# Does CHIA have lottery encoded in it's nature?

I’m getting back on the beloved horse

Since big numbers law exists and all, each of us should get pretty same amount of reward per total weight of farm more or less but we don’t! What is it? Is there abnormal fluctation involved in algorithms on purpose or what? Is lottery factor has been programmed?

Ehh he-khee

Yes. It is no different than buying lottery tickets. Statistically, it all equals out but any one of us could be at either end of that gaussian probability curve. Some knuckleheads make one plot and win. Others make 1000 plots and still at zero.

That’s where pooling is a rational choice. You essentially lump together enough data points to eliminate the ends of the curve.

There are other factors at play though. Speed is not inconsequential. Given a situation where mulitple equally valid proofs are submitted, the probability leans away from slower proofs. That’s oversimplification, but think of it as a class all raising their hands. The teacher will award the best answer, but if a better answer comes a fraction too late, it’s irrelevant.

Please make yourself familar to the terms of Law of large numbers - Wikipedia
and Expected value - Wikipedia.

I don’t care for lyrics I care for fair game.

And IF (!!!) Chia isn’t THAT fair and has EX fluctuation i’d like to know about it.

I’m not mad at you, common What part of documentation spread the light on this?

if 10 people role the dice 6000 times each, all of them will get count of SIX near to 1000. This is math - large numbers law. However, It doesnt work with CHIA, i just try to figure why and how does it work exactly.

Just because mathematical probably approaches zero does not mean it IS zero. What you just stated is statistical probability theory, involving actual large numbers, not a law with an easily conceivable numerical ceiling under which all things become equal.

And yes, chia follows that “law”. Literally because EVERYTHING follows that law. You’re just missing some part of the picture I think.

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The confusion in this area seems to stem from people thinking that their small numbers are large numbers.

To get to a 50% probability of winning in a given month, you need about 1800 plots at current netspace (according to the chia calculator). A 50% probability per month is equivalent to 1 coin toss per month. A coin toss is an independent event (i.e. one coin toss does not influence the rest).

You can use this calculator to quickly tell you the probability of getting X heads in X flips (mapping X to months with no wins).

Chia has only really been around for a few months, and not winning in 3 months with an expected 50% monthly win has probability 12.5%, i.e. 1 in 8 farmers with around 1800 plots will have no wins after 3 months.

TLDR, a single farmer with a few thousand plots for a few months is not as big a sample as you might think it is. Plus, the reports of no wins are more likely than reports of wins, I’ve read about plenty of people who have said they haven’t won with X plots, but I’ve never felt the need to tell anyone how much I’ve won with Y plots.

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Actually, are you doing one toss per month or two? My understanding is that it is two tosses, as that implies that on average you should win. If that is the case, your probability to not get any chia after three months is just 1.45%, basically zilch.

The important number is the one in the bottom right corner, i.e. probability of winning in one month is around 50%. The phrase ‘about 1 month’ used in the calculator is possibly misleading.

I picked the numbers and rounded a little to make the math more intuitive.

Yes, you are right, my mistake.

Although, potentially a better way of looking at that is to use Poisson distribution to see what results you should be getting in a given period. Chia Decentralized (semi official YT channel) has an excellent video (and Excel spreadsheet).

I would like to see that distribution implemented in the chia UI, as it may help people better understand where they are in the process.

Looking at your example (1800) plots you can see a hard decline in your chances of winning zero chia around those three months. You add one more month, and your chances are being close to nothing.

Also, one more thing that using a single number is bad is that it kind of implies that once you win your chia (say after those three months), the process will repeat (as your luck is bad) and you will need to wait another three months. However, that Poisson chart clearly shows that when your first chia is delayed, that has zero effects on the next chia that should be won shortly after that, …

Yes, I picked that set of numbers very deliberately, to get to a 50% monthly win probability so I could reduce the problem to an approximate coin toss and I did pick the number of months deliberately to keep the probability of loss in every month in the sample non-negligible.

However…

• it’s a number of plots that plenty of people do think is ‘large’ (10 x 18TB disks is not something most people had sitting around before Chia)
• it’s a realistic length of time (Chia mainnet transactions have not yet been live for 4 months)

The process does repeat in a way - in that in this simplification the next month is an independent event with the same probability as any of the previous events - but that indeed doesn’t mean that it will be less likely to win again on the next month (but it certainly might take 3 months again, it’s not that unlikely - I mean I’d play a lottery with those odds).

Agreed though, for any set of numbers that haven’t been selected to fit this coin-flip simplification, doing calculations for those real numbers using a Possion distribution will be more generally useful.

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Agreed. Especially about your first bullet (what people assume is ‘large’). It should be stressed more.

Although, there was another thread that in Discussions part of github, where several people with farms over 1PB (expected wins shorter than 2 days) were reporting no wins for about a month. As you said, it is possible to be the one that doesn’t win, it is most likely that you will be more vocal. However, it is rather less likely that several farmers totaling about 100PB didn’t win zilch in a month. Especially, if that corresponds with the release of cha v1.2.0. Unfortunately, no one from Chia chimed in in that thread.

Below is a chart that runs binomial distribution for 1,800 plots for 30, 60, 90, 180 days. So, yeah all those wins are independent, but you cannot do stats on them independently (therefore we have binomial or Poisson curves)

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Yeah, no wins in a month with 1PB of space would definitely warrant a deep investigation of the setup.

Until I got my first win, I had no idea my setup was working, everything looks right but you can never be quite sure, getting at least one win, and then pooling has definitely let me relax somewhat.

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Exactly my feelings (sitting on pins till the first block, and kind of thankful of at least getting something through pooling)! Although, if you have over 1PB, and your expected win is about 2 days, there is really no point to belong to a pool, as within a week of no wins you know that you need to start monitoring your farm.

What is really frustrating (to me) is that there are no stats in the official UI at all. Yeah, they display some BS numbers that they may need for debugging, but there is not much about the health of your farm, no breakdown based on your harvesters, etc.

I do run PSChiaPlotter heat maps, and see results that I don’t really understand, and have no clue even how to tackle those.

That git thread is interesting indeed.

But… since I started pooling, what I earn is what I expect to earn based on the calculator, with a little expected daily variance, so I’m sceptical that there is any kind of systemic issue, unless the pool is just giving me money for free, I’ve also won a block for the pool, and that was post version 1.2.1, with around 300TiB of plots.

However, would be interested to see either a Chia team response to that thread, or some kind of solid proof in those reports (although I’m not sure what I’d accept as valid proof).

That was also my response in one of those threads - if that is the case, pools should see that first.

However, potential problem with assuming that pools would be the first to notice is that most of big (whatever it means) farms run solo. Also, is that systemic, I doubt as well, but is there a some bug - maybe.

Potentially, a simple thing to do would be to do chia (e.g., 1:5, or so), that would speed up stats, thus most of the people that think that they are affected would get at least something. Although, that may diminish the value of pools, if that is of importance to Chia team.

As far as your statement about those ‘solid proofs,’ you are right, without some support from the Chia team it is just possibility vs. likelihood. The sad part is that it is putting a stain on Chia ecosystem.

Again, no one from the Chia team chimed in in threads that i followed. It is easy to call everyone crazy, but difficult to pull the data, and it looks like that is exactly what Chia team does - not supporting those people, not providing better stats.