Yes, here it is the SELF-VOTING constant. As you may know, the proof-of-brain is the core of Steemit, you need to prove that you have the knowledge, that you are intelligent, that you have a brain in order to receive rewards. And you prove that contributing with something valuable. This is what makes STEEM valuable despite its inflation.

Is it possible to cheat the system and be rewarded without proof-of-brain? One of the ways is the Self-voting in its maximum expression. I'm not telling about the self-vote after the publication of a well-elaborated post, but the abuse of self-voting. For instance, suppose a BOT that publishes posts with no important content (posts like "Hi I'm a bot. End") and upvotes himself. The question is: How profitable is it? Is it worth cheating the system? Let's see the numbers.

Use of the voting power

The voting power is regenerated at a rate of 20% per day. Then the best way to use it is consuming it at a rate of 20% per day. Additionally, the worth of the vote is proportional to the voting power, the more voting power the more the vote will be worth. In this sense, it is better to keep it 100%.

Suppose the voting power at 100%. Then an upvote will consume 2% of it. How long does it take to regenerate?

Then the best option is to take a self-vote every 144 minutes with a weight of 100%. He just has to publish anything, with any text (no proof-of-brain), either in a post or a comment.

Reward of a single vote

Denoting Vp as the voting power, SP as the steem power, w as the weight of the vote, the worth of the vote is:

where g is a global variable of steem (for details see this post). If we vote using a weight of 100% every 144 minutes, the voting power will be 100%. In this order, the formula is as follows.

The self-voter is both the author and the curator, then 100% of the worth of the vote will be the reward. Note that it is proportional to the steem power.

Compound interest

Now, let's take that the generated rewards are claimed every 5 days, and those gains are added to the initial steem power. In this sense, we have a compound interest.

In 5 days the rewards will be:

A year has 365 days, which are 73 periods of 5 days. Then after a year, the self-voter will have:

Calculation of g

In order to calculate g we have to access steemd.com and take the following 4 values:

• total_vesting_fund_steem: 198267727.562 STEEM
• total_vesting_shares: 406099974728.553817 VESTS
• reward_balance: 703878.279 STEEM
• recent_claims: 369495749226.845013 VESTS

Note that on recent_claims we need to move the decimal point 6 positions to the left in order to convert it to VESTS. After that, we apply the following formula:

Applying this to the formula of interest compound we found:

This represents an increase of 32.88% (much more than my bank can give me). These values of the blockchain change over time and they depend on several factors, like the number of posts published, and the operations of power up and power down.

Internal price and market price

As I mentioned in a previous post there is an internal price, where the blockchain believes that 1 SBD is 1 USD, and an external price, the real price of the SBD in the market. Currently, the SBD is overvalued, then there are more profits if we take rewards in 50/50.

Let’s see an example. Suppose that the self-voter take the rewards in 50/50. The blockchain wants to give him 8 STEEM, then he receives 4 STEEM POWER, and the other 4 STEEM are transformed into SBD. But the blockchain uses the internal price (see it at steemd.com), which currently is 6.036 SBD/STEEM. Then after multiplying we obtain: 6.036 x 4 = 24.144 SBD. After that, he can exchange it in the market, but the market uses another price, the real price, which currently is 0.77 SBD/STEEM (see it at https://steemit.com/market). Then he obtains: 24.144 / 0.77 = 31.356 STEEM.

As you can see the 50% of the payment was 4 STEEM POWER, but the other 50% can be transformed into 31.356 STEEM POWER. There are a big difference and a big change for the self-voters. The question is: How much can they earn in 1 year?

Let pi be the internal price, and pe the external price, then the reward after 5 days is:

In this order

This is much more profitable, and means 248.36% of interests of the initial investment!!. Of course, this gain depends on the price of the SBD remaining stable for one year. But it represents the actual APR for self-voters.

Look the self-voting constant

In summary, we have 2 formulas to get the annual interest for a self-voter. The first one is taking 100% power up:

And the second, taking 50/50 and changing the SBD in the exchanges in order to put everything in power up:

I called this values the SELFVOTING CONSTANT. I also developed a web where you can consult it. Enter to https://joticajulian.github.io/selfvoting-constant/ to see it.

After making these calculations it seems incredible what can be achieved with the SELF-VOTING without proof-of-brain. I clarify that my intention is not to encourage its use, but rather to open the eyes to the community to take it into account in future hard forks.

Important note: As @andrejcibik mentioned, Pure self-voting is selfish and community does not like it. If you steal rewards for bad content, you will get downvoted.

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Posted on Utopian.io - Rewarding Open Source Contributors

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