I ran Dash the other day, and ran into the brutal choice: do you reroll hits (not crits) on the anti-ship?

For clarity, not asking "can you," but "should you." It is a terrible, terrible choice!

I'm a believer in never looking a gift 'hit' in the mouth.

1 black. . . Hmmmmm

I mean, obviously you're not taking him for the anti-ship. But when it comes up... Gah!

I ran Dash the other day, and ran into the brutal choice: do you reroll hits (not crits) on the anti-ship?

For clarity, not asking "can you," but "should you." It is a terrible, terrible choice!

In a vacuum, I'm inclined to reroll the hit. You have a 50% chance of getting the same result, and a 25% chance of the hit-crit result, and just a 25% chance of a worse result. Unless the one hit is the difference between killing a ship and not (in which case, there's really no need to fish for the crit), it seems like the free chance to do bonus damage is going to be worth the risk on whiffing on a single die. Just my two cents.

If I need 2 damage to take down a ship or win the game then sure, otherwise no I would probably not do it unless I hade multiple re-rolls.

yeah when you have a 75% chance of a hit why not

Yeah, but you have 25% chance of increasing damage by 1, 25% chance of whiffing, and 50% chance of no change.

Yeah, but you have 25% chance of increasing damage by 1, 25% chance of whiffing, and 50% chance of no change.

yeah so a 75% chance of the same or better results........

The expected damage from a black die with bomber is exactly 1 (meaning you rolled exactly average), so generally speaking it makes no difference in the long run. If the opponent has no shields remaining, though, then you're better off rerolling as the expected outcome becomes "0.75 cards facedown + 0.25 cards faceup", which means you rolled below average.

must be some new math cause he rolled the average regardless of shields.

Dano on IFF brought up a good point about the rerolls. Would you be able to reroll the same die multiple times until you get the result you wanted or until you run out of dice reroll counts you get for being distance 1 of ships and squadrons.

must be some new math cause he rolled the average regardless of shields.

Not true at all.

Hit+Crit is not the same as Hit+Hit.

If the opponent has 2 or more shields:

Hit + Hit causes 2 damage

Hit + Crit causes 2 damage, which is equivalent

If the opponent has no shields*:

Hit + Hit causes 2 facedown damage cards

Hit + Crit causes 1 facedown and 1 faceup damage card, which is strictly better

The average damage on a black die against a shielded ship is (2+2+1+1+1+1+0+0)/8 = 1 damage

While the average damage against an unshielded ship is (UD+UD+D+D+D+D+0+0)/8 = 0.75D + 0.25U

1 card facedown (1D) is below this average (because U is more valuable** than D), so on a reroll your expected outcome is slightly better than that.

* similar matho applies to the 1-shield case.

** Structural Damage alone raises the value of U to at least 1.15D, making the average damage on a black die ~1.04 cards, even if you ignore all other critical effects.

Expected value on a black die with a reroll is actually a little higher than one I believe the math comes out to 1.25 if you reroll every time you get a not-hitcrit.(1*.75)+(2*.25)

Bleh. Too many calculations. Not that I don't understand them, I simply mean this is a game and everyone's preference towards a gamble is different. I, personally, would just enjoy the game and take it as it comes. Depending on how overconfident I felt ("Yeah, I can do this! Oh, fail") or desperate I am ("going for the win!" *holding breath whilst rolling dice*). But then, I'm more casual with my play style

Expected value on a black die with a reroll is actually a little higher than one I believe the math comes out to 1.25 if you reroll every time you get a not-hitcrit.(1*.75)+(2*.25)

That's correct. But the OP's question was about whether, after you roll a single hit, it's better to reroll or not. So your expected value formula doesn't really apply here since it accounts for the probability of rolling a blank or a hit+crit on your first roll, neither of which is a possible event in the OP's scenario. In purely mathematical terms, the question can be summed as "is the expected value on a single black die, without rerolls, higher than 1?", though of course this does not account for a player's risk-aversion or the overall game environment.

From a mathematical perspective, you should always reroll if the defending hull zone has 0 or 1 shields left. If it has more, then it doesn't really matter (I'm risk-averse so I generally would not).

If it's the last HP on a ship? Sure.

Otherwise, no.

Depends entirely on context. If the ship still has shields on its other hull zones your ships will have to chew threw, or if it's only got that "one more hit..." left, then it's more tempting to fish for crits. But it will always be a judgment call based on the state of the board at the time.

On one hand, if you think of the expected value of a critical hit as >1 damage, then the brute math would say to always reroll. But of course board context is going to determine whether or not that risk/reward is worth it at the given time, and that's a judgment call.

Yeah, but you have 25% chance of increasing damage by 1, 25% chance of whiffing, and 50% chance of no change.

yeah so a 75% chance of the same or better results........

That's not very sound judgment on probability...

Imagine you win $1,000 at the casino. Then the Casino manager comes over and says "Excuse me, would you like to double your money? Here's a D10, and you can roll it once. On a 1-2, you lose your $1,000. On a 3-9 you keep your $1,000. And on a 10 we'll give you ANOTHER $1,000."

