Okay, I messed up my first post here by getting my inequality backward. (For the algebraists among us, I forgot that if you take a logarithm with a base between 0 and 1, you have to reverse the intequality.) Here's how the math works, assuming you have R=F+B focus and blank results on your initial roll.

If you use Chiraneau's ability and then reroll, you add an average of 1+0.5(R-1) hit and crit results to your total. If you reroll and then use Chiraneau's ability, you add an average of 0.5R + (1-0.75^R) hit and crit results. Since we want to know whether (use Chiraneau first) > (use Chiraneau second), we're investigating this proposition:

1+0.5(R-1) > 0.5R + (1-0.75^R)

After some algebra, that works out to

0.75^R > 0.5

or

R < log(0.5)/log(0.75).

So if R < 2.4, meaning if you have a total of 1 or 2 focus and blank results on your initial roll, you should use Chiraneau before rerolling. As Klutz says, this is because you're relatively unlikely to replace your existing focus result with a new one, and the chance of rerolling your focus into a blank is pretty high.

But if R > 2.4, meaning if you have a total of 3 or more focus and blank results on your initial roll, you should use Chiraneau after rerolling. This is as unintuitive for me as for anyone else, but I don't think it's a mistake.

There's only a 25% chance you'll get something worse and a 75% chance you'll get something equivalent or better!!

Thank you, that is the only post so far that I've seen that actually made sense to me. I think you're all saying the same thing, but I'm getting lost a bit in the math.

So if R < 2.4, meaning if you have a total of 1 or 2 focus and blank results on your initial roll, you should use Chiraneau before rerolling. As Klutz says, this is because you're relatively unlikely to replace your existing focus result with a new one, and the chance of rerolling your focus into a blank is pretty high.

But if R > 2.4, meaning if you have a total of 3 or more focus and blank results on your initial roll, you should use Chiraneau after rerolling. This is as unintuitive for me as for anyone else, but I don't think it's a mistake.

I came up with the same results via a different method, so I concur with your findings.

My method was using the expected 1 (for the <focus> changed to a <kaboom> that you're not rerolling)+<booms> rolled for rolling X dice vs Chiraneau expected <booms> rolled for rolling X+1 dice.

Okay, so i brute forced this in excel by calculating all possible outcomes of rolling 3 and 4 dice. I am actually quite surprised at the results. Going off the original premise of rolling 1 focus and 3 blanks, rerolling all of them is better:

Damage done Keep focus, reroll blanks:

4 12.5%

3 37.5%

2 37.5%

1 12.5%

0 00.00%

avg of 2.5 damage

Damage done rerolling everything:

4 18.46%

3 40.92%

2 31.25%

1 08.98%

0 00.39%

avg of 2.68 damage.

It isn't much different, and there is a slim chance you could do no damage at all, but it is just a little bit better.

It isn't much different, and there is a slim chance you could do no damage at all, but it is just a little bit better.

An argument could be made that rolling 3 hits is more than 50% better than rolling 2 hits. This is especially true against higher agility targets.

Therefore, I might suggest a weighted average, giving more weight to high damage rolls. Doing so, no matter what arbitrary weights you go with, will favor the "re-roll everything" option even more!

If you already have an eyeball result at R1-2 (which Cheery /will/ turn to a crit), why would you not keep the eyeball and reroll any non-hits?

If you already have an eyeball result at R1-2 (which Cheery /will/ turn to a crit), why would you not keep the eyeball and reroll any non-hits?

Please refer to the previous responses.

Seriously, you just skipped 2 pages of explanations and re-stated OP's question.

why would you not keep the eyeball and reroll any non-hits?

Because odds are you will either get either more hits/crits or at least the same amount, if you reroll all 4 dice. With fairly low odds you'll end up worse off than before.

It isn't much different, and there is a slim chance you could do no damage at all, but it is just a little bit better.

An argument could be made that rolling 3 hits is more than 50% better than rolling 2 hits. This is especially true against higher agility targets.

