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New Tokens with less RNG since it makes people feel good

HadronicHadronic Posts: 323 Mover and Shaker
Alright, so after the great unhoarding thread and now this limiting cascades thread it seems there is a desire for less RNG. 

So I cranked some numbers in my computer and came up with a new token. I had a few goals i was trying to acheive when picking the numbers.

  • I wanted the average of the distribution to be the same as the current token (this is to appease the devs as it means they giving away same average number of rewards)
  •  I wanted the variance of the distribution to be narrower. Meaning everyone will be closer to the expected result on both sides. This is a double edged sword, while it means you're less likely to get burned, its simultaneously harder to get way ahead of the pack based purely on luck.
  • I wanted streak breakers cause no one likes going 80 pulls in a row with no 5*

After playing around with the numbers i found some values that satisfy all 3 of these conditions. Here we have a hybrid token (Hybrid between a binomial distribution and a vaulted distribution)



Increasing the odds after pull 8 like a 15 item vault creates the streak breaking mechanic, but at the same time it would shift the average up. In order to maintain the same average, the binomial distribution odds had to be lowered to 1/8 (currently 3/20).

Using this table, for the new token, I then generated the new distributions to compare to the current Legendary Tokens.
Blue curve - Current Legendary Tokens
Red curve - Hybrid Token


This plot clearly shows the streak breaker in action.


The PDF changes based on the number of total pulls (Similar to a Binomial Distibution) therefore I had to choose a specific value for N. I went with 300 since that is a common target for people opening giant hoards to cover 3 fives at a time.


The average is almost identical (45.08 which is a marginal improvement over 45) but the variance has dropped from 6.2 to a 4.5 producing a much taller and narrower spike.

Another thing to point out which isn't visible in the plot, but the red PDF actually goes to 0 below 20 (because of the streak breaker) but the blue cover has a non zero chance of pulling < 20 5* on 300 pulls.

There are other more complicated ways of accomplishing this but i went with this hybrid method cause both of these token types already exist in game, so presumably its easier to code. 

Comments

  • QuebbsterQuebbster Posts: 7,535 Chairperson of the Boards
    ...I don't get it. Can you dumb it down a bit?
  • jameshjamesh Posts: 965 Critical Contributor
    edited June 13
    If I understand it right, he's suggesting this:
    let P be the probability of drawing a 5* character
    let N be the number of tokens since the last 5* was drawn
    
    P = { 1/8      if N < 8
        { 1/(16-N) if N >= 8
    At N=15, you'd be P rises to a 100% chance of pulling a 5*, at which point N resets.

    The premise is that this should offer similar odds to the current legendary tokens' 1:7 odds due to the guarantee that you'll get at least one 5* every 16 tokens.
  • Arix90Arix90 Posts: 238 Tile Toppler
    edited June 13
    Fire emblem heroes raises 5* odds by 0.25% every pull when you draw a lesser tier and then resets once you pull a 5* we need something similar 
  • HoundofShadowHoundofShadow Posts: 1,161 Chairperson of the Boards
    You should do a calculation for how much Iso-8 the devs should allow players to earn per day as well Because that's the obvious complaints followed by Roster Slots if you improve the RNG problem.
  • brollbroll Posts: 4,333 Chairperson of the Boards
    Quebbster said:
    ...I don't get it. Can you dumb it down a bit?
    I think what he's suggesting is variable odds on 5* pulls.  So when each time you pull an LT your odds change based on how long it's been since you got a 5*.  First pull your odds are only 6% (lower than the constant 12.5% now), but at 8 pulls it evens out to 12.5% and by the 15th pull if you haven't gotten a 5* you are guaranteed one.

    Either that or he's suggesting they replace the LT stores with 15 item vaults with 1 5* and 14 4*s.

    Also I thought the actual odds were 15% (~1:7) not 12.5% (exactly 1:8)?
  • HadronicHadronic Posts: 323 Mover and Shaker
    jamesh said:
    If I understand it right, he's suggesting this:
    let P be the probability of drawing a 5* character
    let N be the number of tokens since the last 5* was drawn
    
    P = { 1/8      if N < 8
        { 1/(16-N) if N >= 8
    At N=15, you'd be P rises to a 100% chance of pulling a 5*, at which point N resets.

    The premise is that this should offer similar odds to the current legendary tokens' 1:7 odds due to the guarantee that you'll get at least one 5* every 16 tokens.
    you understand it right
  • smkspysmkspy Posts: 2,010 Chairperson of the Boards
    edited June 13
    Just make true streak breakers, a guaranteed 5 on a ten pull of getting nine straight 4s...if dreams had wings.
  • DormammuDormammu Posts: 2,841 Chairperson of the Boards
    Ummmm, can you repeat all the stuff about the things?  :dizzy:
  • bbiglerbbigler Posts: 939 Critical Contributor
    edited June 13
    There have been many great ideas recommended on this forum over the years, and one thing I learned from all these discussions is that they will never implement what you recommend no matter how good an idea it is.  This is probably a simple fact that the devs don't read these posts and Brigby doesn't relay these ideas back to them (probably because they already have future dev plans anyway and don't want to try ideas that aren't their own). 

