I've been playing BCC enhanced bombers the 'safe' way, that is, to take the reroll only when I get blanks. But after relooking at the math again I realised it might be better to take that reroll for black dice more often:

Expected dmg when only blanks rerolled = Expected dmg of black die + chance to reroll * expected dmg of reroll

= 1 + 0.25*1 = 1.25

Expected dmg when single hits and blanks rerolled = Expected dmg of black die if single hits count as blanks + chance to reroll * expected dmg of reroll

= 0.5 + 0.75*1 = 1.25

so it's the same expected damage whether one rerolls for the crits or plays safe, though playing it safe might have lower variance. But when it comes to generating crits:

Chance to crit when only blanks rerolled = 0.25 + 0.25*0.25 = 0.3125 --> 31.25%

Chance to crit when single hits and blanks rerolled = 0.25 + 0.75*0.25 = 0.4375 --> 43 .75%

so it's actually better to try for the crits especially if one are already hitting hull, or there is a crit ability like Norra's in effect.

blues and reds do less damage if one tries to push for rerolls, so I've left that out coz it's not likely one wants to game for crits at the cost of damage. I think?

What do you think? Happy Thursday

With a black dice bomber I would usually stick on a single hit and not chance the symetrical reroll to convert that into hit/crit or (equally possibly) get a blank. The decision however will be influenced by a number of factors.

• Nora close by, as you say, if the target has reasonable shields then the extra reward of a crit tips the balance infavour of taking the risk.
• Chance of doing a crit. The enemy has no shields for this attack and is unable to redirect or contain it. Dodonna makes this even more worthwhile.
• Enemy has a contain, brace or redirect but you want to put pressure on these defence tokens so that other attacks later in the turn will benefit.
• Enemy is near death and 2 points of damage (and maybe a structural damage crit) would get you a kill but one point wouldn't.

I recently played a game with BCC and Dash Rendar who when attacking a ship now gets 2 rerolls. I found myself usually rerolling the single hit the first time but only using the second reroll if that was a blank result.

With blue bomber dice you only get the crit benefit and don't do extra damage so the rewards don't really compensate for the risks. Red dice are very fickle so I nearly always stick with a single hit result.

This is the same math I use when looking at rerolls to trigger ACM or APT.

I will reroll hits if I’m fishing for crit effect and did not get one initially.

If I already have the crit effect On a die, then I don’t reroll hits. I aim for consistency.

I was watching an older worlds clip and a guy had 2 of these. Did it get an errata?

6 minutes ago, TasteTheRainbow said:

I was watching an older worlds clip and a guy had 2 of these. Did it get an errata?

Yes, BCC rerolls used to stack. Now you can only benefit from one.

I feel like crit fishing is better when you have a larger number of bombers activating at once, or hitting the same target in the squadron phase. Because if I toss 5 bombers at you and can get 5 hit-crits before shooting that's much more powerful than one or two, even if a bomber or two reroll into blank. Similarly in the squadron phase any bomber you can get onto a target has a chance of pressuing the alreay exhausted defence tokens provided you shot the target in the ship phase.

Otherwise I see it as a do I need to kill you, or to hurt you. If my VSD has a double arc at close and sending in 5 bombers to soften the target up that's probably not the time to fish. The Quasar trying to save itself probably needs the damage to not get killed.

See it the other way around:

If you reroll a blank, your chance for another blank is only 6,25%. This means, you have a 93,75% chance for at least one damage, if you only reroll on a blank.
But if you reroll a hit on the first roll, your chance for a blank on the second goes up to 18,75%. This means you chance for at least one damage is going down to 81,25%.

You are ending 3 times as often with no damage at all. And this is not worth it.

5 hours ago, Tokra said:

See it the other way around:

If you reroll a blank, your chance for another blank is only 6,25%. This means, you have a 93,75% chance for at least one damage, if you only reroll on a blank.
But if you reroll a hit on the first roll, your chance for a blank on the second goes up to 18,75%. This means you chance for at least one damage is going down to 81,25%.

You are ending 3 times as often with no damage at all. And this is not worth it.

A previous outcome has no effect on the probability of the next outcome here. If you flip a coin and get heads 5 times in a row, you still have a 50% chance to get heads on the next flip.

