TAPPMATH (Posts about Dash)

The Wisdom of the Masternodes

Darren Tapp — Sat, 01 Aug 2020 08:49:21 GMT

Oddly, there have been several occasions when markets reacted as if they had a better understanding of events than should have been possible. This happens often enough that it's difficult to blame these phenomena solely on insider trading.

When witness to the results of a Dash Network voting cycle, I have often been perplexed about the decisions made by the masternodes. I have been surprised to see existing valuable infrastructure defunded, for example. However, I believe these decisions have been ultimately proven wise as time unfolds. It is easy to be upset about withheld or terminated funding. But it is also difficult to identify the opportunities made available by those freed resources. If I had to judge the Dash DAO as an entity by the decisions that it has made, I would judge this entity to be wise. I lament that the DAO cannot manifest and explain its reasoning.

I believe there is wisdom behind the decision of the DAO not to fund recent DIF proposals. I believe the DAO has identified how interests have gotten out-of-whack. Muddled. I believe the DAO is holding out until the DIF can demonstrate a more efficient use of resources. I believe this so strongly, that I am putting my time where my mouth is by becoming a DIF protector.

A Conflict of Interest

Let us consider a masternode owner, Alice. Alice pays $20 a month for access to a server where she runs the software required to service the Dash Network. Alice's node serves the network and is placed on the rewards queue. Alice waits patiently as every other node is called before hers, and then her number comes up and she receives 1.44236253 DASH and fees as a payment. Alice faithfully researches proposals every cycle and offers up her vote.

Alice then notices that there is a proposal for the DIF that would fund a masternode run by the DIF. Alice understands that another masternode would incrementally lengthen the line at the payment queue. Alice also understands that if the DIF runs masternodes then her veto as part of the DAO will be similarly diluted. For these reasons alone Alice might not vote to fund the DIF.

A DIF that seeks funding from the DAO for the purpose of running masternodes, even if run through a third party, will always make their proposals incrementally less attractive. Such a DIF is a competitor to masternode owners, like Alice. Despite the fact that the DIF is supposedly working hand-in-hand with the DAO, we may even go as far to say that such a DIF is instead marginally adversarial to Alice and therefore even the DAO.

Trolls on the Internet

Having been around for a while I see some people on the internet argue that Dash Core Group (DCG) should not run masternodes. This is a straw man argument since DCG does not run masternodes. However, the same conflict of interest would apply if they did.

There are those that misrepresent facts and extend this line of reasoning, arguing that contractors paid by DCG should not run masternodes. That argument simply doesn't follow though. People who have an interest in a masternode are naturally going to be incented to do beneficial work for DCG. As long as the payment is representative of the value provided, there simply is no conflict of interest. This argument gets even weaker when it is considered that some working for DCG are working for no, or reduced pay (note that we hope this situation will improve in months to come).

More than Money

Money is meaningless if it doesn't buy anything. I would expect the DIF to hedge in order to protect wealth. Running a masternode sets up a game theoretic situation that is not conducive to cooperation. I hope the DIF can convert money into assets that add value instead of using money to dilute the value of running a masternode.

Dash Investment Foundation Goals

Darren Tapp — Sun, 26 Jul 2020 17:06:32 GMT

This post presents a proposed adjustment and clarification of the prioritized goals of the Dash Investment Foundation (DIF) and how to measure the successful achievement of those goals. As with any project, goals and success criteria need to be well articulated and agreed upon.

In my view, the DIF should pursue two main goals, each aligned to the two types of investment the DIF engages in.

Venture Capital: Provide a process and a legal framework that will allow the network to fund for-profit ventures in exchange for equity.
Assets Under Management: Generally increase assets under management.

I consider these goals to be listed in the optimal order of priority. The first goal is directly based on the announcement introducing the Dash Investment Foundation. The Dash Investment Foundation enables the Dash treasury to serve as a source of venture capital and not just as a provider of grants for work on the network and projects. In this article, I outline how I expect that process to work.

A discussion of Assets Under Management will be reserved for a separate post.

Clarifying Terms

In the world of investing, an association of people may pool resources. We can call this association of people a fund, effectively. And as with most funds, they will likely choose to focus on a targeted type of investment.

Private Equity

It might be the case that the fund is established to invest in new companies (startups). Such a fund is called a venture fund or a private equity fund and the money raised by a startup is called venture capital. A share in the ownership of the company is called private equity and is exchanged for those venture capital funds.