Therefore, I might suggest a weighted average, giving more weight to high damage rolls. Doing so, no matter what arbitrary weights you go with, will favor the "re-roll everything" option even more!

True, but those numbers do ignore the difference between hit and crit.

Keep focus avgs 1.125 hits and 1.375 crits, reroll all avgs 1.5 hits but only 1.18 crits.

I suppose it would depend on what you are shooting at, do you really need to take the risk to get that ~10% chance of an extra hit, or do you want to go for a slim chance at double crits?

Ultimatley, I think the two choices are so close that its 6 of one or half a dozen of the other.

I have nothing to add as far as numbers but as far as a personal preference I will keep the focus and reroll anything else that missed because I like sure results.

Okay, so i brute forced this in excel by calculating all possible outcomes of rolling 3 and 4 dice. I am actually quite surprised at the results. Going off the original premise of rolling 1 focus and 3 blanks, rerolling all of them is better:

Damage done Keep focus, reroll blanks:

4 12.5%

3 37.5%

2 37.5%

1 12.5%

0 00.00%

avg of 2.5 damage

Damage done rerolling everything:

4 18.46%

3 40.92%

2 31.25%

1 08.98%

0 00.39%

avg of 2.68 damage.

It isn't much different, and there is a slim chance you could do no damage at all, but it is just a little bit better.

In Hooths example it's interesting how the percentage of 4 hits from re-rolling everything pulls away from re-rolling 3.

Glad you guys are here; I'm so far removed from from using advanced math that I forgot most of it anyways.(I took differential equations 3 times 2 Fs and then final an A.)

With all the talk of 'Using Chiraneau before rerolling' i feel compelled to point out you can't actually do that. Focus modifications to dice occur last. Defender gets to manipulate dice first, then you need to reroll first (but you don't need to reroll everything or even anything of course), then finally switching focus results (or blank results for concussion missiles) to hit/crits.

It is important to note this as it does effect what a defender might do with that astromech that uses a target lock to force an attacker to reroll (and you would have technically spent Chiraneaus ability already, even if you had done it illegally). Order is important

Focus modifications to dice occur last. ...then you need to reroll first (but you don't need to reroll everything or even anything of course), then finally switching focus results (or blank results for concussion missiles) to hit/crits.

That isn't true. Page 11 of the rulebook is quite clear that

If a player wants to resolve multiple modifying abilities, he resolves them in the order of his choosing.

With focus tokens and TLs, it is just such an incredibly good idea to spend the lock first that no one should ever be doing it the other way around.

Okay, I messed up my first post here by getting my inequality backward. (For the algebraists among us, I forgot that if you take a logarithm with a base between 0 and 1, you have to reverse the intequality.) Here's how the math works, assuming you have R=F+B focus and blank results on your initial roll.

If you use Chiraneau's ability and then reroll, you add an average of 1+0.5(R-1) hit and crit results to your total. If you reroll and then use Chiraneau's ability, you add an average of 0.5R + (1-0.75^R) hit and crit results. Since we want to know whether (use Chiraneau first) > (use Chiraneau second), we're investigating this proposition:

1+0.5(R-1) > 0.5R + (1-0.75^R)

After some algebra, that works out to

0.75^R > 0.5

or

R < log(0.5)/log(0.75).

So if R < 2.4, meaning if you have a total of 1 or 2 focus and blank results on your initial roll, you should use Chiraneau before rerolling. As Klutz says, this is because you're relatively unlikely to replace your existing focus result with a new one, and the chance of rerolling your focus into a blank is pretty high.

But if R > 2.4, meaning if you have a total of 3 or more focus and blank results on your initial roll, you should use Chiraneau after rerolling. This is as unintuitive for me as for anyone else, but I don't think it's a mistake.

That's math supports my gut reaction.

If you just have one focus you obviously turn it and are done so no rerolling at all.

