This is a calculator to optimize the balance of spending carats and crystals when pulling for support cards. Using carats to pull on a banner is more efficient when you have not obtained many copies of the cards yet because you do not get any value from pulling additional copies past MLB. As such, when you pull enough copies to be close to MLB, it can be better to stop pulling, finish the current banner cards with crystals, and save further carats for future banners.

It is commonly recommended to budget 400 pulls for a support card banner. This is reasonable advice, but there are some cases where you get particularly unlucky in those first 400 pulls and it is better for efficiency to pull to 600 if you can afford to. On the other hand, there are some cases where you get particularly lucky in the first 200 pulls and it is better to stop and use crystals early. As such, to take full advantage of the efficiency strategy, you should ideally have 600 pulls and multiple crystals available at each banner. This is especially true for banners with two long-lived valuable cards, as you will often be in a spot where it would be better to do more than 400 pulls.

There are three preset banner types: Single Card, Card+Pal, and Double Card.

Single Card banners are straightforward. These are banners where either there is only one rate-up card, or the second rate-up is a card that you don't care about.

Card+Pal banners represent the banners that come at the start of each scenario. Since the pal card is typically usable below MLB and not useful for as long as a primary pull target, the Secondary / Primary Ratio is set significantly below 1. The suggested value of 0.33 is based on the idea that for a card to be worth being a primary pull target, it should be useful for at least three scenarios. The Force LB0 Secondary option is checked because having a single copy of the pal card allows you to borrow another card when it is important to do so.

Double Card banners are those where both cards would be valuable enough to be a primary pull target if they ran separately. The preset uses a Secondary / Primary Ratio of 1, which corresponds to the two cards being equally valuable. A true Double Card banner of this nature is quite rare, so it may also be useful to see how the strategy changes when the ratio is slightly lower (e.g. in the 0.6 to 0.9 range).

First, set the "Number of Pities" input to the number of pities you currently have available. Then, find the cell corresponding to the number of primary and secondary cards that you have. The number in that cell tells you how much partial progress you need to have toward the next pity for it to be more efficient to continue pulling.

A value of 0 means that you should pull even if you're starting a fresh pity. A value of 200 means you should stop no matter where you are in a pity (this is typically only in cells where you are already done maxing the cards so it is obvious to stop). An intermediate value means that you should not start a fresh pity, but you might want to finish a pity in progress. For example, if it says 50, then it is more efficient to continue pulling if you have 50 or more pulls already toward the next pity.

Side note: Since the pity card turns into 10 rainbow cleats which can be used to buy 5 pull tickets, you can consider finishing the spark even with the cards maxed if you are already at 196 pulls or above.

The effect of a crystal isn't sufficient to determine its value. The optimal pulling strategy depends on the relative availability of carats and crystals, and since the optimal pulling strategy is determined by the value of a crystal, this means that the value must also depend on that relative availability. The fact that optimal pulling strategy changes based on the availability can be seen by consider two (unrealistic) extremes.

Imagine if you had an infinite supply of crystals. There is a clear optimal pulling strategy: pull only enough times to get at least one copy of each desired card, then use your infinite crystals to get the rest of the LBs. This corresponds to a crystal value of 0 carats.

On the opposite extreme, imagine if you had an infinite supply of carats. Once again, there is a (different) optimal pulling strategy: pull with carats and either never use crystals, or only use crystals to get the last LB of a card on a banner. This corresponds to a crystal value of 30000 carats.

The goal when picking a crystal value is to match the ratio of crystal and carat spending to the ratio of crystal and carat acquisition. Balancing spend to acquisition means that you are less likely to be forced off of the efficient pull strategy due to running low on one resource while still having enough resources overall to pull on a banner.

The calculator defaults to a crystal value of 13535 carats. Between 13535 and 13536, there is the transition point for the decision of whether to continue pulling on a single card banner when 2 copies away at a fresh pity. This corresponds to a large jump in the average number of crystals used to MLB the card: 1.156 at 13535 and 0.551 at 13536. Because this jump is so large, it means that this particular crystal value covers a wide range of acquisition ratios, so it is likely the right value to use for many players.

For Pal and Double banners, the computed strategy at either of these values uses a very small number of crystals on average, so the calculator defaults to the value that spends more crystals rather than more carats on single banners.

You get more value out of owning a card if it is useful in your support decks for a longer period of time. Thus, for most cards, it is best to MLB the card immediately with crystals instead of waiting for a selector where the card is available. Secondary cards that release near a selector cutoff are likely the best targets.