    What I do see is that they hear our complaints, but they come up with their own solutions.  So, I've stopped trying to recommend specific improvements to the game.  Correct me if I'm wrong, but have they ever implemented exactly what we recommend? 

    It's like this: we complain that we're hungry and ask them for an apple to eat; they hear our complaint and then give us a rice cake.  It may help a little, but it's not what we wanted and not very fulfilling.  We then figure out how to survive eating their rice cakes, but the complaining continues.
  • DAZ0273DAZ0273 Posts: 1,373 Chairperson of the Boards
    Dormammu said:
    Ummmm, can you repeat all the stuff about the things?  :dizzy:
    This is probably how Skynet gets created.
  • HadronicHadronic Posts: 323 Mover and Shaker
    smkspy said:
    Just make true streak breakers, a guaranteed 5 on a ten pull of getting nine straight 4s...if dreams had wings.
    this is a streak breaker, (the numbers are just larger)
    a guaranteed 5 on a fifteen pull of getting fourteen straight 4s
  • smkspysmkspy Posts: 2,010 Chairperson of the Boards
    Hadronic said:
    smkspy said:
    Just make true streak breakers, a guaranteed 5 on a ten pull of getting nine straight 4s...if dreams had wings.
    this is a streak breaker, (the numbers are just larger)
    a guaranteed 5 on a fifteen pull of getting fourteen straight 
    Yeah, got that...just worded my post poorly, shrugs.
  • skittledaddyskittledaddy Posts: 157 Tile Toppler
    I'm not saying I'm one of them, but are there circumstances where players wouldn't want a gauranteed 5*?
    Just curious...
  • crackninjacrackninja Posts: 234 Tile Toppler
    I actually kind of like the rng side of things... not that I enjoy the 0 for 40 streaks, but it makes things more unpredictable, by nature, and therefore less mechanical. If my planning always panned out exactly as predicted, personally, I would get bored.
    As far as meeting your goals though, yes, this proposed token looks solid.
  • Pants1000Pants1000 Posts: 462 Mover and Shaker
    An easier solution could be legendary 7-pack that guaranteed 6 4* and 1 5*.  If people wanted to avoid RNG, they could save up and buy that.
  • HadronicHadronic Posts: 323 Mover and Shaker
    Pants1000 said:
    An easier solution could be legendary 7-pack that guaranteed 6 4* and 1 5*.  If people wanted to avoid RNG, they could save up and buy that.
    I thought of this but didn't want to completely remove RNG. Just wanted to step it down a notch or two by narrowing the spread. Your idea would lead to a delta function.
    As crackninja states, a little RNG adds excitement. It's fun to beat the odds.
  • HendrossHendross Posts: 750 Critical Contributor
    edited June 13
    How about a 175cp (7*25) Infinity Legendary Token of infinite pulls, that dissolves once you "randomly" pull a 5-star.  Then we can hear people who don't pull enough 4-stars or those who receive a 5-star too soon complain and the "dry" spell recipient can rejoice. 
  • JSP869JSP869 Posts: 394 Mover and Shaker
    I'm not saying I'm one of them, but are there circumstances where players wouldn't want a gauranteed 5*?
    Just curious...

    If you're playing optimally, I don't think you should be opening Legendaries until you have a solid stable of already championed 3* characters, because you shouldn't be trying to fly before you can run (or something like that). You also shouldn't be opening Legendaries unless you have the HP to roster someone new, but that's a given.

    I get that you'd maybe rather not tie up a roster slot with a single-cover 5* for whom it may take you several months (if not a lot longer) to get another cover, but if you want to be able to do all of the Essential nodes in every PvE event, well, this is Marvel Poke-Quest and you've gotta catch 'em all.

    That said, a PvP-focused player recently posted either here or on Reddit about their experience not only not rostering any 5*s they pulled but soft-capping all of their 4*s, too. In doing so they developed a strong roster while still keeping their MMR in check and they were apparently having a relatively easy time in PvP as a result.

    That could be why someone may not want to roster any of the 5*s.

  • T_REZ5000T_REZ5000 Posts: 99 Match Maker
    edited June 14
    This is exactly what I was hoping someone would calculate.  Keeps the overall average the same but reins in the variance so there’s a much lower chance of people getting totally  screwed on their 300 pull hoards (like that guy in the pulling for Cap thread).

    thanks for taking the time to post this Hadronic.  Hopefully the devs see this and at least consider making a similar change.
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