Chance to đŸ§± 4 options twice = 44.5% (5 is 57%)

PC General Discussion
41

Ask the math experts – like yourself. I already said I don’t know the answer. Or was all that Bayes Theorem talk of yours just hot air?

42

You’re the one who said Urza is “All Wrong.” Now you’re saying I’m the one to blame? LOL.

A little self-awareness, please.

43

EDIT: I mistakenly did the original post with 6 rolls when you actually get 7 rolls. I’ll leave the original text but I calculate the chance to brick temper with 4 option in both slots at 49%. Its 7 rolls, 4 options is 16284 total permutations, with 8019 permutation being bricks. 8019/16284 = 0.4894

i.e. 51% chance to succeed.

— original text calculated with six rolls instead of seven —

With six rolls on two temper slots, each with 4 options I calculate the chance that BOTH slots will NOT get the desired option to be ~53%. i.e. 53% chance to brick.

Explanation:

The total number of possible permutation of 4 options in 6 rolls is 4096 (4 to the power of 6).

Each permutation is a sequence of six rolls; a sequence of failures and successes.

  • a failure is a roll where the outcome is one of the three options you do NOT want
  • a success is a roll where the outcome is the single option you do want

Lets represnt fails as a little ‘x’ and successes as a big ‘X.’ Now we can represent a set of permutations (six rolls) as a string of ‘x’ and ‘X’.

There will be 64 (2 to power of 6) such strings:

  • xxxxxx (all fails)
  • xxxxxX (last roll succeeded)
  • xxxxXx
  • 

  • XXXXXx
  • XXXXXX (all success)

Every string that has only a single big ‘X’ or no big ‘X’ at all is a brick. Every string that has more than one big ‘X’ is not a brick.

There are only seven strings that are bricks.

  • xxxxxx
  • xxxxxX
  • xxxxXx
  • xxxXxx
  • xxXxxx
  • xXxxxx
  • Xxxxxx

The trick to remember is that each big ‘X’ is a single option, while every little ‘x’ represents 3 possible options. Meaning the above strings do not represent a single permutation, but a set of permutations.
e.g. there are 729 (3 to the power of 6) permutations represented by the string ‘xxxxxx’ and 243 (3 to the power of 5) permutations presented by the strings with a single big X.

So the total ‘brick’ permutations are

  • xxxxxx = 729 permutations
  • xxxxxX = 243 permutations
  • xxxxXx = 243 permutations
  • xxxXxx = 243 permutations
  • xxXxxx = 243 permutations
  • xXxxxx = 243 permutations
  • Xxxxxx = 243 permutations

or 729 + (6 * 243) = 2187.

Meaning there are 2187 failstates (bricks) out of the total 4096 possibilities.

2187/4096 = 0.5339

Or a ~47% chance to get what you desired on both slots.

Thats what I get.

Obviously a player doesn’t keep rolling once they get two success, but that is irrelevant when looking at the total possibility space to calculate the probability.

Check my work.

1 Like
44

just gonna delete this for now, will come back with fresh eyes in the morning.

45

Well the problem arises in how is the thing being calculated, the odds of getting an affix should be equally distributed, but, the code has a pre-gemerated set of numbers aka seeds, that nobody knows hows being generated, therefore options can be excluded and our math cant fit, therefore I said before that your math is right but but must be “restarted” every try. Theres nothing that tells you that getting x increments or lowers thethe posibility of gettin y, known as conditional probability, i would not spend time in this as everything you try will fail for a single individual ans would only work for an infinite number of tries

46

Right, well my answer is that I want the expected outcome to be a mid roll of a mid affix for your build, but for there to be a chance of getting an even better affix in each slot, so that you occasionally get that awesome top-end outcome. I want the low-end outcome to still improve the base item in some way that is relevant to your build.

I also think maybe chance to cast twice, as much fun as it is, is too powerful / important to be part of the mechanic with limited chances. They should turn those powers into aspects and then focus more on stuff you have to invest in to see the big gains, like LHC, effect size, effect / cc duration, CDR.

47

I strive to push hard. i made it to 123 pre nerf. that was the limit for my gear. My bow was a single ga dex bow that I got on day 3. I must say its very feels bad farming for 3 weeks hard and never getting a upgrade because tempering bricks them all. 4 good bricked bows in stash bricked and dozens of other items all bricked.

48

I think your math checks out. Basically came to the same conclusion.

