Catching chance

This honestly will be hard to verify, but is there some kind of error with this catching thing?

After playing for this long, I always feel there is something weird about the catching chance. The catch chance seems to be less than what it is stated.

I have been trying to catch at 49% a lot lately. If it is a truly 49%, then pretty much every 2 catch attempts, I should get one (on average). However, I have been seeing a lot of time where I have to try like 5-8 times for one successful catch. There is even once I tried 10 times to get one at 49% which is extremely extremely difficult (like 0.0016 chance).

By mean of true average, if I see a lot of consecutive failures, then I should see a lot of consecutive success to make it at a near 50% probability, however, I rare rare rarely seen 3 consecutive successful catches not to mention like 5-8 consecutive successful catches.

The 2% epic catch is the same. I always do it at 2%, which should average like 50 cards per catch, but I have been using like 120+ cards for the last 4 out of 5 catches.

Of course I could be just unlucky. Does anyone else feels the same?

[Shadehawk]

I see what you are saying on the first part, the 49% thing is happening to me as well. But for the second, the mathematical probability is not 50 cards = 1 catch. Many people make the mistake of adding the percentages, wherein these cases that is not how it works. It is a combination binomial of some degree. So you have a 2% chance to catch the epic, you miss, it is still 2%. It does not change to 4% just because you missed the first time.

Using exponential mathematical probability, the miss rate, .98 will go to the 'n'th power ('n' being however many seals you throw at it. So let's say you throw 50 seals at an epic. Normally, it would be assumed 50*(.2)=1=100%; therefore, after 50 shots you should have one. However, take .98^50 and you get .3641 or 36.41%, meaning you would have a 36.41% of missing all of them, or a 63.59% chance of catching it ONCE. That gives you a rough 2/3 chance of catching it as oppose to a guaranteed catch after 50 cards. You would think that after maybe 100 seal cards you would have a guaranteed catch right? Still no. Take .98^100, which would equal .1326 or 13.26%, meaning yet again, you still only have a 86.64% chance of catching it ONCE, and therefore by squaring it, a 75.06% chance of catching TWO.

So what is the "guaranteed" number of cards?

Using logs (the mathematical kind) (QUICK EXPLANATION: log of x to log base y = n translates to exponents as y^n = x.), so for this example, y is the percentage chance to miss = .98. N is the number of tries, in this case, cards thrown. X is the final product of miss chances. I have set X to .0001 in this scenario to give a .9999 or 99.99% success rate. So log of .0001 to log base .98, once entered into the calculator is equivalent to 455.90, which rounds to approximately 456. This is the N variable. Remember, N is equal to the # of seal cards. So it takes 456 seal cards to pretty much guarantee ONE epic catch. ONE.

So what is considered 'lucky' and what is 'unlucky'?

Using the same method, with X set to .5, giving a 50% chance of catching the monster ONCE. The given value is 34.30, so approximately 34 seal cards. This is when the chance reaches exactly 50%. If you catch an epic in 34 seal cards or less, consider yourself extremely lucky. Now, setting X to .25, giving a 75% success rate for ONE catch, the result is 68.62, roughly double earlier's, or 69. If it takes you more than 69 seal cards to catch the monster, you can start feeling unlucky, but should not be shocked. Remember as well, the number is only decreasing at a .98 rate, so the chance is not raised as high as you would expect with the following cards after 75.

I hope this made everything more clear, if desired, I will post this in the General Discussion section for everyone to see.

Here is the link for the logarithmic calculator in case you want to try some rates on your own: http://www.rapidtables.com/calc/math/Log_Calculator.htm

Regards,
-Shadehawk

That was way too hard to follow at 2 am ;P makes sense though. Proves why my catching luck is horrible.

Thanks for your clear explanation.

I guess I will just deem myself very very unlucky then for spending 120-140 card to catch 1 epic for my last 4 out of 5 epic catches.

I hope the true law of probability will eventually catch up to me so at some point, I will be at to catch like 4, 5 epics each with only less than 10 card spent.

Of course, the true law of probability will only work with a large amount of samples. Maybe when I played this game for another 100 years, I will see that to happen at one point.

