I was just doing some math over the interaction of black dice with Ordnance Experts, and I found a interesting result.

For 1 black die:

Rerolling only blanks: E(damage of first roll) + E(damage of reroll) = (0.75 * (8/6)) + (0.25 * 1) = 1.25

Rerolling blanks and hits: E(damage of first roll) + E(damage of reroll) = (0.25 * (4/2)) + (0.75 * 1) = 1.25

Visualisation: The probability of the die showing a non-reroll face(hit and hit/crit in the first scenario) and the expected damage over the number of faces, plus the probability of the die showing a face to reroll and the expected damage from the reroll(that is, 1).

Am I doing anything wrong?

Does that mean it is statistically the same over the long term whether one rerolls their hits or not?(with rerolling blanks and hits scenario swingier but with same expectation). This will help speed up decision-making in play with OE around.

Conclusion: I should keep my hits for more stable damage, unless I have black crit upgrades or I need to get that last damage in.

If you fish for a crit, you reroll everything: the more die the better chances of rolling one. The rest is personal preferance and/or situational: If you need 1 point extra dmg to finish off a ship and not waste another attack on the ship, It might worth risking. You know, by rerolling a hit you end up 25% of the times Better, 25% worse, 50% same on average. I tend to keep hits if its an unharmed ship, id feel worse if i rolled a blank than be happy for a crit(this is the personal preferance part).

Sure, think about it this way- there's two blanks, and two crits. So naturally your odds of improving a hit are the same as your odds of making it worse.

As mentioned, though, crits change the math a bit. The first crit is worth slightly more than two damage , because it also allows you to activate a crit effect (default or otherwise). (To make math easy you could just take the odds of a third damage via Structurals, but that's getting into needless mathhammer.)

Therefore, rerolling the entire pool if you lack a crit is expected-value positive . The odds of blanks and crits are the same, but crits are slightly better than blanks are worse. Even though only the first crit matters (unless you're using some sort of spend effect), it still nudges the EV past the line. So, mathematically, you should always fish for crits, if you have an effect to activate that will go through. (If you're not hitting hull or they're Containing, then it's a wash [except insofar as you can burn their Contain, wherein it becomes EV positive again].)

However , I personally find that rerolling a bunch of hits into blanks feels a lot worse than rerolling into a bunch of crits feels good, and that emotional variable is not insignificant or trivial. A small EV gain isn't worth feeling gutted by a trash roll, if that gutting causes you to tilt or just to be unhappy with the game. (It's a game!)

To summarize always fish for crits; unless you don't like to, in which case don't.

.

Also if you do 6 damage from say 4 black dice from Demolisher and you know the enemy will brace your attack you might as well reroll a single black hit as if you roll blank you still do 3 damage after bracing and a hit/crit will net you more.

Attempting to figure this out with math is useless. Sacrifice a chicken to the dice gods and pray for their favor, and you'll be ok.....

on on a more serious note, I hate math, but here's my take. Demo with OE and APT, no CF dial, so four dice broadside. Assume two blanks, two hits. The blanks are auto reroll (duh) and so are the two hits ( because I need those crits). If I had rolled instead hit, hit/crit and blanks, I would only reroll the blanks. Math is not needed here....lol.

More math:

For 1 Black Dice:

Re-rolling only Blanks: 31.25% chance of Hit-Crit. 6.25% chance of Blank

Re-rolling Blanks and Hits: 43.75% chance of Hit-Crit. 18.75% chance of Blank

Interpret that as you please.

Rerolling everything but crits:

Blank: 6.25 (blank+blank) +12.5 (hit+blank) = 18.75%

Hit: 12.5 (blank+hit) + 25 (hit+hit) = 37.5%

Crit: 25 (crit) + 6.25 (blank+crit) + 12.5 (hit+crit) = 43.75%

Rerolling only blanks:

Blank 6.25% (blank+blank)

Hit: 50 (hit) + 12.5 (blank+hit) = 62.5%

Crit: 25 (crit) + 6.25 (blank+crit) = 31.25%

So rerolling hard you decrease the chances of getting something a bit (around -13%) but increase the chances of getting crits the same points and those crits came with a hit so the difference as average damage is zero.

Applying this to a real case is easy:

If you want to put out damage, as the average is the same keep the hits.

If you want nasty effects reroll hard, at the end "you are not loosing damage".

If loosing the hit is worse than getting the crit (let's say you are just farming points from Precision Strike against an almost dead ship). Don't reroll unless you are at a win or loose situation.

After BBC nerf the only situation where it matters is stacking OE with Vader, CF token and TFO. The CF token is just 1 die and TFO are 2 so you can calculate with other pieces like rerolled damage against a brace, or maybe a rerolled blank rerollable. Not a big deal. Only Vader would bring a real dilemma about it.

3 hours ago, Mad Cat said:

Also if you do 6 damage from say 4 black dice from Demolisher and you know the enemy will brace your attack you might as well reroll a single black hit as if you roll blank you still do 3 damage after bracing and a hit/crit will net you more.

Nice. I forgot about this kink in the brace token. Good one.

If you have a crit effect that didn't proc or will get the crit through and rolled no crits, reroll aggressively; otherwise, it's personal preference with I think a slight edge to conservative (0+6 damage is harder to mitigate than 3+3, so consistency wins out).

More interesting is how the calculus changes with multiple rerolls, especially reds...

Another saturday morning with no $#@king article....

37 minutes ago, Ophion said:

Another saturday morning with no $#@king article....

Where are you that it is Saturday*? It's still Friday in FFG HQ, and that's the timezone that counts.

*If you don't mind me asking, of course. It's more a rhetorical question though.

Edit 2: Also, you may be in the wrong thread here. . .

It also matters tremendously what the defensive options are on the target ship. For example: if the enemy can force me to reroll multiple dice and in attacking with critical effects, then it is necessary to get as many critical hits as possible to maximize the number of chances that a defensive reroll gets another critical result.

2 hours ago, GhostofNobodyInParticular said:

Where are you that it is Saturday*? It's still Friday in FFG HQ, and that's the timezone that counts.

*If you don't mind me asking, of course. It's more a rhetorical question though.

Edit 2: Also, you may be in the wrong thread here. . .

Ha. Complete fail!

Australia btw.

Just a regular hit is the most common. So you want to reroll a hit into a hit crit trying to squeeze out that last bit damage.

Well just like a hit is 50% on the reroll you have the same odds of not changing. But on changing well half of the other side is those hit crits you want and the other half is blanks which you don't want.

An Old saying goes a bird in hand is worth 2 in the bush. If you have the hit you have a bird in the hand. IF you want to reroll anything reroll blue dice. At least you will be able to take out a token assuming you are not shooting at squadrons.

Statistically the mean value is the same, however rerolling black hits leads to a higher variance and its very situational to decide if that higher variance will harm you or help you. Setting brace issue (as well as crit triggered effects) aside, the important questions are: what is a chance of killing the ship outright with a good roll and will a bad roll harm your chances to kill this ship later (for example, if you expect to deal 4-6 damage per attack, it doesn't really matter that previous attack left the target at 4 hp as opposed to 2). Keep in mind that the amount of variance can be controlled by selecting the number of single-hit dice to reroll (it doesnt have to be all or nothing affair).