So I defined ‘1’ as success and ‘0’ as non success. Meaning getting the right Temper but if you want to allow rerolling one could just multiply the chance of hitting the temper with the chance of hitting the desired range.

Then i listed all “possible” events. (you wouldn’t reroll a max Temper :wink: )
So the Bracket denote first and second temper.
the number behind is the percentage of this event to occure.
the zero Temper is just printed once but in fact must be calculated for every ‘pyramid’ and averaged.

if both Tempers have the same percentage you can skip the second iteration otherwise you have to calculate with switched first and second chance and average afterwards.

chances
first:0.25
second:0.25
[1][1]                : 0.0625
[1][0, 1]             : 0.046875
[1][0, 0, 1]          : 0.03515625
[1][0, 0, 0, 1]       : 0.0263671875
[1][0, 0, 0, 0, 1]    : 0.019775390625
[1][0, 0, 0, 0, 0, 1] : 0.01483154296875
[1][0, 0, 0, 0, 0, 0] : 0.04449462890625
[0, 1][1]             : 0.046875
[0, 1][0, 1]          : 0.03515625
[0, 1][0, 0, 1]       : 0.0263671875
[0, 1][0, 0, 0, 1]    : 0.019775390625
[0, 1][0, 0, 0, 0, 1] : 0.01483154296875
[0, 1][0, 0, 0, 0, 0] : 0.04449462890625
[0, 0, 1][1]          : 0.03515625
[0, 0, 1][0, 1]       : 0.0263671875
[0, 0, 1][0, 0, 1]    : 0.019775390625
[0, 0, 1][0, 0, 0, 1] : 0.01483154296875
[0, 0, 1][0, 0, 0, 0] : 0.04449462890625
[0, 0, 0, 1][1]       : 0.0263671875
[0, 0, 0, 1][0, 1]    : 0.019775390625
[0, 0, 0, 1][0, 0, 1] : 0.01483154296875
[0, 0, 0, 1][0, 0, 0] : 0.04449462890625
[0, 0, 0, 0, 1][1]    : 0.019775390625
[0, 0, 0, 0, 1][0, 1] : 0.01483154296875
[0, 0, 0, 0, 1][0, 0] : 0.04449462890625
[0, 0, 0, 0, 0, 1][1] : 0.01483154296875
[0, 0, 0, 0, 0, 1][0] : 0.04449462890625
[0, 0, 0, 0, 0, 0][1] : 0.04449462890625
[0, 0, 0, 0, 0, 0, 0] : 0.13348388671875
---
chances
first:0.25
second:0.25
[1][1]                : 0.0625
[1][0, 1]             : 0.046875
[1][0, 0, 1]          : 0.03515625
[1][0, 0, 0, 1]       : 0.0263671875
[1][0, 0, 0, 0, 1]    : 0.019775390625
[1][0, 0, 0, 0, 0, 1] : 0.01483154296875
[1][0, 0, 0, 0, 0, 0] : 0.04449462890625
[0, 1][1]             : 0.046875
[0, 1][0, 1]          : 0.03515625
[0, 1][0, 0, 1]       : 0.0263671875
[0, 1][0, 0, 0, 1]    : 0.019775390625
[0, 1][0, 0, 0, 0, 1] : 0.01483154296875
[0, 1][0, 0, 0, 0, 0] : 0.04449462890625
[0, 0, 1][1]          : 0.03515625
[0, 0, 1][0, 1]       : 0.0263671875
[0, 0, 1][0, 0, 1]    : 0.019775390625
[0, 0, 1][0, 0, 0, 1] : 0.01483154296875
[0, 0, 1][0, 0, 0, 0] : 0.04449462890625
[0, 0, 0, 1][1]       : 0.0263671875
[0, 0, 0, 1][0, 1]    : 0.019775390625
[0, 0, 0, 1][0, 0, 1] : 0.01483154296875
[0, 0, 0, 1][0, 0, 0] : 0.04449462890625
[0, 0, 0, 0, 1][1]    : 0.019775390625
[0, 0, 0, 0, 1][0, 1] : 0.01483154296875
[0, 0, 0, 0, 1][0, 0] : 0.04449462890625
[0, 0, 0, 0, 0, 1][1] : 0.01483154296875
[0, 0, 0, 0, 0, 1][0] : 0.04449462890625
[0, 0, 0, 0, 0, 0][1] : 0.04449462890625
[0, 0, 0, 0, 0, 0, 0] : 0.13348388671875
---
attempts:7
zero:0.13348388671875
one:0.31146240234375
two:0.5550537109375
useful:0.86651611328125
bricked:0.4449462890625
debug:1.0
3 Likes
49

The reason none who knows how to do it is doing it is because it’s exceptionally complicated and not worth the trouble. All the options listed here incpuding the op give a close enough approximation that it doesn’t really matter as far as the point of the discussion.