[Shadehawk]

Nope, the law of probability won't help you catch up. What's in the past is in the past. You have an equal chance of being lucky and unlucky in the future. There is no karma is math, sorry.

[Shadehawk]

That was way too hard to follow at 2 am ;P makes sense though. Proves why my catching luck is horrible.

Yeah, took me like an hour to write at 2 am. I had to check all of my sources and such to make sure I wasn't making any mistakes.

lol shade TL;DR
but really good job, you must be interesting in parties

[Shadehawk]

Funny Stavey, funny... cause I'm not... I speak math, that's about it

Not rub salt in a wound, on my main account, I caught Patta on the first card back when everyone was getting the first epic seal with 1 card. Then when Haypi put "No items" restrictions on SS-8, The day after they fixed it and put items back on, I caught 2 Patta with 4 cards total. I also have caught seafoam, Neo, Meniss, and I never used more than 50 cards.

Today on an alt account I sealed a Patta, it took 40 cards over about 4 attempts. But I got it.

It is all about chance and maybe a little luck. I know some players that used 200+ cards on different Epics and barely got them.

I wish you luck, you will get it soon. What I and many do too, is try sealing with say 30-40 cards. Set a limit before hand, if you don't get it, wait an hour or 2. Try again later.


Good luck!!

I see what you are saying on the first part, the 49% thing is happening to me as well. But for the second, the mathematical probability is not 50 cards = 1 catch. Many people make the mistake of adding the percentages, wherein these cases that is not how it works. It is a combination binomial of some degree. So you have a 2% chance to catch the epic, you miss, it is still 2%. It does not change to 4% just because you missed the first time.

Using exponential mathematical probability, the miss rate, .98 will go to the 'n'th power ('n' being however many seals you throw at it. So let's say you throw 50 seals at an epic. Normally, it would be assumed 50*(.2)=1=100%; therefore, after 50 shots you should have one. However, take .98^50 and you get .3641 or 36.41%, meaning you would have a 36.41% of missing all of them, or a 63.59% chance of catching it ONCE. That gives you a rough 2/3 chance of catching it as oppose to a guaranteed catch after 50 cards. You would think that after maybe 100 seal cards you would have a guaranteed catch right? Still no. Take .98^100, which would equal .1326 or 13.26%, meaning yet again, you still only have a 86.64% chance of catching it ONCE, and therefore by squaring it, a 75.06% chance of catching TWO.

So what is the "guaranteed" number of cards?

Using logs (the mathematical kind) (QUICK EXPLANATION: log of x to log base y = n translates to exponents as y^n = x.), so for this example, y is the percentage chance to miss = .98. N is the number of tries, in this case, cards thrown. X is the final product of miss chances. I have set X to .0001 in this scenario to give a .9999 or 99.99% success rate. So log of .0001 to log base .98, once entered into the calculator is equivalent to 455.90, which rounds to approximately 456. This is the N variable. Remember, N is equal to the # of seal cards. So it takes 456 seal cards to pretty much guarantee ONE epic catch. ONE.

So what is considered 'lucky' and what is 'unlucky'?

Using the same method, with X set to .5, giving a 50% chance of catching the monster ONCE. The given value is 34.30, so approximately 34 seal cards. This is when the chance reaches exactly 50%. If you catch an epic in 34 seal cards or less, consider yourself extremely lucky. Now, setting X to .25, giving a 75% success rate for ONE catch, the result is 68.62, roughly double earlier's, or 69. If it takes you more than 69 seal cards to catch the monster, you can start feeling unlucky, but should not be shocked. Remember as well, the number is only decreasing at a .98 rate, so the chance is not raised as high as you would expect with the following cards after 75.

I hope this made everything more clear, if desired, I will post this in the General Discussion section for everyone to see.

Here is the link for the logarithmic calculator in case you want to try some rates on your own: http://www.rapidtables.com/calc/math/Log_Calculator.htm

Regards,
-Shadehawk

If there was a "thanks" reward system in this forum, you would definitely get one for that post. Thank you very much, shade.