Public equity in the form of common stock is similar in concept but comes with fewer ownership privileges and is exchanged on the open market at a stock exchange. A private company does not offer public ownership shares. A public company offers both. Startups begin as private entities funded by private equity funds and angel investors.

Angel investors are individuals who stake their own money in a startup in the form of a private equity investment.

Hedging

A fund could also be established that actively trades in the market with the goal of making money. Perhaps the first rule of making money is not losing money. One way to avoid losing money is by hedging. Consider this: Maybe we know that there is a 60% chance of a particular asset appreciating. We might be able to bet on the asset going up in price but at the same time hedge. To hedge would be to make a contrary bet that will make the downside less likely or have less severe of an impact. This is difficult to describe in a couple sentences, but the 60% chance of asset price appreciation could mean the hedged position has an 80% chance of returning a profit. One way we can help ensure a fund makes money with more consistency is to hedge.

A fund of this nature is called a hedge fund. The name helps guide the operation of the fund. This more consistent and increased chance of profit comes with a cost. An increased chance of a profit generally means that the profit will be less than if the position was not hedged.

Investing Approach

Private Equity

I interviewed a successful angel investor who warned me that only about 10% of startups are successful. A few implications of this statement:

An angel would need to invest in 10 startups until they could reasonably expect a return.
Even if an angel invests in ten startups, there is still a 34% chance that all startups will have no return.
In order for an angel to be profitable, they must select investments with a return which is generally greater than 10 fold.

Let that sink in for a moment.

Professionals who invest in private equity fund a tremendous number of projects that never provide any return. What chance can an amateur have? In a sense, the DIF can also be viewed as a startup which categorizes the DIF in this same class of entities that fail 90% of the time.

Hedge Fund

The skills needed to establish a successful hedge fund diverge substantially from those needed to establish a private equity fund. Hedge funds will often hire people who are particularly good at math. Such people are called quants, short for quantitative analysts. My gym buddy in grad school, Ganesh, became a quant. The type of math used by a hedge fund might depend on the particular specialty of the fund. Here's a video of my favorite fictional quant: Peter Sullivan from the movie Margin Call. Be aware, there is cursing in this video.

The DIF in Context

From my assessment, for the past year, the DIF has taken on the role of a both a venture capital firm and a hedge fund. Attempting to tackle both roles dramatically increases the amount of mental effort needed. It also requires a much broader set of skills compared to what is needed for just one of these endeavors. I do see an opportunity for the DIF to take on both roles. However, for the purposes of this article I will only discuss the venture capital side of the house.

In his original vision for the DIF, Ryan Taylor identified a missed opportunity—correctly, in my view—involving the Dash DAO (Decentralized Autonomous Organization). Traditionally, the Dash DAO has no means to invest and only a means to issue grants. Ryan noted that the network at times funded for-profit ventures, but, since the only tool available was a grant, there was never an exchange of equity in return. And in other cases, companies that would have potentially benefited the network's infrastructure (an oblique dividend) were passed over because DAO voters were hesitant to issue a grant to a private business. To voters, there was often no direct and obvious benefit to anyone but the business itself.

The DIF was created to address this with an alternative model of funding. The DIF allows for a level of flexibility in contrast to the rigidity of the Dash DAO. Scenarios that benefit the Dash Network by empowering a for-profit entity through funding are made more attractive by offering equity in exchange.

A More Productive, More Manageable Workload for the DIF

Traditionally, startups seek out their own funding. A venture fund that instead goes looking for startups is much more likely to find poorer quality projects. Therefore, the Dash DAO and DIF should avoid seeking startups for investment. Startups should instead seek out the DAO for funding. The DIF would then serve as the point of contact and facilitator for startups who want to conduct business with the Dash DAO.

Once contact has been made, a startup would approach the DIF and offer a certain amount of equity for some value of DASH. For example, "ACME Startup is prepared to offer a 10% stake in our company in exchange for 120 DASH." At that point, the DIF would be expected to begin an investigation into the business, establishing:

The startup does not break any laws.
The startup is generally moral and ethical.
The startup has an appropriate legal structure that will allow a claim of equity to be enforced by a reasonable jurisdiction.
The DIF and the Dash DAO have no conflict of interest by accepting equity.
The startup has a business plan that is clear to understand.
The startup is willing to disclose financial information such as balance sheets and cash flow statements.