If you have one focus and one other non-hitting die then you turn the one up and may reroll the other as you odds of improving aren't great enough.

At 3 or more non-hitting dice I feel you should roll with the punches and assume at least one will come up with a hit effect or another focus that you can then turn. It's true that 1/8 of the time you could turn rolling 3 dice with a Focus result into 3 [blanks] but the other 7/8 you should do almost as well or better.

I will admit that most of the math minimizes the added bonus that a [kaboom] may provide over a simple [boom] but when you think about it are you really going to complain? They work the same when it comes to knocking off shields. If you actually do get to deal cards there is always the chance that the face-up one the [kaboom] throws will be one that the target can ignore or shrug off easily enough.

Fool the dice gods live in a nice cottage down in Kent, and only accept cola and cheetos as sacrifice.

Kids these days and their "new" gods, with their "instant gratification"...

Do not underestimate the great power of the old gods!

Yeah, but you have to wait for the stars to be right, first.

With all the talk of 'Using Chiraneau before rerolling' i feel compelled to point out you can't actually do that. Focus modifications to dice occur last. Defender gets to manipulate dice first, then you need to reroll first (but you don't need to reroll everything or even anything of course), then finally switching focus results (or blank results for concussion missiles) to hit/crits.

It's true that the defender has the first opportunity to modify the attacker's dice, but otherwise I'm not sure where you're getting this.

In fact, the only mention of it is quite the opposite: the rulebook states that the players may resolve effects that modify the dice in any order they want. It's just common practice to resolve any reroll effects first so you get maximum value out of your Focus token. There's nothing that says you must do it that way.

Keep in mind the order that dice are modified. You can't just change a focus to hit right away. The defender has a chance to modify your attack dice first (if able).

With all the talk of 'Using Chiraneau before rerolling' i feel compelled to point out you can't actually do that. Focus modifications to dice occur last. Defender gets to manipulate dice first, then you need to reroll first (but you don't need to reroll everything or even anything of course), then finally switching focus results (or blank results for concussion missiles) to hit/crits.

It's true that the defender has the first opportunity to modify the attacker's dice, but otherwise I'm not sure where you're getting this.

Hmm.... idk where I got it from, its just how we've always done it.

1) Initial Roll

2) Defender gets to modify if appropriate

3) Attack gets to use re-rolls

4) Focus and other effects occur.

Apart from the defender getting the first opportunity maybe order isn't enforced. But it is smart (maybe)

With all the talk of 'Using Chiraneau before rerolling' i feel compelled to point out you can't actually do that. Focus modifications to dice occur last. Defender gets to manipulate dice first, then you need to reroll first (but you don't need to reroll everything or even anything of course), then finally switching focus results (or blank results for concussion missiles) to hit/crits.

It's true that the defender has the first opportunity to modify the attacker's dice, but otherwise I'm not sure where you're getting this.

Hmm.... idk where I got it from, its just how we've always done it.

1) Initial Roll

2) Defender gets to modify if appropriate

3) Attack gets to use re-rolls

4) Focus and other effects occur.

Apart from the defender getting the first opportunity maybe order isn't enforced. But it is smart (maybe)

Looking at the other post I think OP may be asking if it would be better to roll a focus dice result with any number of blank/focus results in hopes that you only end up with one focus that can be modified to a critical hit.

Hmm.... idk where I got it from, its just how we've always done it.

1) Initial Roll

2) Defender gets to modify if appropriate

3) Attack gets to use re-rolls

4) Focus and other effects occur.

Apart from the defender getting the first opportunity maybe order isn't enforced. But it is smart (maybe)

The only order that needs to be respected is :

Apart from the defender getting the first opportunity maybe order isn't enforced. But it is smart (maybe)

Order isn't enforced by the rules. But if you have both a reroll effect and a focus effect you are better off using the reroll first, because you may roll more <focus> results which you can use your focus effect on.

If you use focus then reroll, you don't have a focus to convert any future <focus> results with. So it's not required but it is smart in general.