6 hours ago, Tokra said:

If you reroll a blank, your chance for another blank is only 6,25%. This means, you have a 93,75% chance for at least one damage, if you only reroll on a blank.
But if you reroll a hit on the first roll, your chance for a blank on the second goes up to 18,75%. This means you chance for at least one damage is going down to 81,25%.

No. If you reroll a blank black die, you have a 1/4 (25%) chance of rolling a blank. Not a 6.25%. As @The Jabbawookie mentioned, the second roll of the die is independent of the first roll. No matter what you rolled on previous rolls, rolling a black die always has a 1/4 chance of rolling a blank, a 1/4 chance of rolling a hit + crit and a 1/2 chance of rolling a single hit.

1 hour ago, The Jabbawookie said:

A previous outcome has no effect on the probability of the next outcome here. If you flip a coin and get heads 5 times in a row, you still have a 50% chance to get heads on the next flip.

Yes. for the next flip. But we are not talking about the next flip, we are talking about the chance that you get head 5 times in a row, and not what you can get on the 6th flip.

40 minutes ago, LordCola said:

No. If you reroll a blank black die, you have a 1/4 (25%) chance of rolling a blank. Not a 6.25%. As @The Jabbawookie mentioned, the second roll of the die is independent of the first roll. No matter what you rolled on previous rolls, rolling a black die always has a 1/4 chance of rolling a blank, a 1/4 chance of rolling a hit + crit and a 1/2 chance of rolling a single hit.

Again, it does not matter what the chance is for the next roll. I talk about the chance for no damage with the reroll.

You are both ignoring the first roll and just watch the second roll. But this first roll had a 25% on a result that you want and would keep. And you have to add in this calculation.

If you roll a black die, you have a 25% chance for a blank and a 50% chance for a hit.

Now you reroll this black die.
When you reroll on a blank, you have again a 25% chance for a blank. This gives 0.25*0.25 for no damage. This is 6.25% chance for no damage.
But if you reroll the hits as well, you increase the chance for no damage to 0.75 (blank and hit) * 0.25 (blank). You tripple the chance for no damage. Because the hit, that you had earlier, can suddenly become a blank, changing your 1 damage to 0 damage.

We can as well check the chance for the hit+crit for both cases.
In the first case (reroll only on the blank) you have a 31.25% chance for a hit+crit. If you reroll the hit on the first roll as well, you increase the chance to 43.75%.
The difference is the same 12.5% But the no damage is increasing by the factor 3 (from 6.25% to 18.75%). And the hit+crit is only increasing by a factor of 1.4 (from 31.25% to 43.75%).
Compared to the risk increase of no damage, this little increase in more damage is not really worth it (imo).

On 10/10/2019 at 3:46 AM, Mad Cat said:

• Enemy is near death and 2 points of damage (and maybe a structural damage crit) would get you a kill but one point wouldn't.

That's seriously the ONLY time I re-roll the hit, even on black dice. I've done hit->blank far too many times to count. The ONLY time I re-roll the hit if it's a kill-shot to get both and a single hit isn't, and still only when that matters very much for that moment in the game (IE., last shot of round 6, or maybe my own ship is nearly dead and won't survive the activation of the nearly-dead enemy ship I'm shooting at, etc). That is, situations where one hit that doesn't kill the ship is exactly as good to me as a blank dice, THEN I'll re-roll it (and get the expected blank and roll my eyes, but whatever I'm no worse off).

29 minutes ago, Tokra said:

Yes. for the next flip. But we are not talking about the next flip, we are talking about the chance that you get head 5 times in a row, and not what you can get on the 6th flip.

Again, it does not matter what the chance is for the next roll. I talk about the chance for no damage with the reroll.

You are both ignoring the first roll and just watch the second roll. But this first roll had a 25% on a result that you want and would keep. And you have to add in this calculation.

If you roll a black die, you have a 25% chance for a blank and a 50% chance for a hit.

