#coin bonus

[gyftwalablog]

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[shmozie]

Berry horde.... Whenever I fish up a coin bonus karp, I take my time by avoiding berries and never train. The only JP I gain are from events after battling and Feebas. I tap a maxed out Rowlett for coins and then Slowpoke to reset its skill. Then Meowth, Snorlax and Mudkip for more coins, berries and an item. Then I battle and play until I lose. Then I use Bulbasaur to gain another play and battle again even if I lose because you'll still get coins either way, lol.

[karama9]

I mathed all over the place

So I've been curious about the coin bonus in tsum tsum. It gives you a random % of extra coins after your game in exchange for 500 coins paid at the start of the game, and people have been trying to find out how much coins you had to typically make in a game to end up with an average gain when using the bonus.

Probabilities were compiled based on a lot of users tracking their experience, the profits were calculated against the 500 costs, and it turns out that if you make about 1000 coins a game on average, you will have a net gain using the coin bonus. I got the same result using the stats compiled by the tsum tsum reddit.

The thing is, that didn't seem right to me because most of the time (2/3), the bonus is less than 50%. It is in fact 50% about 26% of the time and only above 50% about 7% of the time.

It's a very nice case of outlier data. The reason the long time expected net gain is above 0 if you make more than 1000 base coins is that there is a small chance of a very big bonus. There is about a 0.3% chance each of getting a bonus of 10 times your base coins or 20 times your base coins (so your profit is, on 1000 coins, 10000 or 20000 coins extra) and a 0.06% chance of getting 50 times your base coins.

So you have a situation where most of the time, you lose money, break even about one time out of 4 and make money less than 1 time out of 10, but hit the jackpot once in a blue moon.

Which is fine if the blue moon happens fairly often, but I figured it may be useful to some player to know just how often to expect it. It's pretty straightforward in terms of frequency: it's the reverse of the possibility. So, if we call "jackpot" getting 1000%, 2000% or 5000% bonus, the odds are 0.62%. This means you would expect it to happen about once in every 161 games. Which doesn't sound too bad, but for 2/3 of the other 160 (107), you lost money, and 1000% coin bonus may not quite be enough to cover your losses, and then you're losing money again for quite possibly another 160 games. But you'll eventually hit a 2000% and a 5000%, and then you'll break even or gain.

Which brings the real question: how many games do you need to play for your actual expected gain to be above 0? See, if you play 10 games, chances are you won't hit a jackpot and since they're the only thing that would eventually break you even, you'll lose money. Same with 30 or even 100 games. Don't get me wrong, you might get lucky, but if we're talking about playing the odds, you're better off not betting unless you're playing a lot of rounds.

And yes, I worked out how many. I calculated how many times you were likely to have each potential %bonus for 30, 100, 500 games, etc. until I finally hit a profit.

For 100 games, the odds are the highest bonus you'll get is 200% and 150%, once each. You'll mostly get 30% and a lot of 10% and 50% too. Your expected net gain is 34,400 (always on 1000 base), and you paid 50x100 = 50,000 coins. Your loss is 15,600 or 156 coins per game.

Even at 500 games, despite the fact you can expect (as in, it's not unlikely) to get both a 1000% and a 2000% once each, your net gain would be 225,100 but you paid 250,000 and you still have a loss of 24,900. That's less per game, only about 50 coins, which is what we'd expect knowing we'll eventually hit a profit.

At 850 games, I still came up with a deficit of 37,900. I finally hit a profit at 900 games, thanks to the expected number of 5000% finally hitting 1 rather than 0. Mind you this happened as soon as the expected number of 5000% was above 0.5, not above 1, so it's still optimistic. The net profit with 900 games was 14,900.

So, when trying to maximize your profit, consider the amount of rounds you can play. If you're saving coins for an upcoming event and you only have a few days and are not going to play anything close to 900 rounds, you're probably better off not using the coin bonus if your base average is 1000. The higher your base average the lower the number of games to profit, of course. With a base average of 1500, you're already making money at 100 games.