Rune shard math

[KarlD]

I have an AW that it's time to upgrade using rune shards. I also happen to have a full broken shard bar from which I can forge a complete rune. My goal is, of course, to use the fewest number of shards to fill my wheel. My question is does anyone know the math behind when I should forge the first rune with the broken shards.

I know that I want to use a shard when the wheel is empty because it is guaranteed to find a spot and not become a broken shard that will be lost because the broken shard bar is full. I also know that if I have only one opening on the wheel and I have a full broken shard bar that I would forge a rune for that last spot. Somewhere in between those situations I want to decide when is the optimal time to forge my first rune from broken shards.

It's not a big deal, but I'm just curious about it. Does anyone here know?

 

[Deleted User - 3932582]

It's not a big deal, but I'm just curious about it. Does anyone here know?

The way I see it, it is never a good idea to use broken shards if you still have runes left - except for the very last open spot. Single broken shard is 10% of filling one rune spot, so that's how much you'll be losing if you break your rune with the shards full. But if you fill in a rune spot with shards, then you reduce probability of your next runes filling in one full spot by 1/9 = 11.1%.

Runes are just much more valuable by themselves, rather than as a source of shards. And nowadays you can come up with enough shards without breaking valuable runes for that.

Of course, if that's one of the runes that you have dozens/hundreds of, then who cares? Or rather then you may consider dumping your shards bar first into something more valuable, and then still spam runes in this cheap AW to fill in shards bar to use elsewhere.

 

[Enevhar Aldarion]

I have so much time in between having AWs in rune shard phase that I am crafting any recipe that uses broken shards every time one shows up, so that I am not wasting broken shards. As for using them to fill spots, there is too much variable for if a shard will fill a spot or break, for me to not use them as soon as I have 10. My luck has ranged from filling the wheel without breaking a single shard to needing 30+ shards to fill it, which means I filled the broken shards twice, and used them twice, before all the spots were full.

 

[KarlD]

Runes are just much more valuable by themselves, rather than as a source of shards.

I don't disagree with you. My feeling had been that I should wait until the last opening on the wheel to forge a rune, but a downside of going the "optimal" route is that I could possibly have an extremely long run of bad luck where I never hit an empty spot and keep losing shards until I run out and still have 2 or more open positions on the wheel. If I forge runes sooner I am guaranteed to fill the wheel with a finite number of shards.

I guess forging runes before the last one is like buying insurance. Statistically speaking insurance is a losing deal, but we buy it anyway to protect against the unlikely event.

Just for the record, I filled 5 spots in a row using shards. I then had 3 in a row become lost broken shards. I forged a rune. I then used 5 more shards to fill in the remaining 3 positions leaving 2 broken shards in the bar. So overall it worked out well even though it was not the optimal approach.

 

[Deleted User - 3932582]

I guess forging runes before the last one is like buying insurance. Statistically speaking insurance is a losing deal, but we buy it anyway to protect against the unlikely event.

And that's the reason why you only buy insurance against events that you can't absorb losses on (e.g. buying extended warranty on 200$ toaster is a terrible deal). There is nothing in runes/shards setup that would be particularly detrimental either way. Once you run out of runes, there is no downside to using shards, and these are easy to refill. So your "extremely long run of bad luck" is limited by the amount of runes you already have. If your number of runes is already low so that you care about this choice, then your downside is very limited.

 

[DeletedUser2959]

I do three then use my broken shards to make #4.

 

[Deleted User - 1178646]

I have an AW that it's time to upgrade using rune shards. I also happen to have a full broken shard bar from which I can forge a complete rune. My goal is, of course, to use the fewest number of shards to fill my wheel. My question is does anyone know the math behind when I should forge the first rune with the broken shards.

I know that I want to use a shard when the wheel is empty because it is guaranteed to find a spot and not become a broken shard that will be lost because the broken shard bar is full. I also know that if I have only one opening on the wheel and I have a full broken shard bar that I would forge a rune for that last spot. Somewhere in between those situations I want to decide when is the optimal time to forge my first rune from broken shards.

It's not a big deal, but I'm just curious about it. Does anyone here know?

Personally I add 2-3 runes first then use the shards. then fill up the remaining.
assuming the first 3 2 fit (first one always fit), then you should be done in 13 runes max. well below the 18 average.

Runes are just much more valuable by themselves, rather than as a source of shards. And nowadays you can come up with enough shards without breaking valuable runes for that.

That so mucht depend on how many you have got lol, I must be freaking rich

Spoiler

I wish I could trade those for the broken runeshards.

 

[KarlD]

Personally I add 2-3 runes first then use the shards. then fill up the remaining.
assuming the first 3 2 fit (first one always fit), then you should be done in 13 runes max. well below the 18 average.

If you fill the first 3 positions with runes and the 4th with broken shards that leaves 5 open positions. You could possibly never hit an open position with a rune and need as many as 50 more runes to complete the wheel. Where did 13 runes max come from?