0.75 x 0.25) = 0.9375 average hits.
So with 4 attack dice and a TL+focus, you will get an average of 3.75 hits, vs 2.0 average hits with no modifiers.
To find out what Predator gives you, I think you would just do 0.75 plus (n-1)x0.50, where n = the number of attack dice. So a HLC with no other actions and Predator would be 0.75+0.50+0.50+0.50=2.25, and with 2 re-rolls it would be 2.5 average damage.
TL and Predator don't do anything with each other, since you can only re-roll a die once per attack. If you have a TL on a ship your attacking, then Predator is pretty much wasted for that attack, unless you are saving the TL for a future attack (at which point Predator will be wasted on that attack).
I don't have the numbers handy and I don't have time to run them anew right now, but here's the short version...
With just a focus token and no rerolls, the distribution of successes (that is, hits+crits) on HLC looks like this:
0 hits - 0% (not actually 0, but very small)
1 hit - 5%
2 hits - 21%
3 hits - 42%
4 hits - 32%
With one reroll from Predator, you convert one blank to a hit 75% of the time. That distribution looks like this:
0 hits - 0%
1 hit - 1%
2 hits - 9%
3 hits - 26%
4 hits - 63%
That's compared to full TL and focus, which does this:
0 hits - 0%
1 hit - 0%
2 hits - 2%
3 hits - 21%
4 hits - 77%
(Two rerolls is in between, obviously, but the math is a hair more complex and I'm on a deadline right now.)
Like you said, not 0%, with TL+Focus, and 4 dice, the odds of getting 0 hits are 65,536 to 1, and the odds of only getting 1 hit are 4,096 to 1.
*sigh*, go ahead, somebody say it...
I don't have the numbers handy and I don't have time to run them anew right now, but here's the short version...
With just a focus token and no rerolls, the distribution of successes (that is, hits+crits) on HLC looks like this:
0 hits - 0% (not actually 0, but very small)
1 hit - 5%
2 hits - 21%
3 hits - 42%
4 hits - 32%
With one reroll from Predator, you convert one blank to a hit 75% of the time. That distribution looks like this:
0 hits - 0%
1 hit - 1%
2 hits - 9%
3 hits - 26%
4 hits - 63%
That's compared to full TL and focus, which does this:
0 hits - 0%
1 hit - 0%
2 hits - 2%
3 hits - 21%
4 hits - 77%
(Two rerolls is in between, obviously, but the math is a hair more complex and I'm on a deadline right now.)
Like you said, not 0%, with TL+Focus, and 4 dice, the odds of getting 0 hits are 65,536 to 1, and the odds of only getting 1 hit are 4,096 to 1.
*sigh*, go ahead, somebody say it...
Never tell me...what to say
For pure offense TL is probably better but being able to focus and still get a re-roll offers some flexibility as you may get to save that focus for defence if you roll well.
Predator is not always the best option but it is always a good one.
Here's an older website, but it has 1 reroll (labeled as Howlrunner) so you can plug numbers in directly and get answers, at least up to 4 attack dice.
I'm also curious how to figure this out using averages. It's a bit odd since you are only re-rolling 1 die out of X.
The short version is, you don't. Because you may reroll a die and may not--that is, because whether or not I reroll Die #4 depends on the values of dice #1-3--the dice are no longer independent of one another. That, in turn, means that the average of the set is no longer the sum of the averages of each individual die.
To find out what Predator gives you, I think you would just do 0.75 plus (n-1)x0.50, where n = the number of attack dice. So a HLC with no other actions and Predator would be 0.75+0.50+0.50+0.50=2.25, and with 2 re-rolls it would be 2.5 average damage.
Once you've found the distribution, though, it's easy enough to compute the mean. With no focus and one reroll, the average is 2.47; with two rerolls, the average is 2.88. With a focus and one reroll, the average is 3.51; with a focus and two rerolls, the average is 3.79 (and you finally hit the OP's estimated 80-85% chance of getting 4 hit results, with 83.1%).
TL and Predator don't do anything with each other, since you can only re-roll a die once per attack. If you have a TL on a ship your attacking, then Predator is pretty much wasted for that attack, unless you are saving the TL for a future attack (at which point Predator will be wasted on that attack).
Edited by Vorpal Sword