Now you reroll this black die.
When you reroll on a blank, you have again a 25% chance for a blank. This gives 0.25*0.25 for no damage. This is 6.25% chance for no damage.
But if you reroll the hits as well, you increase the chance for no damage to 0.75 (blank and hit) * 0.25 (blank). You tripple the chance for no damage. Because the hit, that you had earlier, can suddenly become a blank, changing your 1 damage to 0 damage.

We can as well check the chance for the hit+crit for both cases.
In the first case (reroll only on the blank) you have a 31.25% chance for a hit+crit. If you reroll the hit on the first roll as well, you increase the chance to 43.75%.
The difference is the same 12.5% But the no damage is increasing by the factor 3 (from 6.25% to 18.75%). And the hit+crit is only increasing by a factor of 1.4 (from 31.25% to 43.75%).
Compared to the risk increase of no damage, this little increase in more damage is not really worth it (imo).

Sure, let’s look at overall odds. The ratio of the increase in likelihood for blanks and doubles is only another way of saying you’re losing consistency. The fact that it’s a flat increase on both ends means the average damage is exactly worth it.

Are there other factors, like the objective, the target’s shields, how much the target needs to die, Norra, Luke or Keyan shooting, etc? Yes. But in a vacuum you will be happier more and sadder more, and you will flip more crits, and that’s about it.

We have two different events here.

1) Probability for no damage with a reroll. The probability for this event is indeed (1/4)²

2) Probability of no damage following a roll with no damage. This probability is still 1/4

31 minutes ago, Tokra said:

When you reroll on a blank, you have again a 25% chance for a blank. This gives 0.25*0.25 for no damage. This is 6.25% chance for no damage.

No, what you describe is event 2. The probability that the second roll of the die (after initially rolling a blank) is a blank again is still 1/4.

31 minutes ago, Tokra said:

When you reroll on a blank, you have again a 25% chance for a blank. This gives 0.25*0.25 for no damage. This is 6.25% chance for no damage.
But if you reroll the hits as well, you increase the chance for no damage to 0.75 (blank and hit) * 0.25 (blank). You tripple the chance for no damage. Because the hit, that you had earlier, can suddenly become a blank, changing your 1 damage to 0 damage.

I think I understand what you want to say. Let me rephrase it clearly and tell me if that is what you wanted to express:

P(No damage from a black die with a reroll strategy of only rerolling on blanks with one reroll) = P(Black blank) * P(Black blank) = (1/4)² =(1/16)

and

P(No damage from a black die with a reroll strategy of rerolling on blanks and single hits with one reroll) = ( P(Black blank) + P(Black hit) ) * P(Black blank) = ((1/4) + (1/2) ) * (1/4) = (3/16)

I agree with both of those statements. They are (if a didn't mess the math up 😁 ) in fact factually correct. They are however not what I thought you expressed with your first post.

5 minutes ago, The Jabbawookie said:

Sure, let’s look at overall odds. The ratio of the increase in likelihood for blanks and doubles is only another way of saying you’re losing consistency. The fact that it’s a flat increase on both ends means the average damage is exactly worth it.

Are there other factors, like the objective, the target’s shields, how much the target needs to die, Norra, Luke or Keyan shooting, etc? Yes. But in a vacuum you will be happier more and sadder more, and you will flip more crits, and that’s about it.

And never reroll when the Venus is in line with Mercury, it cannot work in this case. But when the Moon is right below Orion you should always reroll, you just cannot loose in this case 😉

From my experience never reroll if you have a hit (unless you need the two damage for a kill, like @Mad Cat and @xanderf said). Especially NOT with Luke 😁

A confirmed single damage point is fare better that a theoretical two damage points that could become zero damage points. Don’t reroll unless you:

1) absolutely must have two hits

2) have a way to change that blank face to a hit if it appears

3) you don’t really mind if you get a blank face and don’t need to do damage

1 hour ago, player3691565 said:

A confirmed single damage point is fare better that a theoretical two damage points that could become zero damage points.

That’s just it though:

In a vacuum, they are statistically the same except for variance. Objectively.

Anything after that is either an external variable (of which there are many) or personal preference.

38 minutes ago, The Jabbawookie said:

That’s just it though:

In a vacuum, they are statistically the same except for variance. Objectively.

But they really aren't, though, because you already have the hit . It's a close variant of the Monty Hall problem .