As for the discussion, Urza asked “how is it good design”, and it’s perfectly fine when people don’t convince themselves that they are owed the item once it’s got 3 affixes. However hard it is to temper, it’s not in the same ballpark as rolling the final two affixes on a piece of gear was prior to s4.

The only “fix” tempering needs is an attitude adjustment from players.

That said, I’m neither here nor there if they end up changing it due to the ludicrous noise it has brought on. Either they leave it and silly people get annoyed, or they change it and gearing is even easier
 win win.

2 Likes
50

I can’t agree with this more.

The entire discussion that people like Urza keep repeating is based solely on the assumption that their first piece of gear needs to be a success.

No one can defeat the argument that it’s purely emotional. So they say stuff like “but the math!” and ignore the math comparing the new system to the old system. The unequivocal truth is the new system is mathematically better in every way.

People are just crying because they can’t fathom the temper system is replacing the 4th affix, they don’t get that it’s not a tacked on system.

I’ve already posted the comparison math before but they’re ignoring it on purpose.

You need to brick 38 items to be equal to a 4/4 item drop odds.

They’re crying about bricking 1 or 2.

It’s the players not the system.

2 Likes
51

I think math does check out. From me and others calculated to about 4 difference from 45-49%.

I dont think attitude adjustment is needed from players. Its needed from devs. Separate manuals more so bricks dont happen. I showed in my temper 2.0 post. Absolutely 0 reason Im going for orb enchant and keep getting frost bolt. Should be orb manual and ice shard manual ect. Feel guds always beat feel bads. Players are going to only brick so many items before they give up. That is the reality. Maybe we are spoiled. Maybe we are impatient. Maybe we are even gearing easier. Doesnt matter. Reality is still reality and if temper bricks are making ppl quit (which they can figure out with metrics) then change will come. Doesnt matter what we think because quit players dont spend in shop.

Like Mark Rosewater said on card in mtg design it dint matter how a particular card in tourneys was worded correctly but played wrong. Players kept playing it wrong based on wording so the design fault was on wizards of the coast and him. Same here. The perception is bricking is too easy and its affecting players in a big negative way even if we arent bricking as much as we think.

Either change manuals so bricks dont happen or make resplendent sparks reset them.

We can solve this so everyone wins. Keep system in tact. Prevent bricks.

52

Why do you think everyone needs to hear what you say so frequently? Where did your ego come from?

Stop making new threads every time you shart out an idea; they just aren’t that good.

When it has been explained at length that tempering is a massive upgrade to the previous system and that you are much more likely to successfully get items than ever in the past, and you continue to complain about how hard it is to get items, that’s called wilful ignorance. Every single solution that involves increasing the likelihood to successfully temper involves a mandatory reduction in the likelihood of getting the base item in the first place.

https://steamcharts.com/app/2344520

For all the whining going on in the forums, the average D4 player is simply playing the game, having fun, tempering and all. The peak player count for the season happened in late week 3, and there are still as many players playing today as there were on the day the season released. For most people, this is simply not an issue that is stopping them from playing. Other ARPGs would kill to sustain that kind of population. Quit players don’t spend money, you say? Isn’t it lucky, then, that the season has the best retention of any ARPG season so far on steam?

Peak population on opening weekend on steam was 28835, Sunday May 19. Seasonal peak so far is ~38300, Sun-Mon Jun 9-10. June 19, today, peak concurrence 28837. Players are enjoying this season, and sustaining 100% (or more) of your opening seasonal population for a Month is insane. Tempering is the biggest change of the season, so pretending it’s having a wide effect on player engagement that isn’t a positive one is also insane.

2 Likes
53

We gotten boys! Lets keep it up. Just kidding. After the past few days I understand the filter at crafting, rather than the filter at drop is a valid style of itemization, it’s just not one I prefer.

FWIW I haven’t seen this yet, do you have a link to your post?