So, there's an 80% chance of the same or better results!!! Take the deal!!!! (But of course, anyone who took this bet would be either dumb or feeling really really lucky, because the odds you lose your money are twice as likely as the odds you increase your money.

But what makes the OP's question more interesting is that the value of a Crit > Hit, so while the odds of improving are equal to the odds or worsening the roll (so basically a coin toss), the improvement has a greater net value than the loss. Since a Crit > Hit, the expected value says to reroll. Of course, all of this assumes the section Dash is shooting is shieldless, because if there are shields the value of Crit = Hit. And other on-table contexts may not make the risk worth it, even if the expected values suggest re-rolling.

Two games in a Row, I've had Yavaris Y- and B-Wings throw nothing but Blank Blacks...

... so if I get a Hit, I'm keeping it.

must be some new math cause he rolled the average regardless of shields.

Not true at all.

Hit+Crit is not the same as Hit+Hit.

If the opponent has 2 or more shields:

Hit + Hit causes 2 damage

Hit + Crit causes 2 damage, which is equivalent

If the opponent has no shields*:

Hit + Hit causes 2 facedown damage cards

Hit + Crit causes 1 facedown and 1 faceup damage card, which is strictly better

The average damage on a black die against a shielded ship is (2+2+1+1+1+1+0+0)/8 = 1 damage

While the average damage against an unshielded ship is (UD+UD+D+D+D+D+0+0)/8 = 0.75D + 0.25U

1 card facedown (1D) is below this average (because U is more valuable** than D), so on a reroll your expected outcome is slightly better than that.

* similar matho applies to the 1-shield case.

** Structural Damage alone raises the value of U to at least 1.15D, making the average damage on a black die ~1.04 cards, even if you ignore all other critical effects.

we're talking about one dice right......

Just the facts, ma'am.

Remember that on black dice you have a 75% chance of rolling a hit or critical result. These are good chances if you're on your last roll and an extra point of damage could achieve something important.

Let's assume am optimal scenario: Dash has been activated by Yavaris with Adar Talon. He'll get to attack twice in the ship phase and reactivate as a Rogue in the squadron phase for a third attack on his current target, or to move on if that target dies.

Dash gets a successful first hit and reduces that target to two hull points. He gets a second regular hit. At this point, it is mathematically optimal to reroll the successful hit. He has a 75% chance of either maintaining or improving his damage output. If the ship survives, he can then reactivate and make another attempt during the squadron phase.

Scenario 2

On the other hand, let's say that instead he rolled the damage and on the second hit stripped all the shields off the facing Yavaris will attack this activation. It is far better to allow the hit and take the shots at unshielded hull, which will potentially do far higher damage. Dash himself can reactivate and either continue to attack his target if it survives (at which point we revert to scenario one) or reposition himself to attack another ship or squadron.

Expected value on a black die with a reroll is actually a little higher than one I believe the math comes out to 1.25 if you reroll every time you get a not-hitcrit.(1*.75)+(2*.25)

That's correct. But the OP's question was about whether, after you roll a single hit, it's better to reroll or not. So your expected value formula doesn't really apply here since it accounts for the probability of rolling a blank or a hit+crit on your first roll, neither of which is a possible event in the OP's scenario. In purely mathematical terms, the question can be summed as "is the expected value on a single black die, without rerolls, higher than 1?", though of course this does not account for a player's risk-aversion or the overall game environment.

From a mathematical perspective, you should always reroll if the defending hull zone has 0 or 1 shields left. If it has more, then it doesn't really matter (I'm risk-averse so I generally would not).

Obviously you make an exception for leathal damage because that's the only time getting more damage doesn't matter.

Just out of curiosity, anyone who featured Keyan heavily in Wave I care to comment on how they generally approached this problem when attacking hull zones without shields? His special ability in that circumstance is essentially the same (except he's rolling two black dice instead of one, so it potentially poses twice the conundrum).

I've never been lucky enough to have Keyan squaring off against an unshielded hull zone, so I don't have any insight into it (besides the fact that I'd obviously reroll blanks). So in a neutral situation, where you rolled two dice, got a hit on each, and know that the ship will survive whether you land two hits or four, would you settle, reroll one in the hopes of increasing damage (and landing a crit), or tempt the fates and try for the knock-out?

Edit: The reason I ask is because we're starting to see more of these selective reroll cards. Vader and Ordnance Experts are the key new additions, and before that we had CF tokens (on a single die) and Leading Shots (not useable on black dice, but available for reds). They're obviously most useful when blanks are rolled, but if you land just a bunch of generic hits and have a reroll option (either for free, like Ordnance Experts or Keyan or Dash, or at a cost like Vader or Leading Shots), would you generally settle for the damage you've rolled (and just reroll blanks), or would you be more aggressive in trying to pump up your overall damage output (especially on black dice, where the odds of losing damage are relatively low compared to the odds of rolling the same damage, and comparable to the odds of rolling higher damage).