This is a sampling.

With this information in hand, the DIF will be in an informed position to form an opinion about the startup and the value of the proposal.

A simple example: ACME Startup seeks a 120 DASH investment

For our example, maybe ACME Startup satisfies all of the requirements, but the DIF feels the offer is simply too expensive. The DIF begins negotiations. The DIF counteroffers with, "We really like your proposal, but we would feel more comfortable if you offered 20% equity for 120 DASH." To which ACME responds, "We'll change our offer to 15% equity in exchange for 120 DASH." In our example, the DIF deems that fair and agrees.

Negotiations over, ACME Startup submits a proposal to the network and asks for 125 DASH (the extra 5 to recover the 5 DASH proposal fee) in exchange for an 15% stake in the company. A representative of the DIF should then state the DIFs opinion. For example, "The DIF Feels that ACME startup contributes meaningfully to the Dash ecosystem. We find 15% equity acceptable and consider the price fair."

The DIF will offer similar guidance for each proposed project:

We'll accept the equity but the price is too high.
We feel that due to the nature of the business, it would be harmful to accept equity and we will refuse it.
We were not informed about this project and are unable to accept equity.

A well-executed negotiation before submission to the network should result in the startup and the DIF speaking with a unified voice. It will also allow some due diligence to be communicated by the DIF.

Note: masternode owners are still expected to do their own due diligence.

Even if negotiations were unsuccessful, the result is still a proposal process with far more clarity. Let's say, for example, ACME Startup offered 5% equity in exchange for 120 DASH, but the DIF stood firm on a 20% stake as being the fair market value. ACME could still make their proposal. The DIF would then be in a position to deliver an informed response.

Perhaps, they would not attempt to block the proposal from passing, while still accepting the equity. The statement in that case might go something like, "We don't feel the valuation is fair to the DAO, but we will accept the equity." And perhaps ACME would respond with, "The valuation is fair because blah, blah, blah." Positions are articulated and the masternodes (who direct the DIF) are then free to decide, but from a more informed position.

This is a process that can be implemented today. There is no need to wait for an investment adviser (though the Dash DAO could benefit from having an investment adviser).

Measurement of Success

In this section I'll outline a minimal condition for success for the DIF. Please understand that great care has been taken to maximize the value provided to all players, including the DAO. This is simply game theory, my dear Watson.

I propose the DIF—for the year from August 2020 to July 2021—will be deemed successful if,

A proposal (or proposals) is passed by the network resulting in equity received by the DIF, which is then is sold to angel investors for $50,000 or greater.

If this modest success condition is met, all the "profit" to the network would be intangible, that is, without a clear valuation (a benefited network by DAO-enabled company). The DAO has money. More money is nice, but the money has meaning only when the money provides a good or service that is valuable. If this success condition is met then the DAO would have funded a company that will enhance Dash Network's infrastructure. At the same time, the DAO will own a successful incubator or partner with an angel who maintains the investment while cycling funds back to the DIF so the cycle can continue.

Why Angels?

Angels not only provide money to startups, angels also provide guidance, connections, and networking. An angel offers these services with the goal of positioning their investment, the startup, for success, which, at some point, an angel hopes to sell for a profit.

The DIF does not have the skills that angels do. Additionally, angels specialize. They each have very specialized skills and only fund ventures that fall with the limits of their skillset. Currently, there is no way that the DIF can be as attractive of a business partner as a self-selected angel.

Generally, if the DIF partners with angels that can support DAO-funded ventures, that is a value-add for those ventures. But this relationship would also enhance the funding and facilitation services the DIF provides. Additionally, as the relationshp with angels and the angel community strengthens and expands, the value the DIF brings to the network should compound.

Selling to angels helps close the loop. Without angels, the process is . . .

DAO invests 500 DASH on a startup.
The DIF holds the equity for two, five, or ten years before the equity pays out, if ever.

Instead, with angels (the price of DASH is $100 for this example), the process becomes . . .

DAO spends 500 DASH.
The equity is sold for $50,000 within three months and the $50,000 is ready to go back to work for the network.

Synergies

Synergy is a stupid buzz word, but synergies do exist.

Partnering with angels opens the door to multi-party deals. Perhaps two angels and the DAO go in together on a venture. Maybe an angel funds a venture and a proposal is never brought to the DAO; the DIF in that case serving only as matchmaker. Heck, the DIF could still provide value to the network without even putting a proposal in front of the DAO. This opens up many opportunities for the network.

