After 12,000 Rolls, I rolled the Flavor of Time

Well, then it comes down to wording Iria.
In my opinion 63 % = very likely.

Which exact value is your definition of very likely?

Anyhow, ty for the numbers. How did you come up with them?
Figuring out the probability of each roll on your own and then multiplying them? Or is there any sort of geeky program / website for that?

For the life of me, I can’t figure out why you would do this.

Well, a rather philosophical question, isn’t it?

Why sit infront of a computer at home anyhow, if you do so at work already? ^^

Assuming a FoT has a 1890 out of 1891 to be bad. If you roll 1891 of them in a row, you have a (1890/1891)^1891 chance that they are all bad. If you subtract 1 from that chance, you get the probability at least one is good which approaches 1 - 1/e for rare (1/n) events after n tries.

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Yes, it may surprise you but i do know that xD.

I meant, how did you come up with the 1891 in the first place?
“Probability of a FoT with (cold, crit, crit, socket): 1 in 1891

Edit.

I am confused. 1890/1891 delivers a value smaller than 1.
If i multiply this with itself 1891 times i end up at 0.3677

So then it should be:

1- (1890/1891)^1891, right? Otherwise i end up at…well 0.3677 - 1 = negative chance of getting it → rolling till the end of time

Because I enjoy it is the obvious answer. I just can’t imagine someone enjoying reforging something 12,000 times. I guess to each their own.

That is the chance that all the FoT’s are bad. I mistyped about subtracting 1, I should have said subtract that chance from 1 to get the chance of at least one good FoT.

Short answer: Markov chains.

Longer answer (see this post): So which do you think will be harder to get - #16 by Iria-1342

https://i.ibb.co/j866jxJ/ptr.png

Ahh a chain multiplication of probabilities is called Markov chain? neat

It’s a bit of overkill since Markov chains can be used in more complex setups. I just used simple chains (no branches or cycles) by considering each affix rolled one by one.

Ty , thats what i wanted to know.

Whats the advantage of Markov Chains over Monte Carlo Simulations?
Aren’t they superior for any combination of random events?

Scenario…
You are in a swimming pool and one of two things happens when you press it…

  1. 63% = a large bottle of champagne is handed to you
  2. 37% = a hungry shark in a feeding frenzy is let into the pool

Would you feel it very likely that you’d get the champagne?

Things are usually measured by confidence levels, e.g. whilst the expected value might be 1 in 1891, you’d calculate how many attempts it would take to have a 95% or higher likelihood of having one or more successes. In that scenario you’d be working out a value for X that satisfies…

(1890/1891)^X =< 0.05

In that example, the lowest value for X is 5664, i.e. to have a 95% confidence of getting at least one success, you’d need to carry out 5664 reforges, which is almost three times as many as the expected value occurrence.

Monte Carlo simulations are useful when you want to learn how an output distribution behaves given inputs with their own distributions. You need to have access to the generating function (i.e. the cube responsible for rolling amulets) though and virtually infinite crafting materials. The drawback is that they don’t provide the exact answer but rather converge (slowly) to the correct distribution.

Markov chains, as I used them, provide an exact answer on the probability (given the data I based my assumptions on is accurate). If you already know the probability weights for different items and affixes, it makes sense to use a deterministic method like Markov chains.

If instead, I didn’t have any data-mined information on the affix weights and only had an amulet simulator (e.g. rerolling a lot of amulets on PTR). Then you can estimate probability of a good amulet with a lot of trials (and a lot of materials).

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i wouldnt waste 600,000 souls or 12,000 bounty mats to reforge any gear.

Reason : Even if I eventually get a GG primal FoT that gives 16% more damage, i could have gained more than 16% damage and more toughness through mainstat from farming paragons in greater rifts.

Items may not be BIS after each patch. But paragons are always here to stay.

Yes, absolutly!

Also my successrate really depends on the Bottleplacement and the Poolsize in this case

Almost two times out of three, I’d steal your champagne after you get eaten by the shark it seems. :wink:

Can I bring my spear gun to this scenario? Then I can impale whoever tries to steal my bubbles.

But thats just 37% chance of champagne for you then…

I’d rather make a reality show out of this.
American Shark Warrior - TV where the first price are 3 Bottles of Champagne and a Life Insurance and then buy as much champagne as i want from all the income this braindead show generates

i have an ancient perfect one (main stat , chc , chd , cdr) but without legendary power :smiley:

I sit on many boring conference calls…

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