All the tokens for Season XXV

simonsez

CT1888 wrote:

Take that out to the last 4 seasons, where he got 8 Iceman covers from 143; using the same numbers as above, you'd expect 5.36 covers of any character on an even spread.
Over 10 seasons, this clump of 4 will in all likelihood dissappear into the data.
Given the sample sizes we are looking at here, I can't see the as broken as, I have inferred, you do. Please illuminate me.

I'm not interested in what he's gotten over 4 seasons or 10 seasons. I'm not claiming that the odds are in a state of permanent skew. I fully expect over a long period of time they do balance the odds. What I'm saying is, there's some mechanism in place that skews them in the short term (think something like vaults). I don't understand why it's so hard to follow. Based on the odds we're expected to believe, you should not expect to see 4 dupes in 34 pulls. It's pretty basic probability. <1% outcomes shouldn't keep happening at the regularity we keep seeing.

simonsez

Daiches wrote:

I will add my pulls of the season as well

Congratulations on getting 4 X23 purples. You had 52 pulls, so the chances of this happening aren't as remote as the OP pulling a 4-bagger in 34 pulls, but yours was still a less-than-likely event.

carrion_pigeons

simonsez wrote:

CT1888 wrote:

Take that out to the last 4 seasons, where he got 8 Iceman covers from 143; using the same numbers as above, you'd expect 5.36 covers of any character on an even spread.
Over 10 seasons, this clump of 4 will in all likelihood dissappear into the data.
Given the sample sizes we are looking at here, I can't see the as broken as, I have inferred, you do. Please illuminate me.

I'm not interested in what he's gotten over 4 seasons or 10 seasons. I'm not claiming that the odds are in a state of permanent skew. I fully expect over a long period of time they do balance the odds. What I'm saying is, there's some mechanism in place that skews them in the short term (think something like vaults). I don't understand why it's so hard to follow. Based on the odds we're expected to believe, you should not expect to see 4 dupes in 34 pulls. It's pretty basic probability. <1% outcomes shouldn't keep happening at the regularity we keep seeing.

It wasn't. I literally did the math specifically for you on the last page. That particular event is ~4% to happen.

CT1888

simonsez wrote:

I'm not interested in what he's gotten over 4 seasons or 10 seasons. I'm not claiming that the odds are in a state of permanent skew. I fully expect over a long period of time they do balance the odds. What I'm saying is, there's some mechanism in place that skews them in the short term (think something like vaults). I don't understand why it's so hard to follow. Based on the odds we're expected to believe, you should not expect to see 4 dupes in 34 pulls. It's pretty basic probability. <1% outcomes shouldn't keep happening at the regularity we keep seeing.

Thanks, the context is helpful, but I still feel you are over egging the argument.
In the set of 34, the probability of getting a set of 4 Iceman purple covers is <1%, yes. But the probability of getting a set of 4 covers of 1 colour of 1 character is 4%. The probability of getting a set of 4 covers of the same character (regardless of colour) are better still. None of what has come out in these posts look skewed to me, just natural variation from random number generation.

I'm no statistician, but I've played enough D20 table top games to have had nights when I rolled bunches of low numbers and nights when I rolled bunches of high numbers, I've rolled a bunch of natural 20's and finished the night on a high and I've rolled a bunch of 1's and finished the night creating a new character. My dice didn't need an unseen mechanism to give me those, it was just random.

At the core of you argument, is that these <1% events shouldn't happen every time. Beyond the fact that an event of this nature is far more common than that, every time I draw 4 LTs, I get 4 covers. The probability of getting those 4 covers that I draw is less than 1%, so we are seeing events on those odds every time we draw tokens. Yes, it's a bit of a facetious statement, but I use it to demonstrate why I find your argument and logic flawed.

CT1888

OJSP wrote:

If you're not a statistician, You can't really write your opinion to argue a statistician then, can you?

Personally, I like maths, but I can't say I'm a mathematician and I wouldn't try to argue with a mathematician about token odds and complex maths equations.

Well, yes I can, it's my opinion and I find his argument flawed; that there is a mechanism that skews things in the short term but averages them out in the long term based, that the presence of this mechanism seems to be made clear by the presence of clumps of covers, the odds of which occurring he is quoting as <1%, which only holds true if you are basing it on gaining 4 of a specific cover, rather than the probability of gaining a group of four of a cover within the set of draws, the odds of which, as demonstrated above, are significantly higher. It is misleading and undermines his argument.

I've an engineering background with significant maths involved in my studying, so I am quite comfortable following the equations put out and doing basic odds calculations myself. Did I know his occupation before posting previously? No. Does it change how I see the logic of his argument? No. I still see it as fundamentaly flawed.

carrion_pigeons

OJSP wrote:

CT1888 wrote:

Well, yes I can, it's my opinion and I find his argument flawed; that there is a mechanism that skews things in the short term but averages them out in the long term based, that the presence of this mechanism seems to be made clear by the presence of clumps of covers, the odds of which occurring he is quoting as <1%, which only holds true if you are basing it on gaining 4 of a specific cover, rather than the probability of gaining a group of four of a cover within the set of draws, the odds of which, as demonstrated above, are significantly higher. It is misleading and undermines his argument.

I've an engineering background with significant maths involved in my studying, so I am quite comfortable following the equations put out and doing basic odds calculations myself. Did I know his occupation before posting previously? No. Does it change how I see the logic of his argument? No. I still see it as fundamentaly flawed.

That's fine, you can have your opinion.

As long as this discussion doesn't go too far into details, it's quite enjoyable for the lay forumites to read.. but, it creates problems for the mathematicians who like to argue the numbers to get the exact answer. I think to get the exact statistics explained sufficiently, each post would probably be as long as a lecture.

I think finding the right balance is difficult.

That's true. But how about establishing some baselines, so people can compare reality to the baselines? For example:

You are more likely than not to open 2 of the same 4* character out of legendary tokens after 21 covers, this situation is in the middle 50% after 9 covers, and is "unusual" (<5%) only before 3 covers.

You are more likely than not to open 3 of the same 4* character out of legendary tokens after 51 covers, this situation is in the middle 50% after 29 covers, and is "unusual" (<5%) only before 11 covers.

You are more likely than not to open 4 of the same 4* character out of legendary tokens after 80 covers, this situation is in the middle 50% after 53 covers, and is "unusual" (<5%) only before 26 covers.

You are more likely than not to open 5 of the same 4* character out of legendary tokens after 110 covers, this situation is in the middle 50% after 77 covers, and is "unusual" (<5%) only before 43 covers.