I hope this post adequately articulates what I'm proposing and the flexibility it brings to the network.

Don't Believe the Hype!

Darren Tapp — Fri, 24 Apr 2020 16:31:07 GMT

The Bitcoin Halving

The Bitcoin code includes a built-in mechanism to limit the total number of bitcoins. Governed by algorithm, the protocol generates new bitcoins at a fixed rate: a fixed number of coins every ~ten minutes 1. This implies a steady increase in the coin supply. But there's a second half to that algorithm: every four years, the per-ten-minute reward is halved. This ensures that the emission rate of the coin eventually reduces to what becomes effectively zero. Since this creation rate is halved each cycle, the event surrounding this reduction is referred to as the halving.

The third such halving event will occur on or about May 12th. At that moment, each new Bitcoin block will then include 6.25 newly mined (minted) bitcoins compared to the 12.5 mined for each block now. Interestingly, this will be the first time that Bitcoin's monetary inflation rate will be under the Federal Reserve's 2% target for price inflation.

The History

Historically, Bitcoin halvings have been quite uneventful. I teach at the collegiate level; I distinctly remember being between two classes when the first halving occurred. As the event approached, I was engrossed, staring at my computer screen, as I watched each new block being generated. The busy college campus hummed along blithely unaware as first a block was generated with a 50 bitcoin reward, and then in the next moment, a 25 bitcoin reward. Blockchain.info thoughtfully displayed some fireworks on the screen at precisely that historic moment. Shortly thereafter, my students convened for their algebra class: not a single mention, by anyone, of the event for which I was so excited.

From a technical standpoint, the whole flow of events was impressive. I was impressed that humans could write a program that dictated the behavior of a network years into the future.

The effect of the halving—and the corresponding supply reduction it represents—to bitcoin's pricing, was difficult to discern in those first couple four-year iterations. There were price spikes six months after each halving, but whether there was a causal relationship, we simply don't know. A correlation does not automatically imply a causal relationship.

Analysis

Here's the thought process I went through in November of 2012. I made the following assumptions:

Bitcoin is a currency.
Demand for bitcoin is a constant.

Today, the first assumption is no longer valid as the number of transactions can no longer support the currency use case. The second assumption I considered, at least at the time, to be a conservative one. I measured the demand for bitcoins as the amount of money it took to buy the newly mined coins—their value, in fiat.

Long run

Given these assumptions, one would expect the price of bitcoin to double eventually. This assumption had me hopeful about the future price of bitcoin. But I wasn't happy with 'eventually.' I wanted to know just how quickly this doubling would occur?

How Long is the Long Run?

In 2012, the price of one bitcoin was around $10. Therefore, for each 50 bitcoins generated, there was an associated $500 cost burden when they were sold on the open market — $500 every ten minutes. After the halving, only $250 would be needed to buy each new allotment of 25 bitcoins, leaving $250 of unmet demand fed into the market cap. Or I at least assumed. $250 every 10 minutes comes to $1.08 million per month. If this were factored into the market cap algebraically, about 0.01 would be added to the price of bitcoin in the next month.

So, with these assumptions, the price should eventually double, but it would take a great deal of time. Using today's numbers, the time required to double again would be even longer. Much longer.

Further Considerations

Note, even if the analysis found that the price would increase dramatically, the psychological aspects of the bitcoin market may thwart the doubling at the mathematically predicted time frame. When investors are alerted to a likely rise in price, it stands to reason that rational actors would buy that item before the expected price increase. This price pressure (sudden demand) would then increase the price prematurely.

The Hype

On some social media, I commonly see mention of the halving in connection with a price increase. Some quality tweeters have re-tweeted a stock-to-flow analysis applied to bitcoin. But this analysis utilizes stock-to-flow concepts in a way I find to be, frankly, underwhelming. They contend that one parameter, the stock-to-flow ratio, determines the price of an item. A claim that, for me, seems to oversimplify price expectations in this case.

This analysis considers three items: gold, silver, and bitcoin. The stock-to-flow ratio of gold and silver are each measured for one point in time. Those two data points are then used to make predictions about the price of bitcoin over time.

