BenjaminBreeg
05-21-2018, 05:51 PM
Hello,
after I played since the official release and got more and more dissapointed with the game I started some maths to see in how far the game is fair.
I started simple:
For 100€ you get 4000 Ironit which would be 4000/675 = 5,... ; 4000-5*675=625; 625/75 = 8,... ;so 5*10+8= 58 rare souls
We´ll take the case that you want to have one specific 5* toon. Now the Probability, that one drops is 1%, and there are 16 different 5* toons, so you´ve got the chance of 0,01/16 which is 6,25*10^-4 if you want to know...
Now I calculated how many souls you need to open to have a chance of 50% to get the wanted 5*:
you have 1/1600 to get the toon.
So (using Bernoulli):
I calculated in that way, that the chance to not get the wanted toon should be less than 50%:
0,5 ≤ n!/((n-0)!*0!) [this is always 1] * 1/1600^0 [is 1, too]* 1599/1600^n
0,5 ≤ (1599/1600)^n [now use the logarithm]
ln (0,5) ≤ ln((1599/1600)^n) [now I used a logarithm computational rule]
ln (0,5) ≤ n * ln (1599/1600) | : ln(1599/1600) [is smaller than 1 so ≤ is now a ≥]
ln(0,5)/ln(1599/1600) ≥ n
1108,68 ≥ n
That means, that you need to open 1109 souls to get your wanted 5* toon by a chance of 50% through a Rare Soul.
That in Money are: 1109/58 ≈ 19; 19*100€= 1900€
So you would need to spend approximate 1900€ to get the 5* toon by only a chance of 50%.
I calculated the same for a chance of 99%, same way, you need 7366 souls, equal to around 12600€ (I left out the 25 Ironit per pack that are left, would be 50 souls more).
And I myself thought at this point, that 12.600€ are definetly too much for just ONE specific 5* at a chance of 99%.
I think the way how I calculate is clear, now I´ll just list some other cases, with the amount of souls needed to have a 50% or 99% chance to get the wanted:
Rare Soul:
Specific 5*, by chance of 50% : 1109 souls
Specific 5* by chance of 99% : 7366 souls (sheesh)
Specific 4*, by chance of 50%: 277 souls
Specific 4*, by chance of 99%: 1840 souls
Specific 3* by chance of 50% : 25 souls
Specific 3*, 99% : 166 souls
Legendary Soul:
Specific 5*, 50% : 192 legedary souls
Specific 5*, 99% : 1270 legendary souls (wow!!)
Specific 4*, 50% : 44 legendary souls
Specific 4*, 99% : 290 legendary souls
G/A Soul:
Specific 5*, 50% : 323 souls
Specific 5*, 99% : 2147 souls (ops, thats quite a bit)
Specific 4*, 50% : 57 souls
Specific 4*, 99% : 377 souls
Specific 3*, 50% : 16 souls
Specific 3*, 99% : 101 souls (for a specific three star...)
If you have questions or ways I could calculate even better, pls tell me.
For me, I have to say, the Immortal Event with these numbers, are the reasons to leave the game, since everything is completely random, RNG is really much worse that I thought and toons are actually the only key to get really better.
Thanks to all who read till here, I hope it´s understandable, otherwise pls ask so I can explain why I calculated in this way.
Thanks to all my troopers which I had, but really... With these numbers I can´t see a reason why I should play this game any longer.
Regards
BenjaminBreeg aka Athanasios
after I played since the official release and got more and more dissapointed with the game I started some maths to see in how far the game is fair.
I started simple:
For 100€ you get 4000 Ironit which would be 4000/675 = 5,... ; 4000-5*675=625; 625/75 = 8,... ;so 5*10+8= 58 rare souls
We´ll take the case that you want to have one specific 5* toon. Now the Probability, that one drops is 1%, and there are 16 different 5* toons, so you´ve got the chance of 0,01/16 which is 6,25*10^-4 if you want to know...
Now I calculated how many souls you need to open to have a chance of 50% to get the wanted 5*:
you have 1/1600 to get the toon.
So (using Bernoulli):
I calculated in that way, that the chance to not get the wanted toon should be less than 50%:
0,5 ≤ n!/((n-0)!*0!) [this is always 1] * 1/1600^0 [is 1, too]* 1599/1600^n
0,5 ≤ (1599/1600)^n [now use the logarithm]
ln (0,5) ≤ ln((1599/1600)^n) [now I used a logarithm computational rule]
ln (0,5) ≤ n * ln (1599/1600) | : ln(1599/1600) [is smaller than 1 so ≤ is now a ≥]
ln(0,5)/ln(1599/1600) ≥ n
1108,68 ≥ n
That means, that you need to open 1109 souls to get your wanted 5* toon by a chance of 50% through a Rare Soul.
That in Money are: 1109/58 ≈ 19; 19*100€= 1900€
So you would need to spend approximate 1900€ to get the 5* toon by only a chance of 50%.
I calculated the same for a chance of 99%, same way, you need 7366 souls, equal to around 12600€ (I left out the 25 Ironit per pack that are left, would be 50 souls more).
And I myself thought at this point, that 12.600€ are definetly too much for just ONE specific 5* at a chance of 99%.
I think the way how I calculate is clear, now I´ll just list some other cases, with the amount of souls needed to have a 50% or 99% chance to get the wanted:
Rare Soul:
Specific 5*, by chance of 50% : 1109 souls
Specific 5* by chance of 99% : 7366 souls (sheesh)
Specific 4*, by chance of 50%: 277 souls
Specific 4*, by chance of 99%: 1840 souls
Specific 3* by chance of 50% : 25 souls
Specific 3*, 99% : 166 souls
Legendary Soul:
Specific 5*, 50% : 192 legedary souls
Specific 5*, 99% : 1270 legendary souls (wow!!)
Specific 4*, 50% : 44 legendary souls
Specific 4*, 99% : 290 legendary souls
G/A Soul:
Specific 5*, 50% : 323 souls
Specific 5*, 99% : 2147 souls (ops, thats quite a bit)
Specific 4*, 50% : 57 souls
Specific 4*, 99% : 377 souls
Specific 3*, 50% : 16 souls
Specific 3*, 99% : 101 souls (for a specific three star...)
If you have questions or ways I could calculate even better, pls tell me.
For me, I have to say, the Immortal Event with these numbers, are the reasons to leave the game, since everything is completely random, RNG is really much worse that I thought and toons are actually the only key to get really better.
Thanks to all who read till here, I hope it´s understandable, otherwise pls ask so I can explain why I calculated in this way.
Thanks to all my troopers which I had, but really... With these numbers I can´t see a reason why I should play this game any longer.
Regards
BenjaminBreeg aka Athanasios