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EDIT (1/28/22) I made a few corrections to the numbers and added information about ranked mode and potential for mitigating the grind significantly through cloud save manipulation.
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I decided to do some math to figure out what kind of grind we're looking at for buying everything from the store. These are what you need to buy from the store in order to get every achievement, and their costs (assuming everything is consistent):
Greetings: 102 x 300 coins each = 30,600 total
Nameplates: 59 x 500 coins each = 29,500 total
Titles: 130 x 500 coins each = 65,000 total
Outfits: 100 x 800 coins each = 80,000 total
Instruments: 45 x 300 coins each = 13,500 total
Songs: 20 x 3,000 coins each = 60,000 total
There is no counter for number of instruments in the game, but I bought a few instruments and determined there are 45 total thanks to the achievement tracker. Credits to Enluna for the info on the number of songs in the store.
If you total up all these values, you will need:
278,600 coins
in order to complete the game.
And of course, this is assuming you wait every day for the store to reset to buy everything you need. Every time you reroll the store, you will need to add 1,000 coins to that total.
As far as I know, there are only two ways to earn money in this game: Taiko Mode and Ranked Matches.
You earn coins as follows in Taiko Mode:
bonus song 100 coins (three songs are highlighted daily. You can only get this bonus three times per day, once on each highlighted song)
easy clear 30 coins
easy full combo 60 coins
easy donderful combo 100 coins
normal clear 40 coins
normal full combo 70 coins
normal donderful combo 110 coins*
hard clear 50 coins
hard full combo 80 coins
hard donderful combo 120 coins*
extreme clear 60 coins
extreme full combo 90 coins
extreme donderful combo 130 coins*
*this is extrapolated data. I've only achieved donderful combo on easy so far, so I'm just copying the pattern from clears and full combos.
first silver crown (clear) 70 coins
first gold crown (full combo) 160 coins
first rainbow crown (donderful combo) 250 coins
Crown coin bonuses stack, and ignore difficulty. If you earn a gold crown on your first play, then you will gain 230 coins, and if you earn a rainbow crown on your first play, then you will gain 480 coins. Each difficulty on each song count this bonus separately, so you could potentially earn these 480 coins 4-5 times per song.
Star difficulty and divergent tracks do not affect coins earned at all. Purple extreme tracks give the same amount of coins as regular extreme tracks.
Clear means the percentage bar is in the yellow portion at the end of the song.
Full combo means you hit every note with OK or GOOD.
Donderful combo means you hit every note with GOOD. This is incredibly hard to do consistently even on easy, because the GOOD timing is very tight.
The best case scenario for coins earned in a single play is getting a donderful combo on your first play of an expert song that happens to be one of the daily bonus songs. In that case you would earn 480 + 130 + 100 = 710 coins. Even in this impossible situation, it would take 278,600 / 710 = 393 full plays. Doesn't sound too bad yet, but let's look at a more realistic situation.
Let's assume you are pretty good at the game, and can full combo every easy, normal, and hard chart, and clear every extreme chart, but just can't clear any purple extreme charts. You initially play every song on every difficulty (minus purple extreme), ignoring the bonus charts, for a total of 75 * 4 = 300 plays, in order to get as many first time crown bonuses as possible.
You start with 500 coins, and you would earn:
Easy: (60 + 230) * 75 = 21,750
Normal: (70 + 230) * 75 = 22,500
Hard: (80 + 230) * 75 = 23,250
Extreme: (60 + 70) * 75 = 9,750
Total: 77,750 coins
After this, you would still need 278,600 - 77,750 = 200,850 coins. Now, at this point, let's assume that you log in every day and complete the three bonus songs with hard full combos diligently, and you get the bonus coins every single play. You would earn 100 + 80 = 180 coins per play. At this point, you would need 200,850 / 180 = 1,116 more plays to get enough coins to buy everything you need from the shop, for a total of 1,416 plays. This is a scenario that is basically ideal, and only if you are pretty good at the game. Getting full combos on hard is no easy task.
If you assume 1min 30 sec songs (average anime opening song length) and no menuing or loading, 1,416 plays would equate to 35 hours and 24 minutes of pure gameplay.
However, as stated above, you can also earn coins through ranked mode, and at a much better rate than single player taiko if you can manage to win regularly. The breakdown on how much coins you earn are as follows:
Win: 200 coins
Loss: 20 coins
Streak Bonus: 50 coins
You achieve this bonus for every win during a streak of 2 or greater
Accumulated wins bonus: 100 coins
You achieve this bonus every 10th win.
Bonus hours: earn double the coins during these hours.
Bonus Hours are from 6-8AM daily for me, and I am in the CST time zone, so that would be 12PM to 2PM GMT.
Rank does not seem to affect coins gained at all. The game gives you a choice of which rank to start in. If you are purely trying to win as many matches as possible, you would think it would probably be in your best interest to start in C rank, the lowest rank. But it might be tough to beat players in C rank if you have trouble hitting the GOOD timing or if you can't roll as fast as everyone, since most people will be hitting Full Combos on every song. C rank plays on easy, B rank plays on normal, and A rank plays on hard. I'd advise picking the highest rank where you can still easily pass most or all songs.
If you continuously win on a streak, you would be earning 250 coins per match regularly, and 500 coins per match during bonus hours. The best possible scenario is achieving your 10th win during a streak and during bonus hours, for a total of 700 coins in a single match.
Here are a few scenarios to see how this would shake out for various skill levels:
If you never lost and only played during bonus hours, you would average (500 * 10 + 200) / 10 = 520 coins per match, so it would take 278,600 / 520 = 536 plays.
If you alternated wins and losses, which would be the worst case scenario for an average player (you would probably still streak occasionally with 50% win rate), you would average ((400 + 40) * 10 + 200) / 20 = 230 coins per match, so it would take 278,600 / 230 = 1,212 plays.
If you were above average and followed the pattern Win, Win, Loss, Win, Win, Loss, etc., you would average ((400 + 500 + 40) * 5 + 200) / 15 = 326.6 coins per match, so it would take 278,600 / 326.6 = 853 plays.
If you were below average and followed the pattern Loss, Loss, Win, Loss, Loss, Win, etc., you would average ((40 + 40 + 400) * 10 + 200) / 30 = 166.6 coins per match, so it would take 278,600 / 166.6 = 1,672 plays.
You would have to double the number of plays in each scenario if you played ranked matches outside of bonus hours.
So if you are an average player and never hit streaks, you would still be earning coins faster in ranked mode than in single player, because in single player you would be earning less than 100 coins per song outside of the 3 daily bonus songs. Average players playing ranked matches outside of bonus hours should be gaining approximately 115 coins per match, so unless you are losing more than 50% of the time, Ranked Matches are your best bet for gaining coins. However, you have to deal with matchmaking, and it's doubtful that these servers will remain active for very long, so you have to take that into account too. Also, the average skill level of the people in matchmaking right now is very high. I'm in between B+ rank and A rank, and most people I match to get very close to 1,000,000 points every song, even on Hard 7* difficulty songs. So it will be very difficult to maintain even a 50% win streak legitimately.
Finally, there is something that was brought to my attention by Saurvivalist that could potentially greatly mitigate the grind, and that is cloud save manipulation. Basically, you can buy everything from one category, grab the achievement, then quickly delete your local save and sync to the cloud where you should have all your money again. Check out Saurvivalist's forum post, "The Grind Is Easier", for more details on how to do that exactly.