Magic Tower Portal Odds for Idiots (No Math Req’d)

[Harbinger1777]

I promise to keep this simple. All of the math is done for you by a calculator.

We are gonna calculate the odds of pulling 1 or more event 5s (s for star) from the Magic Tower Portal (Summon) in however many pulls you want.

**Caution: this tutorial only works for the Magic Tower Portal (Summon), NOT ANY OTHER SUMMON—the numbers are different for those and explaining them would make me remove the “for Idiots” from the title just kidding, but it would be rather lengthy that way.

Clues to make this easy

In the steps below: Names of the input fields on calculator tab are in bold, the numbers that you type into that field are in italics. For you visual ppl, in each step, the number in italics you need to type in the hand-scribbled yellow box in the corresponding pic given at the bottom of the step.

Also, you only need to open a single calculator tab in step (1), use the same calculator tab in all steps.

Steps:

Step (1) Open the calculator in another tab and accept the cookie thing then scroll down a little it to this part of the webpage:

Step (2) Type the number 0.013 the top input field labeled “Probability of Success on a Trial” on the calculator tab as shown in this pic:

Step (3) Note: In this step, the numbers in italics are example numbers to type in, you will need to come up with a number yourself (and this is the only number you have to think of yourself, I give three simple examples of this number later in this step).

On the calculator tab in the input field labeled “Number of Trials” type the number of pulls you want to consider (the one you need to come up with yourself). Examples: (a) so if you have 2600 gems to spend then that’s a 10x pull, so type 10 here, just like the pic; (b) if you have 1300 tower coins you wanna use, that’s 13x pulls, so type 13 here; (c) if you’re with # no spend , and you saved no gems and have no free pulls saved, type 0 here )

In the pic for this step I choose 10 to be the number you need to come up with yourself

Step (4) In the input field labeled “Number of Successes (x)” type the number 1.

Step (5) Click the blue “Calculate” button at the bottom on the calculator tab as shown below:

Step (6) Read the the odds (ie the answer) off the output field labeled “Cumulative probability P(X >= 1)” on the calculator tab as shown in the below example to be

0.12266

[which uses 10 for the number you come up with yourself in step (3)]

Note: that unless you used 10 for your number of pulls to consider in step (3), your number will generally be different from the example answer 0.12266

Last thing to do is shift the decimal two places to the right in the answer and tack on the %-symbol at the end. So for our example,

0.12266 —> 12.266%

**If decimals aren’t your thing, simply type the decimal got from the calculator tab this step (eg 0.12266) into the calculator app on your phone (not the webpage we’ve been using all along), multiply it by 100 and press the “=“ button. Shown below is what you see after pressing the “=“ button:

<End of Steps>

Let’s talk about what this percentage means a bit. If you wanted to tell your guildie the odds we just calculated in the example, you’d say that,

The chances of pulling one or more event 5s (s for star) from the Magic Tower Portal in 10 pulls is 12.266%.

[MasterTMO]

On a 10-pull from the Tower Event:

• getting all 10 3 stars (S1 or Event): 3.26%
• getting at least 1 5 star (S1 or Event): 22.37%
  ** (getting no 5 stars at all: 77.63%)
• getting at least 1 Event hero (3-5 star): 77.09%
  ** getting 0 Event heroes at all: 22.91%
• getting at least 1 Epic+ Event hero (4-5 star): 51.60%
• getting at least 1 Legendary Event hero (5 star): 12.27%

[Harbinger1777]

@MasterTMO check your discord DM from Harbinger please?

[Cheds]

You have this all wrong my friend.

The chances of getting a 5* hero are exactly 50/50

Either you get one or you don’t. Much simpler maths for everyone to understand

[drdare]

All these probability makes sense only if the numbers work naturally. The whole random number is not statistically consistent as there are a few who have made at least 150 pulls to get no legends, and there are a few who do a 3 single pull to get 3 legends.
The probability of getting a legend is just 50%. Either you get it or you dont get it. And much to my observation in the last 3 years is that the randomness of a successful pull has been related to quadrant of the time. I had more success when pulling in a specific quadrant of the time. My success was usually when I pulled between 40second and 50 second window in the the even hours, where I also use to get the HOTM. During odd hours i used to pull between 20 and 30 seconds. I made a successful pull in this portal using this method even yesterday twice.
There is no true random number gen that is setup in the game, It is just controlled randomness using patterns.

[Senyagami]

Can you explain more about your pattern?

[ffphier]

[drdare]

I am not a spender and pull only once a month with one offer (a total of 20 pulls a month)
So I tracked the successful pulls based on time of pull since 2019.
Of the successful 90+ unique legends I pulled 47 of them were landed between the 20 to 30 seconds in the odd (1, 3, 5, 7, 9…) hours.
But problem is there is 10 seconds and i havent been able to narrow down lesser that that.
The rest of the cards were pulled between 40 to 50 seconds of the even (2,4,6…) hours. This hour has been most successful with my HOTM cards. I used this to some decent success for HOTM.