Though, to be convincing, the author has much more work to do. At a minimum, I would expect them to show how this stock-to-flow theory has successfully determined the price of gold throughout its history. Specifically, how does this ratio explain gold's rise from $300 in 1973 to $1,700 today? Additionally, other failures of prediction for similar commodities—litecoin, for example—need to be addressed.

1: The timing of the per-block emission rate is approximate, but it averages to approximately every ten minutes.

Darren Tapp Featured on Dash Podcast 137

Darren Tapp — Wed, 15 Jan 2020 17:43:46 GMT

Last Friday I was interviewed by Dash News, We covered topics relating to chainlocks and their security. We also talked about reducing proof of work for Dash. We discuss how SPV wallets could take advantage of chain locks to provide more security even with less work in every block.

We talked about the economics research going on right now at ASU. That is the part of research that I am involved in and most excited about. We talk about a lot of options. The hosts relate these decisions to being a central bank, and there is a parallel that can be drawn. Perhaps I didn't get across that the goal is to have a hands off economic policy. My hope is that a stable economic model can be adopted and hardcoded without intervention after the change. I lament that we did not talk about the Zero Knowledge Proof research also being worked on by the ASU blockchain research lab. I expect an update on that by the end of the school year.

I was asked about Dash's monetary inflation. It was purported that Dash's monetary inflation was high, and it is compared to other cryptocurrency projects. I'm hoping that any changes to the inflation schedule result in less issued Dash.

There is some discussion about masternode voting participation. Now that voting keys are on chain then it would be nice if a phone app allowed for voting on your phone. I think that would encourage more voting. Mark suggested that TAPPMATH could explain the calculations in the chainlocks security analysis in more detail.

If you haven't had a chance to watch this episode please find a video of it below.

Security Analysis of ChainLocks complete

Darren Tapp — Thu, 02 Jan 2020 19:41:35 GMT

In Satoshi Nakamoto's bitcoin paper there is section 11 with the title "Calculations". This section basically proves that bitcoin is very secure as long as at least half of the hashing power is behaving as expected.

Last year, the cryptocurrency Dash introduced a secondary consensus mechanism called ChainLocks. The technical specification of ChainLocks was explained in a document known as Dash Improvement Proposal 008 or DIP008. When this document was published I quickly went to calculate the security provided by the new specification. The large 400 node quorum means that the spread sheet I had for such calculations choked hard. So it was time to pull out the big guns, Python.

Within a half an hour I was maxing out a processor of my old laptop with calculations. I was happy that minutes later I had an answer, and the answer was affirmative. ChainLocks did provide security from purposefully malicious actors. I went back to other tasks now that I was convinced of the security of ChainLocks. Then I received a few questions about how to perform these calculations. So I shared my Python script. Thephez on github made this Python script much more efficient. It would run in seconds instead of minutes.

I then thought back to Satoshi's paper. It was really that Calculations section that was the convincing part. So in the open source spirit I formally wrote up the security analysis and submitted a pull request. Today, that pull request was merged. DIP008 now has a calculations section.

The calculations rely on binomial coefficients. As an example you can type "7 choose 5" in google and get 21. The number 7 choose 5 is written \[ _7 C_5 = {7 \choose 5} = 21\]

My main complaint is that GitHub's markdown does not out of the box render all mathematics. I used the notation $ _n C_r $ for $n$ choose $r$ because markdown of github supports that better. I generally think $ { n \choose r }$ is a more common notation.

My favorite quote is:

The attacker would have a less than one in 100 trillion chance of producing at least one malicious ChainLock in the next sextillion (10^21) years.

This is assuming that thirty percent or less of the Masternodes are controlled by an attacker.

The heart of the calculations is in the function pcalc below.

dip008functions.py (Source)

def binom(x, y):
    try:
        binom = fac(x) // fac(y) // fac(x - y)
    except ValueError:
        binom = 0
    return binom


###This function takes inputs and outputs the probability
#of success in one trial
#pcalc is short for probability calculation
def pcalc(masternodes,quorumsize,attacksuccess,Byznodes):
    SampleSpace = binom(masternodes,quorumsize)
    pctemp=0
    for x in range(attacksuccess, quorumsize+1):
        pctemp = pctemp + binom(Byznodes,x)*binom(masternodes-Byznodes,quorumsize-x)
    #at this juncture the answer is pctemp/SampleSpace
    #but that will produce an overflow error.  We use logarithms to
    #calculate this value
    return 10 ** (log(pctemp,10)- log(SampleSpace,10))