The Cupid is basically your gacha aspect of the game that is found in essentially every mobage. The Cupid is one of the two main ways you get high rarity cards in this game, the other being events.
There's a lot to explain about what each gacha entails, but what you need to understand is that there are 3 main types of gachas in BF(Kari).
The Premium/Limited Time Cupid is basically the gacha where you spend coins (コイン) (which are bought with real money) to roll in a certain gacha.
There are multiple kinds of gacha you can roll in with varying cards, such as event cards or birthday cards.
A majority of the cards in this gacha are limited, meaning they won't be available after the gacha time has passed.
Clicking on 出会えるカレ一覧 will give you a list of which cards are available in each gacha and the percentage rates of getting an R, HR, or SR card.
Rolling in these gachas also gives you extra items like tickets, happiness charms, cards related to the gacha you roll in, etc.
Some of the gachas have multiple parts to them.
#連 means how many times you roll, aka how many cards you get in one roll.
At the very end of the page is the cupid ticket gacha. Cupid tickets are free tickets that you can get as event rewards, login bonuses, etc. Each roll gets you a rare or higher card.
By the way, if you download the BF(Kari) app, you get 300 coins for free with one free roll in a certain gacha that gives you 300 coins back.
But be warned: the app version and the browser version do not sync coins. The image is the browser version which shows me having 5 coins, while on the app version, I have over 300.
The Normal Cupid is the one of the two free gachas you can roll.
The Doki Doki Map Cupid (ドキドキMAPキュピ) is your one-free-a-day gacha, in which you can roll 3 times a day for a N to HN card, along with an extra item like tickets, keys, etc.
It resets to the beginning of the map you are on if you do not roll within 24 hours. So make sure you roll at least once every day, or your progress will reset!
On the even numbers of the Doki Doki Map, you will get an SR card of the kare advertised in the ad. These SR cards are not attainable any other way, so make sure you take careful care of them.
Once you reach the last map, map 10, you will get the fourth card and then you will move on to the next Doki Doki Map to get the next kare.
So far there are 6 kares you meet on the Doki Doki Map, so essentially, 6 free SSRs.
Below the Doki Doki Map, is the friend point gacha, where you use friend points to roll for N to R cards. 1 roll is 200 points.
You also have a chance to get R assist kares here, so if you need assist kares, roll here often during events.
The last type of gacha and the second free type of gacha is the Ticket Cupid, in which you use tickets gained from events, login bonuses, etc. to roll for R to SR cards.
There are multiple kinds of tickets, ranging from guaranteed rarity tickets to event card tickets to guaranteed kare tickets.
On event cards tickets, you have a possibility to get a card related to the current event. These tickets have a time limit on them, so use them immediately. They are not guaranteed event cards or assist kares!
On guaranteed kare tickets, you get to choose which kare you want. Which card of his you get is completely random though.
As always, click the 出会えるカレ一覧 to see which cards are available in that gacha. Event cards from previous events or the current event are not available with these types of tickets.
On guaranteed rarity tickets, you will get that rarity card of any kare available in the gacha.
These are labeled as (card rarity)確定 or (card rarity)以上確定, meaning you will get a card of that rarity or you will get a card of that rarity or higher (if you're lucky).
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