My other patterns is the 6 day tile cycle.
Day 1 is tank’s strong tile. So of red tank you get good ratio of blue tiles and so on…
Day 2 is flank strong colour tiles
Day 3 is the opposite flank color tiles
Day 4 is wing strong colour tiles
Day 5 is the opposite wing color tiles
Day 6 for me is green major. Whatever tank it is or whatever teams i bring to fight i get overwhelming green tiles.
The key is to find the pattern that follows the days for each one.
I ran this test on my 2nd account in early 2021 for 3 months and I found the pattern consistent, just that the days were different. My 1st account day 1 was day 4 on my 2nd account.

[Senyagami]

Interesting and why hours, seconds but not minutes?

[Harbinger1777]

@Cheds I’m wondering if the universe had decided to answer my longing for a pet troll.

Lmao either I win the mega millions lottery jackpot, or I don’t. Therefore the lottery is isomorphic to flipping a coin.

[Cheds]

That is exactly correct!

Makes odds more personal when it’s a 50/50.

Like yesterday when I crossed a road with the odds being 50/50 whether I’d get run over or not. Makes you feel alive when you keep winning these 50/50’s

[drdare]

Because I couldn’t make any sense back then with the minute parameter.
I just stopped tracking everything last year as i realised i am not enjoying the game anymore due to all the nerfs and impractical cards that were released.
I do play but not with as much fun as I used to before.

[DGERic]

@drdare

So I tracked the successful pulls based on time of pull since 2019.
Of the successful 90+ unique legends I pulled 47 of them were landed between the 20 to 30 seconds in the odd (1, 3, 5, 7, 9…) hours.
[…]
The rest of the cards were pulled between 40 to 50 seconds of the even (2,4,6…) hours. This hour has been most successful with my HOTM cards. I used this to some decent success for HOTM.

I must be missing something here. The way I read this it sounds like you’ve pulled ~half your 5*'s in odd hours between 20-30 seconds… and you’ve pulled the other ~half of your 5*'s in even hours between 40-50 seconds.

From that I can conclude one of two things:

1. If you only pull at those two times then that outcome makes perfect logical sense: you get half your 5*'s in one 10 second window and half in another 10 second window.
2. But… if you’re also pulling at a bunch of other times and never getting 5* results at those other times, then this is absolutely amazing data.

[Senyagami]

I’ll try this pattern, thanks!

[drdare]

I was able to limit the time frame for single pulls or coin/ token pulls with a decent success rate. (I couldn’t replicate this logic on the ETT pulls)
But when I do a 10x pull i try to time my pull to start at the 19th sec to maximise the chance to use both the windows.
My latest success with a 10x pull was yesterday where I pulled Justice on the 22nd sec and pulled Telonius in the 40 to 50 sec window. I did not land the HOTM though as I didn’t check which hour I was pulling.
My success when i start a 10x pull at the 0th/ 30th/ 40th second has always been 0. But with 19th or 26th sec i land something for sure.
As I do not pull a lot due to my budget criteria, i cannot validate the data on a larger dataset. But every month I land at least 1 legend even though sometimes it is a S1 card.

[DGERic]

@drdare

I am not a spender and pull only once a month with one offer (a total of 20 pulls a month)
So I tracked the successful pulls based on time of pull since 2019.

If you started mid-2019 that’d be 46 months of data, at 20 pulls/month for 920 pulls. If you’ve got 90+ 5*'s from that then you’re at a ~10% success pull rate which is well above the published ~2.5%

@drdare

My success when i start a 10x pull at the 0th/ 30th/ 40th second has always been 0. But with 19th or 26th sec i land something for sure.

Again, if true, that is absolutely amazing data.

If you have 90-ish 5*'s on 92-ish 10x pulls that tracks really well with “landing something for sure”. But… it doesn’t give any chances for any pulls at other times like 0th, 30th, 40th seconds. So something is not adding up.

[drdare]

Yes, I have tried to reason that logic of failed 10x pulls when it is starting at 0/30/40, but I never made any correlation. It might be even dumb luck. So I always stick to what works for me. All these observations worked for me and I cannot say this will work for anyone else.
I have tried the other methods of pulling that is discussed in the forum (Eg., pulling a 3* troop from a single summon and then running 10x). None of them have worked for me ever.
So my observation is something that works for me and I am not recommending this as a working mechanism in the system design.
But if people start looking for such time bound patterns, there is always a way to make it work.
My old alliance friend and I worked on such time based observations and we had a strong run so far. Though his data is different. But what works for him doesnt work for me and vise versa.

We actually started doing this back in the days when we observed that whenever we collect feeders from TC2, we used to get 2* in even seconds and 1 star in odd seconds. We successfully made it work always until them made the collect all feature. Even then, if it is a single collect we used to make it work. Finally, we made the same observations when pulling from the silver coins from daily portal. I used the 20-30 and 40-50 to window to see if i pull any 3stars from there. I did not track the pulls, but i did make a hand full of 3* troops.

Also this works for mystic vision. I regularly pulled decent drops when i pulled on any of the 10th second. 0, 10, 20 … 50)
I used to land a few good 4* loots using this, but it became to cumbersome to look for a clock everytime i opened mystic .