(EDIT: well, I mean, not that close a variant - obviously previous dice results don't impact future dice results. So..."a variant of", anyway.)

43 minutes ago, xanderf said:

But they really aren't, though, because you already have the hit .

A roll of a black die results in an average damage of 1. You already have 1. They are the same average number, with greater variance. If you're going to offer a convincing case beyond that, I'd appreciate some elaboration beyond throwing in a link to the Monty Hall problem. I have way too strong of a caffeine headache right now to math through that with extra variables, especially when it's not applicable anyway for the reason you gave.

The best analogy I can think of in that context is standing onstage with a bike, and trading it away to open one of four doors yourself, no host intervention. 2 have bikes, 1 has a goat and 1 has a car.

6 minutes ago, The Jabbawookie said:

A roll of a black die results in an average damage of 1. You already have 1. They are the same average number, with greater variance. If you're going to offer a convincing reason beyond that, I'd appreciate some elaboration beyond throwing in a link to the Monty Hall problem. I have way too strong of a caffeine headache right now to math through that with 1 goat, 1 car and 2 bicycles, especially when it's not directly applicable anyway.

You have the answer already.

"They are the same average number, with greater variance ."

If you already have the one, you have 0 variance. 'The same number, with greater variance' is not the same number .

What you are looking at is whether 1 is as good as 0, or whether it's better if there is a slight chance of 2. If the former (IE., last shot of round 6, last chance to kill something before it kills you, you are in the right sign for a Mercury retrograde, etc) then sure, reroll. Every other time is the second option - don't!

15 minutes ago, xanderf said:

You have the answer already.

"They are the same average number, with greater variance ."

If you already have the one, you have 0 variance. 'The same number, with greater variance' is not the same number .

What you are looking at is whether 1 is as good as 0, or whether it's better if there is a slight chance of 2. If the former (IE., last shot of round 6, last chance to kill something before it kills you, you are in the right sign for a Mercury retrograde, etc) then sure, reroll. Every other time is the second option - don't!

This is not a mathematical argument in either direction. Because I said the same average number. And that remains true. Given enough attacks over enough games, a group of bombers rerolling aggressively will do the same damage as a group of bombers rerolling conservatively. The risk is equal to the reward.

As an aside, I have a strong tendency to reroll conservatively. I plan to change that now (in general), not because either approach is better, but to stimulate discussion on probability with newer players in the group.

24 minutes ago, The Jabbawookie said:

This is not a mathematical argument in either direction. Because I said the same average number. And that remains true. Given enough attacks over enough games, a group of bombers rerolling aggressively will do the same damage as a group of bombers rerolling conservatively. The risk is equal to the reward.

Given the amount of ships with brace, I would expect aggressive bombers to do slightly less damage.

9 minutes ago, PT106 said:

Given the amount of ships with brace, I would expect aggressive bombers to do slightly less damage.

That would be an external variable (relevant to application, though.) Against a (single) brace target, one might judge whether they have a major attack lined up, whether the target has ECM or not, and whether burning off the brace is likely to make a difference in dropping the ship before it activates next round or hurts the chances of dropping it before it can activate this round. Among other factors.

The point is that they are the same from an abstract mathematical perspective, though there are definitely situations where one is better than the other.

On 10/12/2019 at 9:49 AM, Tokra said:

From my experience never reroll if you have a hit (unless you need the two damage for a kill, like @Mad Cat and @xanderf said). Especially NOT with Luke 😁

Wut?! Luke's main use case is pushing a crit through a shield. If your gonna settle with a mere hit you might as well have just hit the shield. Early game at least with Luke you need to go all in on fishing for a debilitating early critcal hit.

35 minutes ago, CMDR Kastor said:

Wut?! Luke's main use case is pushing a crit through a shield. If your gonna settle with a mere hit you might as well have just hit the shield. Early game at least with Luke you need to go all in on fishing for a debilitating early critcal hit.

Luke has a bad habit on not hitting (as in rolling blanks) 😆 .

I dont math.... like ever... for any reason that is avoidable. However, I've played single black dice imp bombers since... well... forever. I like to consider myself a skilled squad player. I don't fish for crits.

Math is math, but in Armada variance leads to losses.