Yep, Once I saw what you were doing I get 44.5% (@25/75) & 57.7 (@20/80). Granted this is an average with a strict version of success. There are cases where people will trend high or low, others where a 2nd non-optimal choice is still workable etc.

1 Like
54

Forgive me I made a mistake since I was reporting my findings from memory. It’s 33 to 1, not 38.

But, getting a 4/4 ring with any value of desired affix is 0.00000037~ roughly. Since I can’t enchant legacy items I can’t verify total affix choices but I wrote down 42 for a necro ring when I was doing some S2 maths. I’m assuming that was accurate at the time.

The S4 change is down to 19 affix results for a necro ring. That means to get a 3/3 you’re at 0.00017~ roughly.

If you were to use an offensive and resource temper, averaging 4 and 3.5 results respectively, that means you’re looking at a result of 3/3 and 2 desired tempers at 0.000012~ roughly.

The better odds of 0.000012 over 0.00000037 results in 33x better odds. So effectively that means you can blow 32 out of 33 tempers on rings only and be exactly where you were before.

Now, let’s assume my handwritten number is wrong, say it’s 32 instead of 42. That’s still 10.6 to 1. Now let’s say it’s something we know isn’t actually true, let’s say they both have the same number of affixes, 19. That makes getting a 3/3+2 odds of 1.14 to a single 4/4 item. That’s right, it’s easier to get the desired 3 stats and 2 tempers than a single 4/4 drop if the number of affixes were equal (but we know they’re not equal).

Before people chime in with “weighted affixes!”
 they’ve always been weighted. They’re both equal in that regard so it’s a non-factor.

Different pieces of gear result in different odds, but all in all this should prove that people crying about blowing tempers are not aware of the actual odds.

When it comes to getting 4/4 max rolls the old way the odds are extraordinarily low. We don’t have exact odds on GA drops but they’re pretty common. Without having direct numbers, it’s safe to say it’s a fact that 3GA items are less rare than 4/4 max items. Anecdotally, I’ve gotten several 3GA I’ve traded and salvaged, never got a 4/4 anything though.

2 Likes
55

I think there are some affixes that are much rarer this season than any were in previous seasons. Like a 1 in 100. There’s also GAs, which are very rare. So compared to last season, it’s much rarer to find a near-perfect item (2 BiS GAs that aren’t just max life or main stat + 2 useful tempers). That’s one of the reasons people are still playing: there’s still something to chase.

Unlimited temper rerolls would ruin this dynamic, but having the weaker rolls still do something useful would be much more interesting than the current system of 3-4 complete blanks and 1 godly affix.

56

I agree and disagree with this.

I believe most of the whining and complaining comes from players having the wrong attitude and expectations.

However, that doesn’t mean the system is without fault.

In general IMO a crafting system like this, in a game like this, should give a chance to win big and not to lose (just win smaller). This can be done through perception/presentation or actuality.

The MW and GA systems in loot reborn mostly do it this way, and you still see people complaining and throwing tantrums. That’s why I agree with you
 it’s the players.

But I do think temper is tuned wrong if not the wrong system for this. At the least the manuals need to be adjusted to smooth out/eliminate the losing conditions.

You can absolutely get a completely useless affix for your build in tempering and that a loss with little way to be perceived as a win.

A slot machine at a casino tries its very best to make you feel like you have won even when you have definitely lost. That’s what is needed here.

57

Thing is previously you only have to save enough to buy a GG item.

Now it doesn’t matter if you spend 20 trillion you can brick every single one of them.

It’s so much easier before


58

Yeah, I miss the way yellows used to be. If you couldn’t find what you needed, especially on amulets you could go see the vendor. Now yellows are just trash.

59

3GA’s are not as rare as 4/4 items.

That’s an expectation issue. As I just demonstrated with math, you have to brick 33 rings to miss out. No one has bricked 33 rings without getting their preferred tempers. So players have easier entry into that last item starting point (drop odds are so much better), better odds at success once you get there.

Because again
 have you failed 33 items in every slot? No? Then you’re not worse off than finding a 4/4.

You still can though. You can still make a rare into a legendary. Or are you just saying that 1 affix less breaks the game?

Have you failed 33 items in every slot? No? Then you’re not worse off than finding a 4/4. Simple as that.

60

I don’t know what they did but didn’t rob just brick 2 items back to back trying to roll 1 stat even using the so called pity system? So I think it’s just random % every go and for some reason vuln and crit seem to roll a lot less then other stats, I’ve bricked sooo many