Weekly Gold Rolls

[Thieves_Guild_Master]

That is not true.

Sorry, but it is for me as well.

[MaeveTuohy]

Sorry, but it is for me as well.

This horse has been whipped to death. Search the many, many threads on this subject explored in depth by statisticians.

You are imagining it.

[ahpook]

Sorry, but it is for me as well.

No. I will assume hyperbole makes you claim that you receive values that should occur 20% of the time for 80% of your rolls.

However, if you are sincere, then you have a great opportunity here. Many people will claim that they roll outside of the stated probability but the number of attempts and the resulting discrepancy with posted odds is generally non-persuasive due to the limited number of samples compared to the size of the discrepancy. But your claim is so great (not the "it should be 33% but I only see 20%" we usually see posted) you are claiming a full 4 times the expected result. I would gather that with that kind of difference you would see something statistically valid in only 100 or so attempts (feel free to correct me). So for the next 100 days track your silver rolls (number and reward) and come back and show every one that you do roll less than a 21 80% of the time. We will see you on June 11!

[mbartol]

So for the next 100 days track your silver rolls (number and reward) and come back and show every one that you do roll less than a 21 80% of the time. We will see you on June 11!

No we won’t.

[SurlyYuri]

I just wish the "good stuff" was not all bound to account. Nothing like rolling high and getting the same Fast White Stallion that you already have (when you don't have any of the other ones) or an exclusive hair dye you know someone would love but cannot give it to them. Sometimes it is like if you won the lottery to then get to spin a wheel to find out what currency they will give you. Congratulations! You won 1 Billion (processing...) flecks of paint.

I rolled a BtC Flaming Horse cert on HC. Poor thing is still trapped there. At least I haven't rolled a BtC tome for a while.

[MaeveTuohy]

No we won’t.

And why should we wait til then? Unreliable, unconfirmable data can be made up in minutes!

[Sylvado]

And why should we wait til then? Unreliable, unconfirmable data can be made up in minutes!

They forget a lot of us make daily rolls so we already know it is an even distribution.

[Eantarus]

You are imagining it.

Numbers don't lie.

[misterski]

Numbers don't lie.

There are 3 types of lies: lies, d@@@ed lies, and statistics.

[DYWYPI]

Those who gamble are often embarrassed about their addiction and the fact that they can't stop gambling, and therefore tell lies or make up stories about what they're spending their money on, where they were, or what activity they were doing.

[DYWYPI]

The gambler's fallacy is a cognitive bias, meaning that it's a systematic pattern of deviation from rationality, which occurs due to the way people's cognitive system works. It is primarily attributed to the expectation that even short sequences of outcomes will be highly representative of the process that generated them, and to the view of chance as a fair and self-correcting process.

There is insufficient evidence to suggest the "Daily Dice" are rigged regarding the rolls themselves (refer to [Post #40]).

[...] Applying (Pearson's chi-squared test) for that dice should be plenty enough to tell you if the dice is likely to be biased. :-)

One of the more interesting "goodness-of-fit" applications of the chi-square test is to examine issues of "fairness" and "cheating" in games of chance, such as cards, dice, and roulette. ;-)

So we need to look to see if the 'observed values' are close to the 'expected values', which I crudely mentioned in the prior post.

[...]

Robust Statistical Analysis using (Chi-squared test)

Total amount of Observations (dice rolls): 1274
Expected Frequency per any d100 single face occurrence (1274 × 1/100): 12.74

Null Hypothesis (H₀): Dice is fair (unbiased)
Alternative Hypothesis (H₁): Dice is unfair (biased)

Level of Significance, i.e. area in the tail: (alpha) 0.01

Degrees of Freedom (DF); Sample size (total rolls, i.e. distinct possible categories, we used 100 rows to record), minus one (N – 1): 100 – 1 = (DF): 99.

For finding the Critical value (tail of graph and rejection region area). We'll just use 99 for DF, as I don't have specialised statistics software and I'm not calculating it longhand (DF 99 is solid enough) for this dice.

Looking on an official Chi-square table using (DF 99) and (alpha 0.01) Critical value, i.e. P-value (probability): 134.642 rounded 134.64.

Therefore if our dice exceeds the (above) P-value [134.642] "Daily Dice" is likely loaded.



Chi square: X² = sum [(Observed - Expected)²/Expected]

For example using [Post #10] data: Roll 1; Observed value 12, minus Expected value: 12.74 (squared) divisible by Expected 12.74, equals: 0.042983... Then rinse and repeat, i.e. total all the X² for 1274 rolls.

Our Test Statistic equals: 108.4176

We can easily see: 108.4176 is far less than P-value: [134.642].

Therefore we fail to reject: Null Hypothesis (H₀): (we accept) Dice is fair (unbiased)

The roll results and calculations can be found within: [Post #42].

Conclusion

The "Daily dice" DO NOT appear to be loaded. In fact the statistical model shows there is an excellent chance of ~ 99% percent the dice aren't loaded. (That's what the alpha 0.01 value we tested against means basically).

Events are just plain erratic (fundamental uncertainty). Random events are often described as 'clumpy' because clumps of 'wins' or 'losses' sometimes occur.

Nothing is certain; nothing is ever due to happen (independence of events).

Things do not have to even out, but sometimes seem to, as more observations are added (law of large numbers).

Law of Large Numbers: As the sample size increases the average of the actual outcomes will more closely approximate the mathematical probability.

A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data. As a result, the results found in the sample do not represent the results that would be obtained from the entire population.


Another problem is that the human mind is predisposed to find patterns and does so very efficiently. For example, natural formations like the "face" in the Cydonia Mensae region of Mars, or the "Man in the moon", which have human-like features, are interpreted as images of people. If a person was walking in the jungle and saw a pattern of light and dark stripes in the shadows, it would be prudent to assume that the pattern was a tiger and act accordingly. The consequences of incorrectly assuming that the pattern is not a tiger far outweigh those of incorrectly assuming that it is. But when applied to random events, this survival "skill" leads to errors.

We learn through experience and logically induce general rules on that basis. If our experience is limited, we may induce the wrong rule. A chance occurrence may lead to false expectations. As a result, a win the first time one plays a game, or a win after some extraneous event, may lead to the formulation of an erroneous general rule.

[ahpook]

Numbers don't lie.

Too true. Unfortunately Numbers doesn't post here. People do and sometime they post made up numbers. Sometimes they make up stuff:

I made it up to be funny?

Sorry. Was that not evident?

In this case it is evident that you made up the 80% claim. The funny part was the second guy chiming in to back that claim up.

[Just_a_Dude]

For the love of whatever deity you believe in stop with the Bigby's Guiding Hands or at lease may it the reward for a very low roll. I have so many of these in every color that I am just selling them at this point.

I guess some people really like them. They tend to sell pretty quickly on the AH.

[Ereshkigal]

I am so triggered by these I would rather just get nothing or like some crappy curative pots to toss in the bank compulsively than Bigby's hands. Not even gonna lie, they hurt me on a psychological level. Is there a good reason for it? No. But it happens anyway.

meh, i've made a couple billion plat selling bigby's on the market, so while I don't like them, clearly there is a demand.